Hostname: page-component-669899f699-rg895 Total loading time: 0 Render date: 2025-04-29T23:16:37.715Z Has data issue: false hasContentIssue false
  • English
  • Français

Dynamic modeling and simulation of a torque-controlled spatial quadruped robot

Published online by Cambridge University Press:  11 September 2024

Daniel Teixeira de Paula Open the ORCID record for Daniel Teixeira de Paula [Opens in a new window] ,
Eduardo Paciencia Godoy Open the ORCID record for Eduardo Paciencia Godoy [Opens in a new window]  and
Mauricio Becerra-Vargas Open the ORCID record for Mauricio Becerra-Vargas [Opens in a new window]
Daniel Teixeira de Paula*
Affiliation:
São Paulo State University (Unesp), Institute of Science and Technology, Sorocaba, São Paulo, Brasil
Eduardo Paciencia Godoy
Affiliation:
São Paulo State University (Unesp), Institute of Science and Technology, Sorocaba, São Paulo, Brasil
Mauricio Becerra-Vargas
Affiliation:
São Paulo State University (Unesp), Institute of Science and Technology, Sorocaba, São Paulo, Brasil
*
Corresponding author:Daniel Teixeira de Paula; Email: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Evolution has shown that legged locomotion is most adequate for tasks requiring versatile movement on land, allowing animals to traverse a wide variety of environments ranging from natural terrain to artificial, man-made landscapes with great ease. By employing well-designed control schemes, this ability could be replicated for legged robots, enabling them to be used in critical situations that still pose great danger to human integrity, such as search and rescue missions, inspection of hazardous areas, and even space exploration. This work characterizes the quadruped robot and contact dynamics that will compose our in-house simulator to be used for prototyping locomotion control schemes applied to quadruped robots. The proposed simulator computes the robot dynamics using the Recursive Newton-Euler and Composite-Rigid-Body algorithms with a few modifications to make certain aspects relevant for contact detection and control more easily accessible; furthermore, a compliant contact force method alongside stick-slip friction modeled the contact dynamics. To allow the robot to move, a simple PD-independent joint controller was implemented to track a desired leg trajectory. With the same robot and controller implemented using the MuJoCo simulation software, this work evaluates the proposed simulator by comparing characteristic locomotion signals such as the trunk pose and the ground reaction forces. Results showed similar behavior for both simulators, especially with regard to the contact detection, despite the significantly different contact models. Lastly, final remarks to enhance our simulator’s performance are suggested to be explored in future works.

Keywords

quadruped robotdynamic modellegged locomotioncontact dynamicsprototyping
Type
Research Article
Information
Robotica , Volume 42 , Issue 8 , August 2024 , pp. 2761 - 2780
Copyright
© The Author(s), 2024. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Featherstone, R.. Rigid Body Dynamics Algorithms (Springer, New York, NY, 2008).CrossRefGoogle Scholar
Bledt, G., Powell, M. J., Katz, B., Di Carlo, J., Wensing, P. M. and Kim, S., “MIT Cheetah 3: Design and Control of a Robust, Dynamic Quadruped Robot,” In: IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), (Madrid, Spain, IEEE, 2018) pp. 2245–2252.CrossRefGoogle Scholar
Di Carlo, J., Wensing, P. M., Katz, B., Bledt, G. and Kim, S., “Dynamic Locomotion in the MIT Cheetah 3 Through Convex Model-Predictive Control,” In: IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), (Madrid, Spain, IEEE, 2018) pp. 1–9.CrossRefGoogle Scholar
Grandia, R., Farshidian, F., Ranftl, R. and Hutter, M., “Feedback MPC for Torque-Controlled Legged Robots,” In: IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), (Macau, China, IEEE, 2019) pp. 4730–4737.CrossRefGoogle Scholar
Kim, D., Carlo, J. D., Katz, B., Bledt, G. and Kim, S., Highly dynamic quadruped locomotion via whole-body impulse control and model predictive control, (2019).Google Scholar
Mastalli, C., Havoutis, I., Focchi, M., Caldwell, D. G. and Semini, C., “Motion planning for quadrupedal locomotion: Coupled planning, terrain mapping, and whole-body control,” IEEE Trans Robot 36(6), 1635–1648 (2020).CrossRefGoogle Scholar
Minniti, M. V., Grandia, R., Farshidian, F. and Hutter, M., “Adaptive CLF-MPC with application to quadrupedal robots,” IEEE Robot Automa Lett 7(1), 565–572 (2022).CrossRefGoogle Scholar
Neunert, M., Stauble, M., Giftthaler, M., Bellicoso, C. D., Carius, J., Gehring, C., Hutter, M. and Buchli, J., “Whole-body nonlinear model predictive control through contacts for quadrupeds,” IEEE Robot Automa Lett 3(3), 1458–1465 (2018).CrossRefGoogle Scholar
Rathod, N., Bratta, A., Focchi, M., Zanon, M., Villarreal, O., Semini, C. and Bemporad, A., “Model predictive control with environment adaptation for legged locomotion,” IEEE Access 9, 145710–145727 (2021).CrossRefGoogle Scholar
Giftthaler, M., Neunert, M., Stäuble, M. and Buchli, J., “The Control Toolbox - An Open-Source C++ Library for Robotics, Optimal and Model Predictive Control,” In: IEEE International Conference on Simulation, Modeling, and Programming for Autonomous Robots (SIMPAR), (Brisbane, QLD, Australia, IEEE, 2018) pp. 123–129.CrossRefGoogle Scholar
Frigerio, M., Buchli, J. and Caldwell, D. G., “Code Generation of Algebraic Quantities for Robot Controllers,” In: IEEE/RSJ International Conference on Intelligent Robots and Systems, (Vilamoura-Algarve, Portugal, IEEE, 2012) pp. 2346–2351.CrossRefGoogle Scholar
Giftthaler, M., Neunert, M., Stäuble, M., Frigerio, M., Semini, C. and Buchli, J., “Automatic differentiation of rigid body dynamics for optimal control and estimation,” Adv Robotics 31(22), 1225–1237 (2017).CrossRefGoogle Scholar
Semini, C., Tsagarakis, N. G., Guglielmino, E., Focchi, M., Cannella, F. and Caldwell, D. G., “Design of HyQ: A hydraulically and electrically actuated quadruped robot,” Proceed Inst Mech Eng, Part I: J Syst Control Eng 225(6), 831–849 (2011).Google Scholar
Hutter, M., Gehring, C., Jud, D., Lauber, A., Bellicoso, C. D., Tsounis, V., Hwangbo, J., Bodie, K., Fankhauser, P., Bloesch, M., Diethelm, R., Bachmann, S., Melzer, A. and Hoepflinger, M., “ANYmal - A Highly Mobile and Dynamic Quadrupedal Robot,” In: IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), (Daejeon, Korea (South), IEEE, 2016) pp.38–44.CrossRefGoogle Scholar
Fahmi, S., Mastalli, C., Focchi, M. and Semini, C., “Passive whole-body control for quadruped robots: Experimental validation over challenging terrain,” IEEE Robot Automa Lett 4(3), 2553–2560 (2019).CrossRefGoogle Scholar
Katz, B., Carlo, J. D. and Kim, S., “Mini Cheetah: A Platform for Pushing the Limits of Dynamic Quadruped Control,” In: International Conference on Robotics and Automation (ICRA), (Montreal, QC, Canada, IEEE, 2019) pp.6295–6301.CrossRefGoogle Scholar
Felis, M. L., “RBDL: An efficient rigid-body dynamics library using recursive algorithms,” Auton Robot 41(2), 495–511 (2017).CrossRefGoogle Scholar
Todorov, E., Erez, T. and Tassa, Y., “MuJoCo: A Physics Engine for Model-Based Control,” In: IEEE/RSJ International Conference on Intelligent Robots and Systems, (Vilamoura-Algarve, Portugal, IEEE, 2012) pp. 5026–5033.CrossRefGoogle Scholar
Hwangbo, J., Lee, J. and Hutter, M., “Per-contact iteration method for solving contact dynamics,” IEEE Robot Automa Lett 3(2), 895–902 (2018).CrossRefGoogle Scholar
De Paula, D. T., Godoy, E. P. and Becerra-Vargas, M., “Towards Dynamic Quadruped Locomotion: Development of a CPG-driven Foot Trajectory Generator,” In: Proceedings of the 30th Mediterranean Conference on Control and Automation, (Vouliagmeni, Greece, IEEE, 2022) pp. 988–993.CrossRefGoogle Scholar
MIT Biomimetic Robotics Lab, Cheetah-software, (2019). https://github.com/mit-biomimetics/Cheetah-Software.Google Scholar