Fast Inverse Kinematics for Soft Manipulators Using TRR Algorithm
DOI:
https://doi.org/10.17979/ja-cea.2025.46.12253Keywords:
Robotics technology, Robots manipulators, Robotics and mechatronics, Mechatronics, Design methodologies, Neural networksAbstract
When addressing the inverse kinematic model of soft robots, optimisation algorithms are the best option in terms of precision, ease of implementation and constraint management, but they do not usually achieve solutions in sufficiently short times. This article proposes the use of the TRR (Trust Region Reflective) algorithm, a minimisation methodology based on approximating the objective function in regions of variable size. The development is tested on a PETER robot simulator and, subsequently, on the manipulator itself, comparing it in both cases with a neural network trained to model the inverse kinematics of the robot. The average errors obtained in both situations are 0,22mm and 14mm for the TRR and 1,27mm and 15mm for the network. Although the accuracy of the tests on the real robot still has room for improvement, it demonstrates how the presented algorithm is capable of offering accurate solutions in low execution times.
References
Aristidou, A., Lasenby, J., 2011. FABRIK: A fast, iterative solver for the Inverse Kinematics problem. Graphical Models 73, 243–260. URL: http://dx.doi.org/10.1016/j.gmod.2011.05.003, doi:10.1016/j.gmod.2011.05.003.
Bern, J.M., Rus, D., 2021. Soft IK with stiffness control. 2021 IEEE 4th International Conference on Soft Robotics, RoboSoft 2021 , 465-471 doi:10.1109/RoboSoft51838.2021.9479195.
Bern, J.M., Schnider, Y., Banzet, P., Kumar, N., Coros, S., 2020. Soft Robot Control with a Learned Differentiable Model. 2020 3rd IEEE International Conference on Soft Robotics, RoboSoft 2020 , 417-423 doi:10.1109/RoboSoft48309.2020.9116011.
Bhalkikar, A., Lokesh, S., Ashwin, K.P., 2024. Kinematic models for Cabledriven Continuum Robots with multiple segments and varying cable offsets. Mechanism and Machine Theory 200, 105701.
Bianchi, D., Campinoti, G., Comitini, C., Laschi, C., Rizzo, A., Sabatini, A.M., Falotico, E., 2024. SoftSling: A Soft Robotic Arm Control Strategy to Throw Objects with Circular Run-ups. IEEE Robotics and Automation Letters PP, 1–8. doi:10.1109/LRA.2024.3442535.
Blanco, K., Navas, E., Rodriguez-Nieto, D., Emmi, L., Fernandez, R., 2024. Soft Bellow-Based 3D Printed Robot for in-Pipe Inspection Applications. 2024 7th Iberian Robotics Conference, ROBOT 2024 doi:10.1109/ROBOT61475.2024.10797416.
Branch, M.A., Coleman, T.F., Li, Y., 1999. A Subspace, Interior, and Conjugate Gradient Method for Large-Scale Bound-Constrained Minimization Problems. SIAM Journal on Scientific Computing 21, 1–23. URL: https://doi.org/10.1137/S1064827595289108, doi:10.1137/S1064827595289108.
Chiang, S.S., Yang, H., Skorina, E., Onal, C.D., 2021. SLInKi: State Lattice based Inverse Kinematics - A Fast, Accurate, and Flexible IK Solver for Soft Continuum Robot Manipulators, in: IEEE International Conference on Automation Science and Engineering, IEEE. pp. 1871–1877. doi:10.1109/CASE49439.2021.9551686.
García-Samartín, J.F., del Cerro, J., Barrientos, A., 2024a. Inverse kinematic modelling with shape control of a soft robot using genetic algorithms, in: Jornadas de Automática. URL: https://doi.org/10.17979/ja-cea.2024.45.10968, doi:10.17979/ja-cea.2024.45.10968.
García-Samartín, J.F., Charles, M., del Cerro, J., Barrientos, A., 2024b. PETER : a Soft Pneumatic Manipulator with High Resistance and Load Capacity, in: 2024 7th Iberian Robotics Conference (ROBOT), Madrid. pp. 1–6. doi:10.1109/ROBOT61475.2024.10796857.
García-Samartín, J.F., Molina-Gómez, R., Barrientos, A., 2024c. Model-Free Control of a Soft Pneumatic Segment. Biomimetics 9. doi:https://doi.org/10.3390/biomimetics9030127.
García-Samartín, J.F., Rieker, A., Barrientos, A., 2024d. Design, Manufacturing, and Open-Loop Control of a Soft Pneumatic Arm. Actuators 13. URL: https://www.mdpi.com/2076-0825/13/1/36, doi:10.3390/act13010036.
Kaviri, M., Fesharaki, A.J., Sadeghnejad, S., 2023. Soft robotics in medical applications: State of the art, challenges, and recent advances, in: Boubaker, O. (Ed.), Medical and Healthcare Robotics. Academic Press. Medical Robots and Devices: New Developments and Advances. chapter 2, pp. 25–61. URL: https://www.sciencedirect.com/science/article/pii/B9780443184604000093, doi:https://doi.org/10.1016/B978-0-443-18460-4.00009-3.
Keyvanara, M., Goshtasbi, A., Kuling, I.A., 2023. A Geometric Approach towards Inverse Kinematics of Soft Extensible Pneumatic Actuators Intended for Trajectory Tracking. Sensors 23, 1–16. doi:10.3390/s23156882.
Liu, J., Song, Z., Lu, Y., Yang, H., Chen, X., Duo, Y., Chen, B., Kong, S., Shao, Z., Gong, Z., Wang, S., Ding, X., Yu, J., Wen, L., 2024. An Underwater Robotic System with a Soft Continuum Manipulator for Autonomous Aquatic Grasping. IEEE/ASME Transactions on Mechatronics 29, 1007–1018. doi:10.1109/TMECH.2023.3321054.
Martín, A., Barrientos, A., Del Cerro, J., 2018. The natural-CCD algorithm, a novel method to solve the inverse kinematics of hyper-redundant and soft robots. Soft Robotics 5, 242–257. doi:10.1089/soro.2017.0009.
Navas, E., Fernández, R., Sepúlveda, D., Armada, M., Gonzalez-De-santos, P., 2021. Soft grippers for automatic crop harvesting: A review. Sensors 21. doi:10.3390/s21082689.
Seleem, I.A., El-Hussieny, H., Ishii, H., 2023. Imitation-based Path Planning and Nonlinear Model Predictive Control of a Multi-Section Continuum Robots. Journal of Intelligent and Robotic Systems: Theory and Applications 108. doi:10.1007/s10846-023-01811-8.
Seyidoğlu, B., Rafsanjani, A., 2024. A textile origami snake robot for rectilinear locomotion. Device 2. doi:10.1016/j.device.2023.100226.
Shan, Y., Zhao, Y.,Wang, H., Dong, L., Pei, C., Jin, Z., Sun, Y., Liu, T., 2024. Variable stiffness soft robotic gripper: design, development, and prospects. Bioinspiration and Biomimetics 1. doi:10.1088/1748-3190/ad0b8c.
Sun, W., Akashi, N., Kuniyoshi, Y., Nakajima, K., 2022. Physics-Informed Recurrent Neural Networks for Soft Pneumatic Actuators. IEEE Robotics and Automation Letters 7, 6862–6869. doi:10.1109/LRA.2022.3178496.
Terrile, S., Miguelañez, J., Barrientos, A., 2021. A Soft Haptic Glove Actuated with Shape Memory Alloy and Flexible Stretch Sensors. Sensors 21. doi:10.3390/s21165278.
Thuruthel, T.G., Falotico, E., Renda, F., Laschi, C., 2019. Model-Based Reinforcement Learning for Closed-Loop Dynamic Control of Soft Robotic Manipulators. IEEE Transactions on Robotics 35, 127–134. doi:10.1109/TRO.2018.2878318.
Wagaa, N., Kallel, H., Mellouli, N., 2023. Analytical and deep learning approaches for solving the inverse kinematic problem of a high degrees of freedom robotic arm. Engineering Applications of Artificial Intelligence 123, 106301. URL: https://doi.org/10.1016/j.engappai.2023.106301, doi:10.1016/j.engappai.2023.106301.
Wan, Z., Sun, Y., Qin, Y., Skorina, E.H., Gasoto, R., Luo, M., Fu, J., Onal, C.D., 2023. Design, Analysis, and Real-Time Simulation of a 3D Soft Robotic Snake. Soft Robotics 10, 258–268. doi:10.1089/soro.2021.0144.
Wu, M., Zhang, Y., Wu, X., Li, Z., Chen, W., Hao, L., 2023. Reviewof Modeling and Control Methods of Soft Robots Based on Machine Learning. Chinese Control Conference, CCC 2023-July, 4318–4323. doi:10.23919/CCC58697.2023.10240787.
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Copyright (c) 2025 Jorge Francisco García Samartín, Mar Martín-Díaz, Jaime del Cerro, Antonio Barrientos
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