Kinomatic

kinomatic

Authors:
(1) Jorge Francisco Garcia-Samartın, Centro de Automatica y Robotica (UPM-CSIC), Universidad Politecnica de Madrid — Consejo Superior de Investigaciones Cientıficas, Jose Gutierrez Abascal 2, 28006 Madrid, Spain (jorge.gsamartin@upm.es);
(2) Adrian Rieker, Centro de Automatica y Robotica (UPM-CSIC), Universidad Politecnica de Madrid — Consejo Superior de Investigaciones Cientıficas, Jose Gutierrez Abascal 2, 28006 Madrid, Spain;
(3) Antonio Barrientos, Centro de Automatica y Robotica (UPM-CSIC), Universidad Politecnica de Madrid — Consejo Superior de Investigaciones Cientıficas, Jose Gutierrez Abascal 2, 28006 Madrid, Spain. Table of Links Abstract and 1 Introduction 2 Related Works 2.1 Pneumatic Actuation 2.2 Pneumatic Arms 2.3 Control of Soft Robots 3 PAUL: Design and Manufacturing 3.1 Robot Design 3.2 Material Selection 3.3 Manufacturing 3.4 Actuation Bank 4 Data Acquisition and Open-Loop Control 4.1 Hardware Setup 4.2 Vision Capture System 4.3 Dataset Generation: Table-Based Models 4.4 Open-Loop Control 5 Results 5.1 Final PAUL version 5.2 Workspace Analysis 5.3 Performance of the Table-Based Models 5.4 Bending Experiments 5.5 Weight Carrying Experiments 6 Conclusions Funding Information A. Conducted Experiments and References 5.5 Weight Carrying Experiments Finally, the load capacity of the robot and the performance of the kinematic model were evaluated and data was collected in vacuum, with different loads. For this purpose, an element similar to the joints between segments, also printed in PLA, was attached to the robot and different metal weights were placed on it. The device in question can be seen in Figure 20 The experiments consisted of taking PAUL to 10 different points in his workspace and comparing the position he reached with the position he would have reached if he had had no weight. The comparison was therefore made using the forward kinematic model, due to its greater accuracy. Four different weights were tested: 55, 90, 130 and 155 g. These values are similar to those used in other works in the field for totally soft robots –excluding the hybrid ones, which, of course, have a much larger weight carrying capacity– [47, 61]. Figure 21 shows the results obtained. The mean errors are respectively 5.11, 4.40, 8.61 and 10.01 mm. From these data it can be deduced that, far from increasing progressively with weight, there are two categories: one that groups the experiments with loads of 55 and 90 g and another that groups those of 130 and 155 g. For the lower load values, the PAUL model predicts values with errors similar to those obtained by consulting the direct kinematics in the table obtained without weights. In the other cases, the results are clearly worse. It can also be seen that the lower error values, however, are quite similar in all cases. This is due to the fact that, at the points closest to the centre of its working space, the manipulator is able to position itself with much less error, regardless of the weight it is carrying. What the load produces, therefore, is not a systematic increase in error but a decrease in the working space, as PAUL lacks the strength to reach the areas furthest from the centre with the extra weight. Table 5 compares PAUL performance those achieved in other works. Although there is room for improvement, the results obtained here are better than those of the closed-loop control of [47], where the average error obtained is 2 cm, and to those of the wired manipulator of [61]. While the latter seems to be independent of load, PAUL sees its error increase with increasing weight, which seems to indicate that, at higher weights, PAUL will indeed underperform. Two aspects remain to be analysed. On the one hand, to see if between 90 and 130 g the increase in error is progressive or if, on the contrary, there is a point that clearly divides the two groups. On the other hand, it would also be necessary to study how an improvement in the accuracy when empty would affect the accuracy when loaded: whether the robot would remain as accurate or whether these errors would not decrease. This paper is available on arxiv under CC BY-NC-SA 4.0 DEED license. Authors: (1) Jorge Francisco Garcia-Samartın, Centro de Automatica y Robotica (UPM-CSIC), Universidad Politecnica de Madrid — Consejo Superior de Investigaciones Cientıficas, Jose Gutierrez Abascal 2, 28006 Madrid, Spain (jorge.gsamartin@upm.es); (2) Adrian Rieker, Centro de Automatica y Robotica (UPM-CSIC), Universidad Politecnica de Madrid — Consejo Superior de Investigaciones Cientıficas, Jose Gutierrez Abascal 2, 28006 Madrid, Spain; (3) Antonio Barrientos, Centro de Automatica y Robotica (UPM-CSIC), Universidad Politecnica de Madrid — Consejo Superior de Investigaciones Cientıficas, Jose Gutierrez Abascal 2, 28006 Madrid, Spain. Authors: Authors: (1) Jorge Francisco Garcia-Samartın, Centro de Automatica y Robotica (UPM-CSIC), Universidad Politecnica de Madrid — Consejo Superior de Investigaciones Cientıficas, Jose Gutierrez Abascal 2, 28006 Madrid, Spain (jorge.gsamartin@upm.es); (2) Adrian Rieker, Centro de Automatica y Robotica (UPM-CSIC), Universidad Politecnica de Madrid — Consejo Superior de Investigaciones Cientıficas, Jose Gutierrez Abascal 2, 28006 Madrid, Spain; (3) Antonio Barrientos, Centro de Automatica y Robotica (UPM-CSIC), Universidad Politecnica de Madrid — Consejo Superior de Investigaciones Cientıficas, Jose Gutierrez Abascal 2, 28006 Madrid, Spain. Table of Links Abstract and 1 Introduction Abstract and 1 Introduction 2 Related Works 2.1 Pneumatic Actuation 2.1 Pneumatic Actuation 2.2 Pneumatic Arms 2.2 Pneumatic Arms 2.3 Control of Soft Robots 2.3 Control of Soft Robots 3 PAUL: Design and Manufacturing 3.1 Robot Design 3.1 Robot Design 3.2 Material Selection 3.2 Material Selection 3.3 Manufacturing 3.3 Manufacturing 3.4 Actuation Bank 3.4 Actuation Bank 4 Data Acquisition and Open-Loop Control 4.1 Hardware Setup 4.1 Hardware Setup 4.2 Vision Capture System 4.2 Vision Capture System 4.3 Dataset Generation: Table-Based Models 4.3 Dataset Generation: Table-Based Models 4.4 Open-Loop Control 4.4 Open-Loop Control 5 Results 5.1 Final PAUL version 5.1 Final PAUL version 5.2 Workspace Analysis 5.2 Workspace Analysis 5.3 Performance of the Table-Based Models 5.3 Performance of the Table-Based Models 5.4 Bending Experiments 5.4 Bending Experiments 5.5 Weight Carrying Experiments 5.5 Weight Carrying Experiments 6 Conclusions 6 Conclusions Funding Information Funding Information A. Conducted Experiments and References A. Conducted Experiments and References 5.5 Weight Carrying Experiments Finally, the load capacity of the robot and the performance of the kinematic model were evaluated and data was collected in vacuum, with different loads. For this purpose, an element similar to the joints between segments, also printed in PLA, was attached to the robot and different metal weights were placed on it. The device in question can be seen in Figure 20 The experiments consisted of taking PAUL to 10 different points in his workspace and comparing the position he reached with the position he would have reached if he had had no weight. The comparison was therefore made using the forward kinematic model, due to its greater accuracy. Four different weights were tested: 55, 90, 130 and 155 g. These values are similar to those used in other works in the field for totally soft robots –excluding the hybrid ones, which, of course, have a much larger weight carrying capacity– [47, 61]. Figure 21 shows the results obtained. The mean errors are respectively 5.11, 4.40, 8.61 and 10.01 mm. From these data it can be deduced that, far from increasing progressively with weight, there are two categories: one that groups the experiments with loads of 55 and 90 g and another that groups those of 130 and 155 g. For the lower load values, the PAUL model predicts values with errors similar to those obtained by consulting the direct kinematics in the table obtained without weights. In the other cases, the results are clearly worse. It can also be seen that the lower error values, however, are quite similar in all cases. This is due to the fact that, at the points closest to the centre of its working space, the manipulator is able to position itself with much less error, regardless of the weight it is carrying. What the load produces, therefore, is not a systematic increase in error but a decrease in the working space, as PAUL lacks the strength to reach the areas furthest from the centre with the extra weight. Table 5 compares PAUL performance those achieved in other works. Although there is room for improvement, the results obtained here are better than those of the closed-loop control of [47], where the average error obtained is 2 cm, and to those of the wired manipulator of [61]. While the latter seems to be independent of load, PAUL sees its error increase with increasing weight, which seems to indicate that, at higher weights, PAUL will indeed underperform. Two aspects remain to be analysed. On the one hand, to see if between 90 and 130 g the increase in error is progressive or if, on the contrary, there is a point that clearly divides the two groups. On the other hand, it would also be necessary to study how an improvement in the accuracy when empty would affect the accuracy when loaded: whether the robot would remain as accurate or whether these errors would not decrease. This paper is available on arxiv under CC BY-NC-SA 4.0 DEED license. This paper is available on arxiv under CC BY-NC-SA 4.0 DEED license. available on arxiv

Evaluating PAUL’s Weight Carrying Capacity and Kinematic Model Performance

Αξιολόγηση της ικανότητας μεταφοράς βάρους και της απόδοσης του κινηματικού μοντέλου του PAUL

Evaluación de la capacidad de carga de PAUL y del rendimiento del modelo cinemático

Évaluation de la capacité de charge et des performances du modèle cinématique de PAUL

Գնահատելով PAUL-ի քաշը կրելու կարողությունը և կինեմատիկ մոդելի կատարումը

PAULの重量積載能力と運動学モデルのパフォーマンスを評価する

ការវាយតម្លៃសមត្ថភាពផ្ទុកទម្ងន់របស់ PAUL និងការអនុវត្តគំរូ Kinematic

Ocena nośności PAUL-a i wydajności modelu kinematycznego

PAULpa Llasaq apay atiyninta, Modelo Cinemático nisqapa ruwaynintapas chaninchaspa

Qiimaynta Miisaanka PAUL ee Awooda Qaadashada iyo Waxqabadka Model Kinematic

Процена ПАУЛ-овог капацитета носивости и кинематичких перформанси модела

การประเมินความสามารถในการรับน้ำหนักของ PAUL และประสิทธิภาพของแบบจำลองจลนศาสตร์

Ukuhlola I-PAUL's Weight Carrying Capacity and Kinematic Model Performance

Next-Gen 3D Detection: Challenges, Innovations & Future Directions

Authors:
(1) Neil Ashby, National Institute of Standards and Technology, Boulder, CO 80305 (Neil.Ashby@Colorado.Edu);
(2) Bijunath R. Patla, National Institute of Standards and Technology, Boulder, CO 80305 (bijunath.patla@nist.gov). Table of Links Abstract and 1. Introduction Clock in Orbit
2.1 Coordinate Time
2.2 Local Frame for the Moon


Clock Rate Differences Between Earth and Moon


Clocks at Earth-Moon Lagrance Points
4.1 Clock at Lagrange point L1
4.2. Clock at Lagrange point L2
4.3. Clock at Lagrange point L4 or L5


Conclusions Appendix 1: Fermi Coordinates with Origin at the Center of the Moon Appendix 2: Construction of Freely Falling Center of Mass Frame Appendix 3: Equations of Motion of Earth and Moon Appendix 4: Comparing Results in Rotating and Non-Rotating Coordinate Systems Acknowledgments and References As humanity aspires to explore the solar system and investigate distant worlds such as the Moon, Mars, and beyond, there is a growing need to establish and broaden coordinate time references that depend on the rate of standard clocks. According to Einstein’s theory of relativity, the rate of a standard clock is influenced by the gravitational potential at the location of the clock and the relative motion of the clock. A coordinate time reference is established by a grid of synchronized clocks traceable to an ideal clock at a predetermined point in space. This allows for the comparison of local time variations of clocks due to gravitational and kinematic effects. We present a relativistic framework to introduce a coordinate time for the Moon. This framework also establishes a relationship between the coordinate times for the Moon and the Earth as determined by standard clocks located on the Earth’s geoid and the Moon’s equator. A clock near the Moon’s equator ticks faster than one near the Earth’s equator, accumulating an extra 56.02 microseconds per day over the duration of a lunar orbit. This formalism is then used to compute the clock rates at Earth-Moon Lagrange points. Accurate estimation of the rate differences of coordinate times across celestial bodies and their inter-comparisons using clocks onboard orbiters at relatively stable Lagrange points as time transfer links is crucial for establishing reliable communications infrastructure. This understanding also underpins precise navigation in cislunar space and on celestial bodies’ surfaces, thus playing a pivotal role in ensuring the interoperability of various position, navigation, and timing (PNT) systems spanning from Earth to the Moon and to the farthest regions of the inner solar system. 1. INTRODUCTION More than 50 years after the first lunar landing, a multinational consortium, which includes NASA, is working towards a return to the Moon under the Artemis Accords [1]. Our ability to explore distant worlds will require the design and development of a communication and navigation infrastructure within and beyond cislunar space. With the expectation of a significant increase in assets on the lunar surface and in cislunar space in the near future, developing a robust architecture for accurate position, navigation, and timing (PNT) applications has become a matter of paramount interest. Communication and navigation systems rely on a network of clocks that are synchronized to each other within a few tens of nanoseconds. As the number of assets on the lunar surface grows, synchronizing local clocks with higher precision using remote clocks on Earth becomes challenging and inefficient. An optimal solution would be to draw from the heritage of global navigation satellite systems (GNSS) by envisioning a system or constellation time common to all assets and then relating this time to clocks on Earth. The relativistic framework presented here enables us to compare clock rates on the Moon and cislunar Lagrange points with respect to clocks on Earth by using a metric appropriate for a locally freely falling frame. The time measured by a clock at any given location is known as the proper time. Relativity of simultaneity implies that no two observers will agree on a given sequence of events if they are in different reference frames [2]. In other words, clocks in different reference frames tick at different rates. The gravitational and motional effects affect the ticking rate of clocks when compared with “ideal” clocks that are at rest and sufficiently far away from any gravitating mass. For example, clocks farther away from Earth tick faster, and clocks in uniform motion will tick slower with respect to “ideal” clocks, and vice-versa. Therefore, choosing an appropriate reference frame becomes essential for obtaining self-consistent results when comparing clocks on two celestial bodies. In this paper, mainly we seek answers to the following questions: What is a good choice for the coordinate system that can be used to relate the proper times on the Earth and the Moon? What is an appropriate choice for the locations of ideal clocks on the surfaces of the Earth and Moon that makes it easier to compare their proper times? What is the proper time difference between clocks on the Moon and the Earth? What are the proper time differences between clocks located at the Earth-Moon Lagrange points and the Earth? The stability offered by Lagrange points provides a low acceleration noise environment for spacecraft with clocks. The relativistic corrections for such clocks can be precisely estimated as their positions and velocities are well-determined and can be used to compare the proper times of clocks on Earth, Moon, and in cislunar orbits. In Section 1, we use the global positioning system (GPS) as an example to illustrate the relativistic effects on clocks if the Moon is treated just like an artificial satellite of the Earth and obtain a rough estimate for the clock rates on the Moon with respect to clocks on the geoid. Section 2 introduces a freely falling coordinate system with its center coinciding with the center of mass of the Earth and Moon. Section 3 compares the rate offset of a clock on the lunar surface to clocks on the geoid using this freely falling coordinate system, assuming the Moon is in a Keplerian orbit around the Earth. The results are compared with precise orbits for the Moon obtained using the latest planetary ephemerides DE440 [3]. Section 4 discusses the time rate offsets at Earth-Moon Lagrange points L1, L2, and L4/L5. Conclusions and future outlook are presented in Section 5. Appendices 1 and 2 introduce the framework for developing the metric used in all calculations. Appendix 3 justifies our assumptions of using a Keplerian model ignoring tidal effects, and a discussion in Appendix 4 establishes general covariance, meaning that the results are coordinate-independent. This paper is available on arxiv under CC0 1.0 license. Authors: (1) Neil Ashby, National Institute of Standards and Technology, Boulder, CO 80305 (Neil.Ashby@Colorado.Edu); (2) Bijunath R. Patla, National Institute of Standards and Technology, Boulder, CO 80305 (bijunath.patla@nist.gov). Authors: Authors: (1) Neil Ashby, National Institute of Standards and Technology, Boulder, CO 80305 ( Neil.Ashby@Colorado.Edu ); Neil.Ashby@Colorado.Edu (2) Bijunath R. Patla, National Institute of Standards and Technology, Boulder, CO 80305 ( bijunath.patla@nist.gov ). bijunath.patla@nist.gov Table of Links Abstract and 1. Introduction Abstract and 1. Introduction Clock in Orbit
2.1 Coordinate Time
2.2 Local Frame for the Moon Clock Rate Differences Between Earth and Moon Clocks at Earth-Moon Lagrance Points
4.1 Clock at Lagrange point L1
4.2. Clock at Lagrange point L2
4.3. Clock at Lagrange point L4 or L5 Conclusions Clock in Orbit 2.1 Coordinate Time 2.2 Local Frame for the Moon Clock in Orbit Clock in Orbit 2.1 Coordinate Time 2.1 Coordinate Time 2.2 Local Frame for the Moon 2.2 Local Frame for the Moon Clock Rate Differences Between Earth and Moon Clock Rate Differences Between Earth and Moon Clock Rate Differences Between Earth and Moon Clocks at Earth-Moon Lagrance Points 4.1 Clock at Lagrange point L1 4.2. Clock at Lagrange point L2 4.3. Clock at Lagrange point L4 or L5 Clocks at Earth-Moon Lagrance Points 4.1 Clock at Lagrange point L1 4.1 Clock at Lagrange point L1 4.2. Clock at Lagrange point L2 4.2. Clock at Lagrange point L2 4.3. Clock at Lagrange point L4 or L5 4.3. Clock at Lagrange point L4 or L5 Conclusions Conclusions Conclusions Appendix 1: Fermi Coordinates with Origin at the Center of the Moon Appendix 1: Fermi Coordinates with Origin at the Center of the Moon Appendix 2: Construction of Freely Falling Center of Mass Frame Appendix 2: Construction of Freely Falling Center of Mass Frame Appendix 3: Equations of Motion of Earth and Moon Appendix 3: Equations of Motion of Earth and Moon Appendix 4: Comparing Results in Rotating and Non-Rotating Coordinate Systems Appendix 4: Comparing Results in Rotating and Non-Rotating Coordinate Systems Acknowledgments and References Acknowledgments and References As humanity aspires to explore the solar system and investigate distant worlds such as the Moon, Mars, and beyond, there is a growing need to establish and broaden coordinate time references that depend on the rate of standard clocks. According to Einstein’s theory of relativity, the rate of a standard clock is influenced by the gravitational potential at the location of the clock and the relative motion of the clock. A coordinate time reference is established by a grid of synchronized clocks traceable to an ideal clock at a predetermined point in space. This allows for the comparison of local time variations of clocks due to gravitational and kinematic effects. We present a relativistic framework to introduce a coordinate time for the Moon. This framework also establishes a relationship between the coordinate times for the Moon and the Earth as determined by standard clocks located on the Earth’s geoid and the Moon’s equator. A clock near the Moon’s equator ticks faster than one near the Earth’s equator, accumulating an extra 56.02 microseconds per day over the duration of a lunar orbit. This formalism is then used to compute the clock rates at Earth-Moon Lagrange points. Accurate estimation of the rate differences of coordinate times across celestial bodies and their inter-comparisons using clocks onboard orbiters at relatively stable Lagrange points as time transfer links is crucial for establishing reliable communications infrastructure. This understanding also underpins precise navigation in cislunar space and on celestial bodies’ surfaces, thus playing a pivotal role in ensuring the interoperability of various position, navigation, and timing (PNT) systems spanning from Earth to the Moon and to the farthest regions of the inner solar system. 1. INTRODUCTION More than 50 years after the first lunar landing, a multinational consortium, which includes NASA, is working towards a return to the Moon under the Artemis Accords [1]. Our ability to explore distant worlds will require the design and development of a communication and navigation infrastructure within and beyond cislunar space. With the expectation of a significant increase in assets on the lunar surface and in cislunar space in the near future, developing a robust architecture for accurate position, navigation, and timing (PNT) applications has become a matter of paramount interest. Communication and navigation systems rely on a network of clocks that are synchronized to each other within a few tens of nanoseconds. As the number of assets on the lunar surface grows, synchronizing local clocks with higher precision using remote clocks on Earth becomes challenging and inefficient. An optimal solution would be to draw from the heritage of global navigation satellite systems (GNSS) by envisioning a system or constellation time common to all assets and then relating this time to clocks on Earth. The relativistic framework presented here enables us to compare clock rates on the Moon and cislunar Lagrange points with respect to clocks on Earth by using a metric appropriate for a locally freely falling frame. The time measured by a clock at any given location is known as the proper time. Relativity of simultaneity implies that no two observers will agree on a given sequence of events if they are in different reference frames [2]. In other words, clocks in different reference frames tick at different rates. The gravitational and motional effects affect the ticking rate of clocks when compared with “ideal” clocks that are at rest and sufficiently far away from any gravitating mass. For example, clocks farther away from Earth tick faster, and clocks in uniform motion will tick slower with respect to “ideal” clocks, and vice-versa. Therefore, choosing an appropriate reference frame becomes essential for obtaining self-consistent results when comparing clocks on two celestial bodies. In this paper, mainly we seek answers to the following questions: What is a good choice for the coordinate system that can be used to relate the proper times on the Earth and the Moon? What is an appropriate choice for the locations of ideal clocks on the surfaces of the Earth and Moon that makes it easier to compare their proper times? What is the proper time difference between clocks on the Moon and the Earth? What are the proper time differences between clocks located at the Earth-Moon Lagrange points and the Earth? The stability offered by Lagrange points provides a low acceleration noise environment for spacecraft with clocks. The relativistic corrections for such clocks can be precisely estimated as their positions and velocities are well-determined and can be used to compare the proper times of clocks on Earth, Moon, and in cislunar orbits. In Section 1, we use the global positioning system (GPS) as an example to illustrate the relativistic effects on clocks if the Moon is treated just like an artificial satellite of the Earth and obtain a rough estimate for the clock rates on the Moon with respect to clocks on the geoid. Section 2 introduces a freely falling coordinate system with its center coinciding with the center of mass of the Earth and Moon. Section 3 compares the rate offset of a clock on the lunar surface to clocks on the geoid using this freely falling coordinate system, assuming the Moon is in a Keplerian orbit around the Earth. The results are compared with precise orbits for the Moon obtained using the latest planetary ephemerides DE440 [3]. Section 4 discusses the time rate offsets at Earth-Moon Lagrange points L1, L2, and L4/L5. Conclusions and future outlook are presented in Section 5. Appendices 1 and 2 introduce the framework for developing the metric used in all calculations. Appendix 3 justifies our assumptions of using a Keplerian model ignoring tidal effects, and a discussion in Appendix 4 establishes general covariance, meaning that the results are coordinate-independent. This paper is available on arxiv under CC0 1.0 license. This paper is available on arxiv under CC0 1.0 license. available on arxiv available on arxiv

Einstein Was Right (Again): Why Moon Clocks Run Faster Than Earth's

Einstein tenia raó (de nou): per què els rellotges lunars funcionen més ràpid que els de la Terra

Ο Αϊνστάιν είχε δίκιο (ξανά): Γιατί τα ρολόγια της Σελήνης τρέχουν πιο γρήγορα από αυτά της γης

Einstein tenía razón (otra vez): por qué los relojes lunares funcionan más rápido que los terrestres

انیشتین راست می گفت (دوباره): چرا ساعت های ماه سریعتر از زمین کار می کنند

Einstein tiña razón (de novo): por que os reloxos da Lúa corren máis rápido que os da Terra

איינשטיין צדק (שוב): מדוע שעוני ירח רצים מהר יותר משל כדור הארץ

Էյնշտեյնը ճիշտ էր (կրկին).

アインシュタインは正しかった（再び）：なぜ月の時計は地球の時計より速いのか

Einstein Betul (Sekali lagi): Mengapa Jam Bulan Berjalan Lebih Laju Daripada Bumi

Эйнштейн дуруст буд (боз): Чаро соатҳои Моҳ назар ба Замин тезтар кор мекунанд

Eýnşteýn dogry aýtdy (Againene): Aý sagatlary näme üçin Eartherden has çalt işleýär?

Einstein đã đúng (một lần nữa): Tại sao đồng hồ Mặt Trăng chạy nhanh hơn đồng hồ Trái Đất

Design, Manufacturing and Open-Loop Control of a Soft Pneumatic Arm: Conclusions

Authors:
(1) Jorge Francisco Garcia-Samartın, Centro de Automatica y Robotica (UPM-CSIC), Universidad Politecnica de Madrid — Consejo Superior de Investigaciones Cientıficas, Jose Gutierrez Abascal 2, 28006 Madrid, Spain (jorge.gsamartin@upm.es);
(2) Adrian Rieker, Centro de Automatica y Robotica (UPM-CSIC), Universidad Politecnica de Madrid — Consejo Superior de Investigaciones Cientıficas, Jose Gutierrez Abascal 2, 28006 Madrid, Spain;
(3) Antonio Barrientos, Centro de Automatica y Robotica (UPM-CSIC), Universidad Politecnica de Madrid — Consejo Superior de Investigaciones Cientıficas, Jose Gutierrez Abascal 2, 28006 Madrid, Spain. Table of Links Abstract and 1 Introduction 2 Related Works 2.1 Pneumatic Actuation 2.2 Pneumatic Arms 2.3 Control of Soft Robots 3 PAUL: Design and Manufacturing 3.1 Robot Design 3.2 Material Selection 3.3 Manufacturing 3.4 Actuation Bank 4 Data Acquisition and Open-Loop Control 4.1 Hardware Setup 4.2 Vision Capture System 4.3 Dataset Generation: Table-Based Models 4.4 Open-Loop Control 5 Results 5.1 Final PAUL version 5.2 Workspace Analysis 5.3 Performance of the Table-Based Models 5.4 Bending Experiments 5.5 Weight Carrying Experiments 6 Conclusions Funding Information A. Conducted Experiments and References 5.3 Performance of the Table-Based Models The size of the table to achieve acceptable kinematic modelling was set experimentally, as no previous references were available and previous works in the literature were very variable in terms of the number of data required. Furthermore, the possibility of an error occurring in the pneumatic system or the buffer of the vision acquisition system collapsing, together with the always present possibility of a leak in the segments, made it advisable to take data in small sessions and subsequently union of all of them. Since the data collection process was automated, this did not pose much of a problem. Although the possibility that the ambient temperature was a factor that influenced the kinematics of the robot was considered during the dataset collection process, it was finally proven that small variations in temperature did not affect the behaviour. Table 3 shows the datasets that were taken, the total time necessary to obtain them and the average time per point. It should be taken into account that not all captured positions were finally used, since, if the camera did not correctly detect the positions of the three beacon spheres, it could not calculate the orientation of the trihedral and therefore returned an error code. Of the 1200 samples collected, 5% had to be discarded, leaving 1146 finally usable. The average time per point, considering all the datasets collected, was 6.76 s, with a standard deviation of 0.63 s. The low variability between capture processes proves the effectiveness of the automated method designed. Once all the datasets were combined, the direct and inverse kinematic models presented here were validated. The validation of the direct model consisted of sending the robot a combination of inflation times and measuring the distance between the position reached, captured by the cameras, and that predicted by the table. Repeating the experiment for 40 points, the histogram of results presented in Figure 15 was observed. The average error is 4.27 mm, the median error 2.72 mm, and the standard deviation 1.99 mm. The high standard deviation and the shape of the histogram, tilted towards low values and with a very long tail, seem to indicate the existence of points where the model presents notable failures along with others with very good results. A future line of interest could be the detailed analysis of the workspace to locate where those regions of lower precision of the model are located and try to look for failures, perhaps leading to a greater density of points in the dataset. In the same way, the inverse kinematic model was tested. To do this, PAUL was given a reference position and orientation to achieve, the necessary times were calculated, using the procedures referred to in Equations (16), and (17) inflation was carried out. Subsequently, the position captured with the cameras was compared with the desired one. As expected, the existence of redundancies, in which equal position values are achieved with very different combinations of inflation times, introduces large uncertainties in the model, which the triangulation presented is not able to capture. Specifically, the inverse kinematic model has an average error of 10.78 mm, a median error of 9.22 mm and a standard deviation of 5.98 mm. While these errors may seem high, they are compared in Table 4 with other open-loop controllers presented in the literature. It can be clearly seen that they are in line with the results obtained and that they are even better than those obtained by smaller robots, where one would expect, due to the smaller working space, a higher accuracy (at least in data-driven models). It is worth highlighting, however, two experiments in which PAUL performed very satisfactorily, because the area of operation was restricted to a region where no redundancies were found to exist. They are available in the video of Appendix A. In the first of them, the robot was forced to reach a set of points located on the horizontal basis plane, also forcing the lower end of the last segment to be parallel to said plane. In all of them, errors less than 7 mm were achieved. Figure 16 shows the results of said experiment. With the aim of facilitating the understanding of the experiment, the beacon was changed for a laser pointer that points to the desired points, on which targets with a radius of 5 mm have been marked, allowing the accuracy achieved to be checked. In the second experiment, shown in Figure 17, points on the lower horizontal plane were also taken as reference, but without imposing that the lower face of the robot should remain parallel to it. In this case, accuracies of 2 cm were achieved. Although the inverse kinematic model therefore presents acceptable results, it must be commented that, in all these experiments, due to the geometry and material of the robot, at the moment in which PAUL reaches the desired position, it tends to acquire a movement damped oscillation. An attempt has been made to reduce it, despite everything, it is a very intrinsic phenomenon to the robot that is difficult to solve. A future line proposed, in this sense, is to try to rigidify the robot by introducing negative pressures that generate vacuum. This paper is available on arxiv under CC BY-NC-SA 4.0 DEED license. Authors: (1) Jorge Francisco Garcia-Samartın, Centro de Automatica y Robotica (UPM-CSIC), Universidad Politecnica de Madrid — Consejo Superior de Investigaciones Cientıficas, Jose Gutierrez Abascal 2, 28006 Madrid, Spain (jorge.gsamartin@upm.es); (2) Adrian Rieker, Centro de Automatica y Robotica (UPM-CSIC), Universidad Politecnica de Madrid — Consejo Superior de Investigaciones Cientıficas, Jose Gutierrez Abascal 2, 28006 Madrid, Spain; (3) Antonio Barrientos, Centro de Automatica y Robotica (UPM-CSIC), Universidad Politecnica de Madrid — Consejo Superior de Investigaciones Cientıficas, Jose Gutierrez Abascal 2, 28006 Madrid, Spain. Authors: Authors: (1) Jorge Francisco Garcia-Samartın, Centro de Automatica y Robotica (UPM-CSIC), Universidad Politecnica de Madrid — Consejo Superior de Investigaciones Cientıficas, Jose Gutierrez Abascal 2, 28006 Madrid, Spain (jorge.gsamartin@upm.es); (2) Adrian Rieker, Centro de Automatica y Robotica (UPM-CSIC), Universidad Politecnica de Madrid — Consejo Superior de Investigaciones Cientıficas, Jose Gutierrez Abascal 2, 28006 Madrid, Spain; (3) Antonio Barrientos, Centro de Automatica y Robotica (UPM-CSIC), Universidad Politecnica de Madrid — Consejo Superior de Investigaciones Cientıficas, Jose Gutierrez Abascal 2, 28006 Madrid, Spain. Table of Links Abstract and 1 Introduction Abstract and 1 Introduction 2 Related Works 2.1 Pneumatic Actuation 2.1 Pneumatic Actuation 2.2 Pneumatic Arms 2.2 Pneumatic Arms 2.3 Control of Soft Robots 2.3 Control of Soft Robots 3 PAUL: Design and Manufacturing 3.1 Robot Design 3.1 Robot Design 3.2 Material Selection 3.2 Material Selection 3.3 Manufacturing 3.3 Manufacturing 3.4 Actuation Bank 3.4 Actuation Bank 4 Data Acquisition and Open-Loop Control 4.1 Hardware Setup 4.1 Hardware Setup 4.2 Vision Capture System 4.2 Vision Capture System 4.3 Dataset Generation: Table-Based Models 4.3 Dataset Generation: Table-Based Models 4.4 Open-Loop Control 4.4 Open-Loop Control 5 Results 5.1 Final PAUL version 5.1 Final PAUL version 5.2 Workspace Analysis 5.2 Workspace Analysis 5.3 Performance of the Table-Based Models 5.3 Performance of the Table-Based Models 5.4 Bending Experiments 5.4 Bending Experiments 5.5 Weight Carrying Experiments 5.5 Weight Carrying Experiments 6 Conclusions 6 Conclusions Funding Information Funding Information A. Conducted Experiments and References A. Conducted Experiments and References 5.3 Performance of the Table-Based Models The size of the table to achieve acceptable kinematic modelling was set experimentally, as no previous references were available and previous works in the literature were very variable in terms of the number of data required. Furthermore, the possibility of an error occurring in the pneumatic system or the buffer of the vision acquisition system collapsing, together with the always present possibility of a leak in the segments, made it advisable to take data in small sessions and subsequently union of all of them. Since the data collection process was automated, this did not pose much of a problem. Although the possibility that the ambient temperature was a factor that influenced the kinematics of the robot was considered during the dataset collection process, it was finally proven that small variations in temperature did not affect the behaviour. Table 3 shows the datasets that were taken, the total time necessary to obtain them and the average time per point. It should be taken into account that not all captured positions were finally used, since, if the camera did not correctly detect the positions of the three beacon spheres, it could not calculate the orientation of the trihedral and therefore returned an error code. Of the 1200 samples collected, 5% had to be discarded, leaving 1146 finally usable. The average time per point, considering all the datasets collected, was 6.76 s, with a standard deviation of 0.63 s. The low variability between capture processes proves the effectiveness of the automated method designed. Once all the datasets were combined, the direct and inverse kinematic models presented here were validated. The validation of the direct model consisted of sending the robot a combination of inflation times and measuring the distance between the position reached, captured by the cameras, and that predicted by the table. Repeating the experiment for 40 points, the histogram of results presented in Figure 15 was observed. The average error is 4.27 mm, the median error 2.72 mm, and the standard deviation 1.99 mm. The high standard deviation and the shape of the histogram, tilted towards low values and with a very long tail, seem to indicate the existence of points where the model presents notable failures along with others with very good results. A future line of interest could be the detailed analysis of the workspace to locate where those regions of lower precision of the model are located and try to look for failures, perhaps leading to a greater density of points in the dataset. In the same way, the inverse kinematic model was tested. To do this, PAUL was given a reference position and orientation to achieve, the necessary times were calculated, using the procedures referred to in Equations (16), and (17) inflation was carried out. Subsequently, the position captured with the cameras was compared with the desired one. As expected, the existence of redundancies, in which equal position values are achieved with very different combinations of inflation times, introduces large uncertainties in the model, which the triangulation presented is not able to capture. Specifically, the inverse kinematic model has an average error of 10.78 mm, a median error of 9.22 mm and a standard deviation of 5.98 mm. While these errors may seem high, they are compared in Table 4 with other open-loop controllers presented in the literature. It can be clearly seen that they are in line with the results obtained and that they are even better than those obtained by smaller robots, where one would expect, due to the smaller working space, a higher accuracy (at least in data-driven models). It is worth highlighting, however, two experiments in which PAUL performed very satisfactorily, because the area of operation was restricted to a region where no redundancies were found to exist. They are available in the video of Appendix A. In the first of them, the robot was forced to reach a set of points located on the horizontal basis plane, also forcing the lower end of the last segment to be parallel to said plane. In all of them, errors less than 7 mm were achieved. Figure 16 shows the results of said experiment. With the aim of facilitating the understanding of the experiment, the beacon was changed for a laser pointer that points to the desired points, on which targets with a radius of 5 mm have been marked, allowing the accuracy achieved to be checked. In the second experiment, shown in Figure 17, points on the lower horizontal plane were also taken as reference, but without imposing that the lower face of the robot should remain parallel to it. In this case, accuracies of 2 cm were achieved. Although the inverse kinematic model therefore presents acceptable results, it must be commented that, in all these experiments, due to the geometry and material of the robot, at the moment in which PAUL reaches the desired position, it tends to acquire a movement damped oscillation. An attempt has been made to reduce it, despite everything, it is a very intrinsic phenomenon to the robot that is difficult to solve. A future line proposed, in this sense, is to try to rigidify the robot by introducing negative pressures that generate vacuum. This paper is available on arxiv under CC BY-NC-SA 4.0 DEED license. This paper is available on arxiv under CC BY-NC-SA 4.0 DEED license. available on arxiv

Soft Robots and Smart Movement

Authors:
(1) Jorge Francisco Garcia-Samartın, Centro de Automatica y Robotica (UPM-CSIC), Universidad Politecnica de Madrid — Consejo Superior de Investigaciones Cientıficas, Jose Gutierrez Abascal 2, 28006 Madrid, Spain (jorge.gsamartin@upm.es);
(2) Adrian Rieker, Centro de Automatica y Robotica (UPM-CSIC), Universidad Politecnica de Madrid — Consejo Superior de Investigaciones Cientıficas, Jose Gutierrez Abascal 2, 28006 Madrid, Spain;
(3) Antonio Barrientos, Centro de Automatica y Robotica (UPM-CSIC), Universidad Politecnica de Madrid — Consejo Superior de Investigaciones Cientıficas, Jose Gutierrez Abascal 2, 28006 Madrid, Spain. Table of Links Abstract and 1 Introduction 2 Related Works 2.1 Pneumatic Actuation 2.2 Pneumatic Arms 2.3 Control of Soft Robots 3 PAUL: Design and Manufacturing 3.1 Robot Design 3.2 Material Selection 3.3 Manufacturing 3.4 Actuation Bank 4 Data Acquisition and Open-Loop Control 4.1 Hardware Setup 4.2 Vision Capture System 4.3 Dataset Generation: Table-Based Models 4.4 Open-Loop Control 5 Results 5.1 Final PAUL version 5.2 Workspace Analysis 5.3 Performance of the Table-Based Models 5.4 Bending Experiments 5.5 Weight Carrying Experiments 6 Conclusions Funding Information A. Conducted Experiments and References 4.3 Dataset Generation: Table-Based Models Due to the complexity of the robot, model-based methodologies, such as PCC or the ones based on Cosserat Rod Theory were discarded. Although the usage of FEM is an avenue that will not be closed in future work, the large number of parameters to be set experimentally for each segment (Young’s modulus, moment of inertia. . . ), given that the manufacturing process is so variable meant that, in this first phase, we opted to use some type of PAUL modelling based on data collection. The output of the system is taken as the position and orientation reached by the final end –thus, at this stage, all the positions of the intermediate segments are ignored– and as input, the inflation times of each of the bladders. As there were not enough pressure sensors available at the time of the construction of the robot, it was decided to take inflation time as an input variable. As the working pressure is limited by the pressure limiting valve and the flow rate into each bladder can be assumed to be constant, the time is equivalent to the volume of air introduced into each cavity. All the control options considered have in common the need for a large amount of empirical data, which leads to the need to develop an experimental design to systematise the collection of this data. Since the capture of this information is done in different phases and the datasets have to represent the behaviour of the robot in an objective way, the re-applicability of the experiment takes on special importance. The data stored in the datasets was the position of the robot tip and the set of inflation times that achieve this configuration. The aforementioned limitation that only two of the three bladders in the segment are inflated reduces redundancies. As previously stated, more than two segments lead to redundancies, which implies that the inverse kinematic model of the robot can have multiple solutions. The data collection process involves several sequential steps. Initially, a set number of samples is determined. For each sample, Matlab commands dispatch a random combination of nine inflation times, corresponding to each valve of PAUL, to the actuation bench. Times are generated below a maximum time limit Tmax, and ensuring that only two cavities per segment are inflated. Following this, the robot’s bladders are inflated based on the sent times. Subsequently, the vision system’s two cameras capture images to determine the position and orientation of the robot’s end. This entire procedure is repeated for the specified number of iterations, and upon completion, the collected data is stored in the dataset The information on swelling times is stored as a percentage, with a value of 0 corresponding to a zero swelling of that segment and 100 corresponding to Tmax, the swelling for the maximum number of milliseconds defined for this data collection session. This value Tmax is stored, together with the values, in the dataset, in order to be able to compare different datasets. The reason for this coding comes from the lack of information, a priori, on what is the maximum pressure that a PAUL bladder admits. Although it is true that it was experimentally determined that inflation times of more than 1500 ms in a row led to punctures, the application of lower times during a repeated number of cycles also generated leaks. On this basis, it was decided never to inflate any valve, either in one or several steps, more than 1000 ms. Along with the inflation times of each bladder, the position and orientation reached by the end tip is stored, based on the camera readings. In particular, the position of the green marker and the orientation of the trihedron are stored. The latter is expressed in Euler angles, as it is a much efficient form of storage than a rotation matrix. In addition, the dataset also contains metadata from the collection process that are believed to influence the results, such as the pneumatic line pressure or the ambient temperature. Some aspects in the pneumatic system merit attention. Initially, bladder inflation and deflation are not symmetrical processes. Geometric constraints in the pneumatic components result in a lower deflation rate compared to inflation. Consequently, when the PAUL receives a deflation time, it multiplies it by an empirically derived factor, approximately 1.45 for a 1.2 bar working pressure. This multiplier compensates for the discrepancy between inflation and deflation times of a singular group of bladders, ensuring that the deflation time aligns with the time required to reach the same inflation point. Similarly, although it is physically possible to inflate several valves at the same time, it has been shown that this parallel flow distribution means that the effective fillings of each valve are not the same as if they were inflated individually. To prevent this phenomenon, it was decided to inflate each bladder individually both during the data acquisition process and utterly, when PAUL was asked to reach certain positions. Finally, there are hysteresis phenomena in the silicone that cause the position reached by inflating for a time t to be different from the position reached by inflating first for a time t1 and then for a time t2 = t − t1. The strategy employed to tackle this problem was to capture the dataset bringing PAUL back to its zero position between each sample. Nevertheless, when controlling the robot in open-loop this is not possible, or, at least, not desirable, as one may wish to follow trajectories or travel through a sequence of points. Therefore, transitioning from position x1 to x2 requires an additional factor of 1.2, also derived experimentally, to account for hysteresis effects. 4.4 Open-Loop Control Once the dataset is generated, it can be used to model the behaviour of PAUL for open-loop control. It is foreseen, as a future line, to train a neural network for the direct kinematics and another one for the inverse kinematics. However, given the large amount of data that may be required (in [62] 24389 samples are used for a three-segment robot like this one), a table look-up method has been used for this work. The method for direct kinematics –which allows obtaining the position and orientation of the final end of the robot from the inflation times of the nine bladders– consists of searching, in the generated dataset in the previous step, the three inflation time values located at a shorter distance from the inflation time given as a reference. Obviously, if the set of inflation times sought were in the table, the value associated with these times would be returned as a result of the direct kinematic model. Otherwise, the average of the position and orientation values associated with the three closest inflation times, weighted by the distance (Euclidean norm) existing between each of them and the values of reference inflation times, is returned as the position and orientation value of the robot. with them, it is possible to calculate the position returned by the direct kinematic model using the expression: This paper is available on arxiv under CC BY-NC-SA 4.0 DEED license. Authors: (1) Jorge Francisco Garcia-Samartın, Centro de Automatica y Robotica (UPM-CSIC), Universidad Politecnica de Madrid — Consejo Superior de Investigaciones Cientıficas, Jose Gutierrez Abascal 2, 28006 Madrid, Spain (jorge.gsamartin@upm.es); (2) Adrian Rieker, Centro de Automatica y Robotica (UPM-CSIC), Universidad Politecnica de Madrid — Consejo Superior de Investigaciones Cientıficas, Jose Gutierrez Abascal 2, 28006 Madrid, Spain; (3) Antonio Barrientos, Centro de Automatica y Robotica (UPM-CSIC), Universidad Politecnica de Madrid — Consejo Superior de Investigaciones Cientıficas, Jose Gutierrez Abascal 2, 28006 Madrid, Spain. Authors: Authors: (1) Jorge Francisco Garcia-Samartın, Centro de Automatica y Robotica (UPM-CSIC), Universidad Politecnica de Madrid — Consejo Superior de Investigaciones Cientıficas, Jose Gutierrez Abascal 2, 28006 Madrid, Spain (jorge.gsamartin@upm.es); (2) Adrian Rieker, Centro de Automatica y Robotica (UPM-CSIC), Universidad Politecnica de Madrid — Consejo Superior de Investigaciones Cientıficas, Jose Gutierrez Abascal 2, 28006 Madrid, Spain; (3) Antonio Barrientos, Centro de Automatica y Robotica (UPM-CSIC), Universidad Politecnica de Madrid — Consejo Superior de Investigaciones Cientıficas, Jose Gutierrez Abascal 2, 28006 Madrid, Spain. Table of Links Abstract and 1 Introduction Abstract and 1 Introduction 2 Related Works 2.1 Pneumatic Actuation 2.1 Pneumatic Actuation 2.2 Pneumatic Arms 2.2 Pneumatic Arms 2.3 Control of Soft Robots 2.3 Control of Soft Robots 3 PAUL: Design and Manufacturing 3.1 Robot Design 3.1 Robot Design 3.2 Material Selection 3.2 Material Selection 3.3 Manufacturing 3.3 Manufacturing 3.4 Actuation Bank 3.4 Actuation Bank 4 Data Acquisition and Open-Loop Control 4.1 Hardware Setup 4.1 Hardware Setup 4.2 Vision Capture System 4.2 Vision Capture System 4.3 Dataset Generation: Table-Based Models 4.3 Dataset Generation: Table-Based Models 4.4 Open-Loop Control 4.4 Open-Loop Control 5 Results 5.1 Final PAUL version 5.1 Final PAUL version 5.2 Workspace Analysis 5.2 Workspace Analysis 5.3 Performance of the Table-Based Models 5.3 Performance of the Table-Based Models 5.4 Bending Experiments 5.4 Bending Experiments 5.5 Weight Carrying Experiments 5.5 Weight Carrying Experiments 6 Conclusions 6 Conclusions Funding Information Funding Information A. Conducted Experiments and References A. Conducted Experiments and References 4.3 Dataset Generation: Table-Based Models Due to the complexity of the robot, model-based methodologies, such as PCC or the ones based on Cosserat Rod Theory were discarded. Although the usage of FEM is an avenue that will not be closed in future work, the large number of parameters to be set experimentally for each segment (Young’s modulus, moment of inertia. . . ), given that the manufacturing process is so variable meant that, in this first phase, we opted to use some type of PAUL modelling based on data collection. The output of the system is taken as the position and orientation reached by the final end –thus, at this stage, all the positions of the intermediate segments are ignored– and as input, the inflation times of each of the bladders. As there were not enough pressure sensors available at the time of the construction of the robot, it was decided to take inflation time as an input variable. As the working pressure is limited by the pressure limiting valve and the flow rate into each bladder can be assumed to be constant, the time is equivalent to the volume of air introduced into each cavity. All the control options considered have in common the need for a large amount of empirical data, which leads to the need to develop an experimental design to systematise the collection of this data. Since the capture of this information is done in different phases and the datasets have to represent the behaviour of the robot in an objective way, the re-applicability of the experiment takes on special importance. The data stored in the datasets was the position of the robot tip and the set of inflation times that achieve this configuration. The aforementioned limitation that only two of the three bladders in the segment are inflated reduces redundancies. As previously stated, more than two segments lead to redundancies, which implies that the inverse kinematic model of the robot can have multiple solutions. The data collection process involves several sequential steps. Initially, a set number of samples is determined. For each sample, Matlab commands dispatch a random combination of nine inflation times, corresponding to each valve of PAUL, to the actuation bench. Times are generated below a maximum time limit Tmax, and ensuring that only two cavities per segment are inflated. Following this, the robot’s bladders are inflated based on the sent times. Subsequently, the vision system’s two cameras capture images to determine the position and orientation of the robot’s end. This entire procedure is repeated for the specified number of iterations, and upon completion, the collected data is stored in the dataset The information on swelling times is stored as a percentage, with a value of 0 corresponding to a zero swelling of that segment and 100 corresponding to Tmax, the swelling for the maximum number of milliseconds defined for this data collection session. This value Tmax is stored, together with the values, in the dataset, in order to be able to compare different datasets. The reason for this coding comes from the lack of information, a priori, on what is the maximum pressure that a PAUL bladder admits. Although it is true that it was experimentally determined that inflation times of more than 1500 ms in a row led to punctures, the application of lower times during a repeated number of cycles also generated leaks. On this basis, it was decided never to inflate any valve, either in one or several steps, more than 1000 ms. Along with the inflation times of each bladder, the position and orientation reached by the end tip is stored, based on the camera readings. In particular, the position of the green marker and the orientation of the trihedron are stored. The latter is expressed in Euler angles, as it is a much efficient form of storage than a rotation matrix. In addition, the dataset also contains metadata from the collection process that are believed to influence the results, such as the pneumatic line pressure or the ambient temperature. Some aspects in the pneumatic system merit attention. Initially, bladder inflation and deflation are not symmetrical processes. Geometric constraints in the pneumatic components result in a lower deflation rate compared to inflation. Consequently, when the PAUL receives a deflation time, it multiplies it by an empirically derived factor, approximately 1.45 for a 1.2 bar working pressure. This multiplier compensates for the discrepancy between inflation and deflation times of a singular group of bladders, ensuring that the deflation time aligns with the time required to reach the same inflation point. Similarly, although it is physically possible to inflate several valves at the same time, it has been shown that this parallel flow distribution means that the effective fillings of each valve are not the same as if they were inflated individually. To prevent this phenomenon, it was decided to inflate each bladder individually both during the data acquisition process and utterly, when PAUL was asked to reach certain positions. Finally, there are hysteresis phenomena in the silicone that cause the position reached by inflating for a time t to be different from the position reached by inflating first for a time t1 and then for a time t2 = t − t1. The strategy employed to tackle this problem was to capture the dataset bringing PAUL back to its zero position between each sample. Nevertheless, when controlling the robot in open-loop this is not possible, or, at least, not desirable, as one may wish to follow trajectories or travel through a sequence of points. Therefore, transitioning from position x1 to x2 requires an additional factor of 1.2, also derived experimentally, to account for hysteresis effects. 4.4 Open-Loop Control Once the dataset is generated, it can be used to model the behaviour of PAUL for open-loop control. It is foreseen, as a future line, to train a neural network for the direct kinematics and another one for the inverse kinematics. However, given the large amount of data that may be required (in [62] 24389 samples are used for a three-segment robot like this one), a table look-up method has been used for this work. The method for direct kinematics –which allows obtaining the position and orientation of the final end of the robot from the inflation times of the nine bladders– consists of searching, in the generated dataset in the previous step, the three inflation time values located at a shorter distance from the inflation time given as a reference. Obviously, if the set of inflation times sought were in the table, the value associated with these times would be returned as a result of the direct kinematic model. Otherwise, the average of the position and orientation values associated with the three closest inflation times, weighted by the distance (Euclidean norm) existing between each of them and the values of reference inflation times, is returned as the position and orientation value of the robot. with them, it is possible to calculate the position returned by the direct kinematic model using the expression: This paper is available on arxiv under CC BY-NC-SA 4.0 DEED license. This paper is available on arxiv under CC BY-NC-SA 4.0 DEED license. available on arxiv

Why PAUL Needs a Massive Dataset to Improve Its Movements

Warum PAUL einen riesigen Datensatz benötigt, um seine Bewegungen zu verbessern

Por qué PAUL necesita un conjunto de datos masivo para mejorar sus movimientos

Zašto PAUL treba ogroman skup podataka za poboljšanje svojih kretanja

PAUL が運動を改善するために大規模なデータセットを必要とする理由

ហេតុអ្វីបានជា PAUL ត្រូវការសំណុំទិន្នន័យដ៏ធំ ដើម្បីកែលម្អចលនារបស់វា។

PAUL이 움직임을 개선하기 위해 방대한 데이터 세트가 필요한 이유

ເປັນຫຍັງ PAUL ຕ້ອງການຊຸດຂໍ້ມູນອັນໃຫຍ່ຫຼວງເພື່ອປັບປຸງການເຄື່ອນໄຫວຂອງມັນ

Kāpēc PAULam ir nepieciešama liela datu kopa, lai uzlabotu tās kustības

Nahoana i PAUL no mila angon-drakitra betsaka hanatsarana ny fihetsiny

De ce PAUL are nevoie de un set de date masiv pentru a-și îmbunătăți mișcările

PAUL හට එහි චලනයන් වැඩිදියුණු කිරීම සඳහා දැවැන්ත දත්ත කට්ටලයක් අවශ්‍ය වන්නේ ඇයි?

کیوں PAUL کو اپنی نقل و حرکت کو بہتر بنانے کے لیے بڑے پیمانے پر ڈیٹا سیٹ کی ضرورت ہے۔

Authors:
(1) Jorge Francisco Garcia-Samartın, Centro de Automatica y Robotica (UPM-CSIC), Universidad Politecnica de Madrid — Consejo Superior de Investigaciones Cientıficas, Jose Gutierrez Abascal 2, 28006 Madrid, Spain (jorge.gsamartin@upm.es);
(2) Adrian Rieker, Centro de Automatica y Robotica (UPM-CSIC), Universidad Politecnica de Madrid — Consejo Superior de Investigaciones Cientıficas, Jose Gutierrez Abascal 2, 28006 Madrid, Spain;
(3) Antonio Barrientos, Centro de Automatica y Robotica (UPM-CSIC), Universidad Politecnica de Madrid — Consejo Superior de Investigaciones Cientıficas, Jose Gutierrez Abascal 2, 28006 Madrid, Spain. Table of Links Abstract and 1 Introduction 2 Related Works 2.1 Pneumatic Actuation 2.2 Pneumatic Arms 2.3 Control of Soft Robots 3 PAUL: Design and Manufacturing 3.1 Robot Design 3.2 Material Selection 3.3 Manufacturing 3.4 Actuation Bank 4 Data Acquisition and Open-Loop Control 4.1 Hardware Setup 4.2 Vision Capture System 4.3 Dataset Generation: Table-Based Models 4.4 Open-Loop Control 5 Results 5.1 Final PAUL version 5.2 Workspace Analysis 5.3 Performance of the Table-Based Models 5.4 Bending Experiments 5.5 Weight Carrying Experiments 6 Conclusions Funding Information A. Conducted Experiments and References Abstract Soft Robots distinguish themselves from traditional robots by embracing flexible kinematics. Because of their recent emergence, there exist numerous uncharted territories, including novel actuators, manufacturing processes, and advanced control methods. This research is centred on the design, fabrication, and control of a pneumatic soft robot. The principal objective is to develop a modular soft robot featuring with multiple segments, each one of three degrees of freedom. This yields to tubular structure with five independent degrees of freedom, enabling motion across three spatial dimensions. Physical construction leverages tin-cured silicone and a wax casting method, refined through iterative processes. 3D-printed PLA moulds, filled with silicone, yield the desired model, while bladder-like structures, are formed within using solidified paraffin wax positive moulds. For control, an empirically fine-tuned open-loop system is adopted. The project culminates in rigorous testing bending ability and weight carrying capacity and possible applications are discussed. Keywords: soft actuator; pneumatics; soft robots materials and design; open-loop control; computer vision capture 1 Introduction The rapid growth of soft robotics in the past decade is driven by their versatile applications in various fields, such as assisting surgeons, taking care of elderly people [1, 2], aiding rehabilitation [3], and enhancing manipulation capabilities [4]. Soft robots significantly differ from their traditional rigid counterparts, demanding innovative solutions across a wide spectrum, encompassing sensors, actuators, and control techniques. While conventional actuation methods can be applied in certain scenarios, such as cable robots where external motors tension the cables [5,6], novel actuators are frequently required. This has led to the development of various actuator types, including pneumatic actuators [7], electroactive polymers (EAP) [8], magnetic actuators [9], twisted and coiled actuators (TCA) [10], and shape memory alloys (SMA) [11, 12]. Among these options, pneumatic actuators stand out due to their cost-effectiveness, simplified manufacturing, straightforward actuation, and impressive load-bearing capacity [13], specially when no high speeds are required. Certainly, these actuators do not necessitate specific manufacturing conditions beyond the curing of silicone, typically conducted at or near room temperature. Moreover, their operation does not demand high-voltage conditions or the generation of external magnetic fields. Furthermore, they excel in achieving continuous deformations in the robots, surpassing those actuated by wires. These advantages have led to their use in grippers [14], inspection tasks [15], locomotion robots [16, 17] wearable devices for rehabilitation [18] or imitating human body parts [19]. The main contribution of this work has been the design, manufacturing and open-loop control of a 5-degrees of freedom (DOF) soft pneumatic arm called PAUL (Pneumatic Articulated Ultrasoft Limb) and depicted in Figure 1, capable of carrying light loads without increasing its precision error. In addition to the precision of its control system without and with external payloads, its workspace and its bending capacity are also analysed. It is not common to find a simultaneous analysis of all these factors in the literature. PAUL is composed of 3 independent modules or segments, made of silicone. Each segment is fed by 3 pneumatic tubes whose inflation give him 3 degrees of freedom: it can bend in two direction, as well as elongate when the three bladders are inflated. To reduce redundancies, it was decided to act only up to two at a time. Combining these components results in a robot with 9 inputs and 5 degrees of freedom in the task space, as no twisting movement is possible in any case. Actuation is achieved by measuring the valve opening duration, while a vision system, based on identifying a trihedron of colours, provides continuous feedback on the position of the end-effector. To address the challenge of modelling these robots, especially given the limitations of existing theoretical models –methods like the Piecewise Constant Curvature (PCC), which are adequate for hyper-redundant robots may lack precision in soft manipulators [20] and parameters for simulations based on the Finite Elements Method (FEM) are difficult to adjust–, an open-loop control system has been developed. This system relies on an experimentally constructed table that correlates valve opening times with the corresponding final positions of the manipulator. This empirical approach allows for reasonably accurate modelling of both the direct and inverse kinematics of the robot, even in the absence of precise theoretical models. The paper is structured as follows: Section 2 presents the main characteristics and working principles of the existing soft pneumatic arms, Section 3 details PAUL design and manufacturing process, highlighting the various modifications that had to be made iteratively and also addressing the construction of the pneumatic actuation bench, Section 4 describes the open loop control system and the steps that had to be taken to get there: the configuration of the robot hardware, the implementation of the vision system and the generation of the data table. The test carried out are commented in Section 5, and finally, Section 6 draws the conclusion. This paper is available on arxiv under CC BY-NC-SA 4.0 DEED license. Authors: (1) Jorge Francisco Garcia-Samartın, Centro de Automatica y Robotica (UPM-CSIC), Universidad Politecnica de Madrid — Consejo Superior de Investigaciones Cientıficas, Jose Gutierrez Abascal 2, 28006 Madrid, Spain (jorge.gsamartin@upm.es); (2) Adrian Rieker, Centro de Automatica y Robotica (UPM-CSIC), Universidad Politecnica de Madrid — Consejo Superior de Investigaciones Cientıficas, Jose Gutierrez Abascal 2, 28006 Madrid, Spain; (3) Antonio Barrientos, Centro de Automatica y Robotica (UPM-CSIC), Universidad Politecnica de Madrid — Consejo Superior de Investigaciones Cientıficas, Jose Gutierrez Abascal 2, 28006 Madrid, Spain. Authors: Authors: (1) Jorge Francisco Garcia-Samartın, Centro de Automatica y Robotica (UPM-CSIC), Universidad Politecnica de Madrid — Consejo Superior de Investigaciones Cientıficas, Jose Gutierrez Abascal 2, 28006 Madrid, Spain (jorge.gsamartin@upm.es); (2) Adrian Rieker, Centro de Automatica y Robotica (UPM-CSIC), Universidad Politecnica de Madrid — Consejo Superior de Investigaciones Cientıficas, Jose Gutierrez Abascal 2, 28006 Madrid, Spain; (3) Antonio Barrientos, Centro de Automatica y Robotica (UPM-CSIC), Universidad Politecnica de Madrid — Consejo Superior de Investigaciones Cientıficas, Jose Gutierrez Abascal 2, 28006 Madrid, Spain. Table of Links Abstract and 1 Introduction Abstract and 1 Introduction 2 Related Works 2.1 Pneumatic Actuation 2.1 Pneumatic Actuation 2.2 Pneumatic Arms 2.2 Pneumatic Arms 2.3 Control of Soft Robots 2.3 Control of Soft Robots 3 PAUL: Design and Manufacturing 3.1 Robot Design 3.1 Robot Design 3.2 Material Selection 3.2 Material Selection 3.3 Manufacturing 3.3 Manufacturing 3.4 Actuation Bank 3.4 Actuation Bank 4 Data Acquisition and Open-Loop Control 4.1 Hardware Setup 4.1 Hardware Setup 4.2 Vision Capture System 4.2 Vision Capture System 4.3 Dataset Generation: Table-Based Models 4.3 Dataset Generation: Table-Based Models 4.4 Open-Loop Control 4.4 Open-Loop Control 5 Results 5.1 Final PAUL version 5.1 Final PAUL version 5.2 Workspace Analysis 5.2 Workspace Analysis 5.3 Performance of the Table-Based Models 5.3 Performance of the Table-Based Models 5.4 Bending Experiments 5.4 Bending Experiments 5.5 Weight Carrying Experiments 5.5 Weight Carrying Experiments 6 Conclusions 6 Conclusions Funding Information Funding Information A. Conducted Experiments and References A. Conducted Experiments and References Abstract Soft Robots distinguish themselves from traditional robots by embracing flexible kinematics. Because of their recent emergence, there exist numerous uncharted territories, including novel actuators, manufacturing processes, and advanced control methods. This research is centred on the design, fabrication, and control of a pneumatic soft robot. The principal objective is to develop a modular soft robot featuring with multiple segments, each one of three degrees of freedom. This yields to tubular structure with five independent degrees of freedom, enabling motion across three spatial dimensions. Physical construction leverages tin-cured silicone and a wax casting method, refined through iterative processes. 3D-printed PLA moulds, filled with silicone, yield the desired model, while bladder-like structures, are formed within using solidified paraffin wax positive moulds. For control, an empirically fine-tuned open-loop system is adopted. The project culminates in rigorous testing bending ability and weight carrying capacity and possible applications are discussed. Keywords : soft actuator; pneumatics; soft robots materials and design; open-loop control; computer vision capture Keywords 1 Introduction The rapid growth of soft robotics in the past decade is driven by their versatile applications in various fields, such as assisting surgeons, taking care of elderly people [1, 2], aiding rehabilitation [3], and enhancing manipulation capabilities [4]. Soft robots significantly differ from their traditional rigid counterparts, demanding innovative solutions across a wide spectrum, encompassing sensors, actuators, and control techniques. While conventional actuation methods can be applied in certain scenarios, such as cable robots where external motors tension the cables [5,6], novel actuators are frequently required. This has led to the development of various actuator types, including pneumatic actuators [7], electroactive polymers (EAP) [8], magnetic actuators [9], twisted and coiled actuators (TCA) [10], and shape memory alloys (SMA) [11, 12]. Among these options, pneumatic actuators stand out due to their cost-effectiveness, simplified manufacturing, straightforward actuation, and impressive load-bearing capacity [13], specially when no high speeds are required. Certainly, these actuators do not necessitate specific manufacturing conditions beyond the curing of silicone, typically conducted at or near room temperature. Moreover, their operation does not demand high-voltage conditions or the generation of external magnetic fields. Furthermore, they excel in achieving continuous deformations in the robots, surpassing those actuated by wires. These advantages have led to their use in grippers [14], inspection tasks [15], locomotion robots [16, 17] wearable devices for rehabilitation [18] or imitating human body parts [19]. The main contribution of this work has been the design, manufacturing and open-loop control of a 5-degrees of freedom (DOF) soft pneumatic arm called PAUL (Pneumatic Articulated Ultrasoft Limb) and depicted in Figure 1, capable of carrying light loads without increasing its precision error. In addition to the precision of its control system without and with external payloads, its workspace and its bending capacity are also analysed. It is not common to find a simultaneous analysis of all these factors in the literature. PAUL is composed of 3 independent modules or segments, made of silicone. Each segment is fed by 3 pneumatic tubes whose inflation give him 3 degrees of freedom: it can bend in two direction, as well as elongate when the three bladders are inflated. To reduce redundancies, it was decided to act only up to two at a time. Combining these components results in a robot with 9 inputs and 5 degrees of freedom in the task space, as no twisting movement is possible in any case. Actuation is achieved by measuring the valve opening duration, while a vision system, based on identifying a trihedron of colours, provides continuous feedback on the position of the end-effector. To address the challenge of modelling these robots, especially given the limitations of existing theoretical models –methods like the Piecewise Constant Curvature (PCC), which are adequate for hyper-redundant robots may lack precision in soft manipulators [20] and parameters for simulations based on the Finite Elements Method (FEM) are difficult to adjust–, an open-loop control system has been developed. This system relies on an experimentally constructed table that correlates valve opening times with the corresponding final positions of the manipulator. This empirical approach allows for reasonably accurate modelling of both the direct and inverse kinematics of the robot, even in the absence of precise theoretical models. The paper is structured as follows: Section 2 presents the main characteristics and working principles of the existing soft pneumatic arms, Section 3 details PAUL design and manufacturing process, highlighting the various modifications that had to be made iteratively and also addressing the construction of the pneumatic actuation bench, Section 4 describes the open loop control system and the steps that had to be taken to get there: the configuration of the robot hardware, the implementation of the vision system and the generation of the data table. The test carried out are commented in Section 5, and finally, Section 6 draws the conclusion. This paper is available on arxiv under CC BY-NC-SA 4.0 DEED license. This paper is available on arxiv under CC BY-NC-SA 4.0 DEED license. available on arxiv

Meet PAUL: A Soft Robot That Moves with Air Pressure

Authors:
(1) Mohammad Shushtari, Department of Mechanical and Mechatronics Engineering, University of Waterloo (smshushtari@uwaterloo.ca);
(2) Julia Foellmer, Mechanics and Ocean Engineering Department, Hamburg University of Technology (julia.foellmer@tuhh.de);
(3) Sanjay Krishna Gouda, Department of Mechanical and Mechatronics Engineering, University of Waterloo and Toronto Rehabilitation Institute (KITE), University Health Network (arash.arami@uwaterloo.ca). Table of Links Abstract and 1 Introduction 2 Results 2.1 Initial Processed Data for a Representative Participant 2.2 Overall Performance Analysis 2.3 Interaction Portrait Analysis 2.4 Individual Adaptation Strategy 3 Discussion 3.1 Human Adaptation 3.2 Importance of IP Analysis 4 Conclusion 5 Methods 5.1 Feedforward Control Strategies 5.2 Experimental Setup 5.3 Experimental Protocol 5.4 Data Analysis Declarations Appendix A Complementary Example Data Appendix B Comparison with Natural Walking References 5.1 Feedforward Control Strategies This section describes three controllers tested in our study. 5.1.1 Time-Based Torque Controller Fig. 8A depicts the block diagram of the Time-Based Torque Controller (TBC). This controller utilizes lookup tables to determine the desired joint torques uE by considering both the gait phase (ϕ(t) and the estimated gait speed (v). To construct the lookup table, measurements of exoskeleton joint torques were taken at different speeds while a participant walked with the exoskeleton governed by a high-gain PD controller. The participant was asked to exert the minimum voluntary effort during walking. The joint trajectories were controlled based on reference trajectories derived from the participant’s walking without the exoskeleton. The input gait phase to the lookup table was obtained by dividing the stride length, calculated using the exoskeleton joint angles (q), by the stride time updated at each heel strike. For this controller, the gait phase (ϕ(t)) was generated based on the desired gait speed, following the formula ϕ(t) = mod(t, T), where T represents the average measured stride time when the participant walked without the exoskeleton at the desired gait speed. For more detailed information about the construction of the lookup table and the gait speed estimator, refer to [26]. 5.1.2 Hybrid Torque Controller Fig. 8B presents the block diagram of the Hybrid Torque Controller (HTC), which combines the torque outputs of two distinct controllers [26]: the Kinematic State Dependent Controller (KSC) and the Gait Phase Dependent Controller (GPC). The KSC incorporates an Artificial Neural Network (ANN) that calculates the required biological torque for the user based on the kinematic measurements of the exoskeleton [27]. On the other hand, the GPC adopts the same structure as the TBC mentioned earlier, however, instead of relying on a time-based gait phase, it utilizes a real-time estimation of the gait phase derived from the kinematic measurements [28]. The outputs of these two controllers are linearly combined in the HTC: uE = wuKSC + (1−w)uGP C , where w represents the weight assigned to the KSC output. 5.1.3 Adaptive Model-based Torque Control The Adaptive Model-based Torque Control (AMTC) depicted in Fig. 8C, leverages the estimated dynamics of the exoskeleton to generate joint torques for control. According to [29], the interaction between the Indego exoskeleton and the human in the sagittal plane can be described by the following dynamical model: This paper is available on arxiv under CC BY-NC-ND 4.0 DEED license. Authors: (1) Mohammad Shushtari, Department of Mechanical and Mechatronics Engineering, University of Waterloo (smshushtari@uwaterloo.ca); (2) Julia Foellmer, Mechanics and Ocean Engineering Department, Hamburg University of Technology (julia.foellmer@tuhh.de); (3) Sanjay Krishna Gouda, Department of Mechanical and Mechatronics Engineering, University of Waterloo and Toronto Rehabilitation Institute (KITE), University Health Network (arash.arami@uwaterloo.ca). Authors: Authors: (1) Mohammad Shushtari, Department of Mechanical and Mechatronics Engineering, University of Waterloo (smshushtari@uwaterloo.ca); (2) Julia Foellmer, Mechanics and Ocean Engineering Department, Hamburg University of Technology (julia.foellmer@tuhh.de); (3) Sanjay Krishna Gouda, Department of Mechanical and Mechatronics Engineering, University of Waterloo and Toronto Rehabilitation Institute (KITE), University Health Network (arash.arami@uwaterloo.ca). Table of Links Abstract and 1 Introduction Abstract and 1 Introduction 2 Results 2.1 Initial Processed Data for a Representative Participant 2.1 Initial Processed Data for a Representative Participant 2.2 Overall Performance Analysis 2.2 Overall Performance Analysis 2.3 Interaction Portrait Analysis 2.3 Interaction Portrait Analysis 2.4 Individual Adaptation Strategy 2.4 Individual Adaptation Strategy 3 Discussion 3.1 Human Adaptation 3.1 Human Adaptation 3.2 Importance of IP Analysis 3.2 Importance of IP Analysis 4 Conclusion 4 Conclusion 5 Methods 5.1 Feedforward Control Strategies 5.1 Feedforward Control Strategies 5.2 Experimental Setup 5.2 Experimental Setup 5.3 Experimental Protocol 5.3 Experimental Protocol 5.4 Data Analysis 5.4 Data Analysis Declarations Declarations Appendix A Complementary Example Data Appendix A Complementary Example Data Appendix B Comparison with Natural Walking Appendix B Comparison with Natural Walking References References 5.1 Feedforward Control Strategies This section describes three controllers tested in our study. 5.1.1 Time-Based Torque Controller Fig. 8A depicts the block diagram of the Time-Based Torque Controller (TBC). This controller utilizes lookup tables to determine the desired joint torques uE by considering both the gait phase (ϕ(t) and the estimated gait speed (v). To construct the lookup table, measurements of exoskeleton joint torques were taken at different speeds while a participant walked with the exoskeleton governed by a high-gain PD controller. The participant was asked to exert the minimum voluntary effort during walking. The joint trajectories were controlled based on reference trajectories derived from the participant’s walking without the exoskeleton. The input gait phase to the lookup table was obtained by dividing the stride length, calculated using the exoskeleton joint angles (q), by the stride time updated at each heel strike. For this controller, the gait phase (ϕ(t)) was generated based on the desired gait speed, following the formula ϕ(t) = mod(t, T), where T represents the average measured stride time when the participant walked without the exoskeleton at the desired gait speed. For more detailed information about the construction of the lookup table and the gait speed estimator, refer to [26]. 5.1.2 Hybrid Torque Controller Fig. 8B presents the block diagram of the Hybrid Torque Controller (HTC), which combines the torque outputs of two distinct controllers [26]: the Kinematic State Dependent Controller (KSC) and the Gait Phase Dependent Controller (GPC). The KSC incorporates an Artificial Neural Network (ANN) that calculates the required biological torque for the user based on the kinematic measurements of the exoskeleton [27]. On the other hand, the GPC adopts the same structure as the TBC mentioned earlier, however, instead of relying on a time-based gait phase, it utilizes a real-time estimation of the gait phase derived from the kinematic measurements [28]. The outputs of these two controllers are linearly combined in the HTC: uE = wuKSC + (1−w)uGP C , where w represents the weight assigned to the KSC output. 5.1.3 Adaptive Model-based Torque Control The Adaptive Model-based Torque Control (AMTC) depicted in Fig. 8C, leverages the estimated dynamics of the exoskeleton to generate joint torques for control. According to [29], the interaction between the Indego exoskeleton and the human in the sagittal plane can be described by the following dynamical model: This paper is available on arxiv under CC BY-NC-ND 4.0 DEED license. This paper is available on arxiv under CC BY-NC-ND 4.0 DEED license. available on arxiv

What’s the Best Way to Control an Exoskeleton?

Authors:
(1) Mohammad Shushtari, Department of Mechanical and Mechatronics Engineering, University of Waterloo (smshushtari@uwaterloo.ca);
(2) Julia Foellmer, Mechanics and Ocean Engineering Department, Hamburg University of Technology (julia.foellmer@tuhh.de);
(3) Sanjay Krishna Gouda, Department of Mechanical and Mechatronics Engineering, University of Waterloo and Toronto Rehabilitation Institute (KITE), University Health Network (arash.arami@uwaterloo.ca). Table of Links Abstract and 1 Introduction 2 Results 2.1 Initial Processed Data for a Representative Participant 2.2 Overall Performance Analysis 2.3 Interaction Portrait Analysis 2.4 Individual Adaptation Strategy 3 Discussion 3.1 Human Adaptation 3.2 Importance of IP Analysis 4 Conclusion 5 Methods 5.1 Feedforward Control Strategies 5.2 Experimental Setup 5.3 Experimental Protocol 5.4 Data Analysis Declarations Appendix A Complementary Example Data Appendix B Comparison with Natural Walking References Abstract Human-robot physical interaction contains crucial information for optimizing user experience, enhancing robot performance, and objectively assessing user adaptation. This study introduces a new method to evaluate human-robot co-adaptation in lower limb exoskeletons by analyzing muscle activity and interaction torque as a two-dimensional random variable. We introduce the Interaction Portrait (IP), which visualizes this variable’s distribution in polar coordinates. We applied this metric to compare a recent torque controller (HTC) based on kinematic state feedback and a novel feedforward controller (AMTC) with online learning, proposed herein, against a time-based controller (TBC) during treadmill walking at varying speeds. Compared to TBC, both HTC and AMTC significantly lower users’ normalized oxygen uptake, suggesting enhanced user-exoskeleton coordination. IP analysis reveals this improvement stems from two distinct coadaptation strategies, unidentifiable by traditional muscle activity or interaction torque analyses alone. HTC encourages users to yield control to the exoskeleton, decreasing muscular effort but increasing interaction torque, as the exoskeleton compensates for user dynamics. Conversely, AMTC promotes user engagement through increased muscular effort and reduced interaction torques, aligning it more closely with rehabilitation and gait training applications. IP phase evolution provides insight into each user’s interaction strategy development, showcasing IP analysis’s potential in comparing and designing novel controllers to optimize human-robot interaction in wearable robots. Keywords: Exoskeleton, Physical Interaction, Control 1 Introduction Assistive and rehabilitation robotics are gaining increasing attention as they deliver a more substantial dose of exercise to users, enhancing their functionality and quality of life while reducing the workload of physical therapists [1, 2]. Despite recent advancements, including human-in-the-loop optimization to improve exoskeleton assistance [3–6], these robotic systems still lack the sophistication to automatically fine-tune the level of support required for each individual user effectively [7, 8]. This personalized touch, instinctive for physical therapists in traditional therapy sessions, remains a challenge for robots. The challenge arises because, although separate performance indicators like metabolic cost [9, 10], muscle activation [11], interaction forces [12], comfort [13], cognitive load [14], and user preference [15] are utilized, the lack of a unified metric that fully encapsulates the nuances of human-robot physical interactions obstructs the precise adjustment and customization of lower limb exoskeleton support [16]. Therefore, this task is often delegated to adaptive controllers with implicit considerations to control the human-exoskeleton physical interaction. The control of human-exoskeleton interaction plays a key role in optimizing the user experience and performance of lower limb exoskeletons for rehabilitation as well as power augmentation applications [17]. In power augmentation scenarios, the user retains full autonomy, and the exoskeleton follows user commands directly or indirectly by interpreting their intended motion. In case of disagreement between the user and the exoskeleton, the exoskeleton must relinquish control in favor of the user [18, 19]. However, in the context of rehabilitation and assistive exoskeletons, human-exoskeleton interaction control is more challenging due to two primary factors. First, the user-performed motion is not always reliable due to musculoskeletal or motor impairments [20] which may undermine the quality of decoded intention solely based on user-robot physical interaction. Second, the exoskeleton should encourage the user to maximize their engagement in motion when possible and assist or correct when the user is unable to perform the motion correctly [21, 22]. Consequently, the exoskeleton must seamlessly transition between the leader and follower roles [23]. To determine the appropriate control strategy for human augmentation and rehabilitation applications, it is crucial to understand human-exoskeleton adaptation as an indicator of how individuals respond to specific exoskeleton control strategies concerning shared motion control [24]. In power augmentation, the ideal scenario involves users adapting to a strategy in which they contribute primarily by guiding the motion, without physical exertion [5]. The exoskeleton takes the responsibility of moving the human body by applying interaction torques or forces to the human body, as demonstrated by reduced muscle activity or metabolic rates [4]. Conversely, in rehabilitation, users must often be guided to increase their muscle activity and actively engage in motion control [25]. The human-exoskeleton interaction torques exhibit a dual behavior in this context. When the user performs the motion correctly, the exoskeleton must transparently follow the user, resulting in zero interaction torques [12]. However, when motion correction is required, the exoskeleton controller should intervene. This intervention creates a conflict necessitating an increase in the interaction torque to rectify the motion. Neither muscular effort nor interaction torques alone can discern the aforementioned conditions. For example, an increase in muscular effort may stem from human-exoskeleton disagreement [20], while it can also signify that the human user is engaged in walking and relies on their motor capacity rather than on exoskeleton assistance. Therefore, to compare different controllers in such cases, interaction torque needs to be considered alongside muscular effort. A low level of interaction torque coupled with higher muscular effort suggests no physical disagreement, indicating that the exoskeleton is following the user and the user is walking with minimal assistance. Otherwise, a higher level of interaction torque along with high muscular effort indicates that the user and exoskeleton do not share the same desired motion patterns, and they are fighting for control [23]. Therefore, determining the suitability of a controller for either power augmentation or rehabilitation applications necessitates co-analysis of muscular effort and interaction torque. This paper is available on arxiv under CC BY-NC-ND 4.0 DEED license. Authors: (1) Mohammad Shushtari, Department of Mechanical and Mechatronics Engineering, University of Waterloo (smshushtari@uwaterloo.ca); (2) Julia Foellmer, Mechanics and Ocean Engineering Department, Hamburg University of Technology (julia.foellmer@tuhh.de); (3) Sanjay Krishna Gouda, Department of Mechanical and Mechatronics Engineering, University of Waterloo and Toronto Rehabilitation Institute (KITE), University Health Network (arash.arami@uwaterloo.ca). Authors: Authors: (1) Mohammad Shushtari, Department of Mechanical and Mechatronics Engineering, University of Waterloo (smshushtari@uwaterloo.ca); (2) Julia Foellmer, Mechanics and Ocean Engineering Department, Hamburg University of Technology (julia.foellmer@tuhh.de); (3) Sanjay Krishna Gouda, Department of Mechanical and Mechatronics Engineering, University of Waterloo and Toronto Rehabilitation Institute (KITE), University Health Network (arash.arami@uwaterloo.ca). Table of Links Abstract and 1 Introduction Abstract and 1 Introduction 2 Results 2.1 Initial Processed Data for a Representative Participant 2.1 Initial Processed Data for a Representative Participant 2.2 Overall Performance Analysis 2.2 Overall Performance Analysis 2.3 Interaction Portrait Analysis 2.3 Interaction Portrait Analysis 2.4 Individual Adaptation Strategy 2.4 Individual Adaptation Strategy 3 Discussion 3.1 Human Adaptation 3.1 Human Adaptation 3.2 Importance of IP Analysis 3.2 Importance of IP Analysis 4 Conclusion 4 Conclusion 5 Methods 5.1 Feedforward Control Strategies 5.1 Feedforward Control Strategies 5.2 Experimental Setup 5.2 Experimental Setup 5.3 Experimental Protocol 5.3 Experimental Protocol 5.4 Data Analysis 5.4 Data Analysis Declarations Declarations Appendix A Complementary Example Data Appendix A Complementary Example Data Appendix B Comparison with Natural Walking Appendix B Comparison with Natural Walking References References Abstract Human-robot physical interaction contains crucial information for optimizing user experience, enhancing robot performance, and objectively assessing user adaptation. This study introduces a new method to evaluate human-robot co-adaptation in lower limb exoskeletons by analyzing muscle activity and interaction torque as a two-dimensional random variable. We introduce the Interaction Portrait (IP), which visualizes this variable’s distribution in polar coordinates. We applied this metric to compare a recent torque controller (HTC) based on kinematic state feedback and a novel feedforward controller (AMTC) with online learning, proposed herein, against a time-based controller (TBC) during treadmill walking at varying speeds. Compared to TBC, both HTC and AMTC significantly lower users’ normalized oxygen uptake, suggesting enhanced user-exoskeleton coordination. IP analysis reveals this improvement stems from two distinct coadaptation strategies, unidentifiable by traditional muscle activity or interaction torque analyses alone. HTC encourages users to yield control to the exoskeleton, decreasing muscular effort but increasing interaction torque, as the exoskeleton compensates for user dynamics. Conversely, AMTC promotes user engagement through increased muscular effort and reduced interaction torques, aligning it more closely with rehabilitation and gait training applications. IP phase evolution provides insight into each user’s interaction strategy development, showcasing IP analysis’s potential in comparing and designing novel controllers to optimize human-robot interaction in wearable robots. Keywords : Exoskeleton, Physical Interaction, Control Keywords 1 Introduction Assistive and rehabilitation robotics are gaining increasing attention as they deliver a more substantial dose of exercise to users, enhancing their functionality and quality of life while reducing the workload of physical therapists [1, 2]. Despite recent advancements, including human-in-the-loop optimization to improve exoskeleton assistance [3–6], these robotic systems still lack the sophistication to automatically fine-tune the level of support required for each individual user effectively [7, 8]. This personalized touch, instinctive for physical therapists in traditional therapy sessions, remains a challenge for robots. The challenge arises because, although separate performance indicators like metabolic cost [9, 10], muscle activation [11], interaction forces [12], comfort [13], cognitive load [14], and user preference [15] are utilized, the lack of a unified metric that fully encapsulates the nuances of human-robot physical interactions obstructs the precise adjustment and customization of lower limb exoskeleton support [16]. Therefore, this task is often delegated to adaptive controllers with implicit considerations to control the human-exoskeleton physical interaction. The control of human-exoskeleton interaction plays a key role in optimizing the user experience and performance of lower limb exoskeletons for rehabilitation as well as power augmentation applications [17]. In power augmentation scenarios, the user retains full autonomy, and the exoskeleton follows user commands directly or indirectly by interpreting their intended motion. In case of disagreement between the user and the exoskeleton, the exoskeleton must relinquish control in favor of the user [18, 19]. However, in the context of rehabilitation and assistive exoskeletons, human-exoskeleton interaction control is more challenging due to two primary factors. First, the user-performed motion is not always reliable due to musculoskeletal or motor impairments [20] which may undermine the quality of decoded intention solely based on user-robot physical interaction. Second, the exoskeleton should encourage the user to maximize their engagement in motion when possible and assist or correct when the user is unable to perform the motion correctly [21, 22]. Consequently, the exoskeleton must seamlessly transition between the leader and follower roles [23]. To determine the appropriate control strategy for human augmentation and rehabilitation applications, it is crucial to understand human-exoskeleton adaptation as an indicator of how individuals respond to specific exoskeleton control strategies concerning shared motion control [24]. In power augmentation, the ideal scenario involves users adapting to a strategy in which they contribute primarily by guiding the motion, without physical exertion [5]. The exoskeleton takes the responsibility of moving the human body by applying interaction torques or forces to the human body, as demonstrated by reduced muscle activity or metabolic rates [4]. Conversely, in rehabilitation, users must often be guided to increase their muscle activity and actively engage in motion control [25]. The human-exoskeleton interaction torques exhibit a dual behavior in this context. When the user performs the motion correctly, the exoskeleton must transparently follow the user, resulting in zero interaction torques [12]. However, when motion correction is required, the exoskeleton controller should intervene. This intervention creates a conflict necessitating an increase in the interaction torque to rectify the motion. Neither muscular effort nor interaction torques alone can discern the aforementioned conditions. For example, an increase in muscular effort may stem from human-exoskeleton disagreement [20], while it can also signify that the human user is engaged in walking and relies on their motor capacity rather than on exoskeleton assistance. Therefore, to compare different controllers in such cases, interaction torque needs to be considered alongside muscular effort. A low level of interaction torque coupled with higher muscular effort suggests no physical disagreement, indicating that the exoskeleton is following the user and the user is walking with minimal assistance. Otherwise, a higher level of interaction torque along with high muscular effort indicates that the user and exoskeleton do not share the same desired motion patterns, and they are fighting for control [23]. Therefore, determining the suitability of a controller for either power augmentation or rehabilitation applications necessitates co-analysis of muscular effort and interaction torque. This paper is available on arxiv under CC BY-NC-ND 4.0 DEED license. This paper is available on arxiv under CC BY-NC-ND 4.0 DEED license. available on arxiv

New Study Shows Exoskeletons Now Adapt to You, Not the Other Way Around

አዲስ ጥናት Exoskeletons አሁን ከእርስዎ ጋር የሚስማሙ እንጂ በተቃራኒው እንዳልሆነ ያሳያል

Yeni Tədqiqat Ekzoskeletlərin İndi Əksinə Yox, Sizə Uyğunlaşdığını Göstərir

Ny undersøgelse viser, at eksoskeletter nu tilpasser sig dig, ikke omvendt

Neue Studie zeigt, dass sich Exoskelette jetzt an Sie anpassen, nicht umgekehrt

Un nuevo estudio demuestra que los exoesqueletos ahora se adaptan a ti, no al revés

מחקר חדש מראה כי השלדים החיצוניים מסתגלים אליך כעת, לא להיפך

Un nuovo studio dimostra che ora gli esoscheletri si adattano a te, non il contrario

新しい研究によると、外骨格は人間に適応しており、その逆ではない

Utafiti Mpya Unaonyesha Mifupa ya Mifupa Sasa Inabadilika Kwako, Sio Njia Nyingine Karibu

Yeni Çalışma, Dış İskeletlerin Artık Size Uyum Sağladığını, Tam Tersinin Olmadığını Gösteriyor

Dyondzo Leyintshwa Yi Kombisa Exoskeletons Sweswi Ti Tlwaelana Na Wena, Hayi Hi Ndlela Yin’wana

新的研究表明，外骨骼现在可以适应你，而不是你适应外骨骼

Advancing the Detection of Ultralight Vector Dark Matter through Novel Analytical Strategies

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