Sagittal SLIP-anchored task space control for a monopode robot traversing irregular terrain

Abstract

As a well-explored template that captures the essential dynamical behaviors of legged locomotion on sagittal plane, the spring-loaded inverted pendulum (SLIP) model has been extensively employed in both biomechanical study and robotics research. Aiming at fully leveraging the merits of the SLIP model to generate the adaptive trajectories of the center of mass (CoM) with maneuverability, this study presents a novel two-layered sagittal SLIP-anchored (SSA) task space control for a monopode robot to deal with terrain irregularity. This work begins with an analytical investigation of sagittal SLIP dynamics by deriving an approximate solution with satisfactory apex prediction accuracy, and a two-layered SSA task space controller is subsequently developed for the monopode robot. The higher layer employs an analytical approximate representation of the sagittal SLIP model to form a deadbeat controller, which generates an adaptive reference trajectory for the CoM. The lower layer enforces the monopode robot to reproduce a generated CoM movement by using a task space controller to transfer the reference CoM commands into joint torques of the multi-degree of freedom monopode robot. Consequently, an adaptive hopping behavior is exhibited by the robot when traversing irregular terrain. Simulation results have demonstrated the effectiveness of the proposed method.

Keywords

legged robots / spring-loaded inverted pendulum / task space control / apex return map / deadbeat control / irregular terrain negotiation

References

[1] Blickhan R, Full R J. Similarity in multilegged locomotion: Bouncing like a monopde. Journal of Comparative Physiology, 1993, 173: 509–517

[2] Hubicki C, Grimes J, Jones M, ATRIAS: Design and validation of a tether-free 3D-capable spring-mass bipedal robot. International Journal of Robotics Research, 2016, 35(12): 1497–1521

[3] Sreenath K, Park H, Poulakakis I, A compliant hybrid zero dynamics controller for stable, efficient and fast bipedal walking on MABEL. International Journal of Robotics Research, 2011, 30(9): 1170–1193

[4] Haldane D W, Yim J K, Fearing R S. Repetitive extreme-acceleration (14-g) spatial jumping with Salto-1P. In: Proceedings of 2017 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). Vancouver: IEEE, 2017, 3345–3351

[5] Seok S, Wang A, Otten D, Actuator design for high force proprioceptive control in fast legged locomotion. In: Proceedings of 2012 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). Vilamoura: IEEE, 2012, 1970–1975

[6] Farley C, Glasheen J, McMahon T. Running springs: Speed and animal size. Journal of Experimental Biology, 1993, 185: 71–86

[7] Blickhan R. The spring-mass model for running and hopping. Journal of Biomechanics, 1989, 22(11–12): 1217–1227

[8] Schwind W J, Koditschek D E. Approximating the stance map of a 2-DOF monoped runner. Journal of Nonlinear Science, 2000, 10(5): 533–568

[9] Ghigliazza R M, Altendorfer R, Holmes P, A simply stabilized running model. SIAM Review, 2005, 47(3): 519–549

[10] Geyer H, Seyfarth A, Blickhan R. Spring-mass running: Simple approximate solution and application to gait stability. Journal of Theoretical Biology, 2005, 232(3): 315–328

[11] ArslanÖ, Saranli U, MorgülÖ. Approximate stance map of the spring mass hopper with gravity correction for nonsymmetric locomotions. In: Proceedings of 2009 IEEE International Conference on Robotics and Automation (ICRA). Kobe: IEEE, 2009, 2388–2393

[12] Shahbazi M, Babuška R, Lopes G A D. Unified modeling and control of walking and running on the spring-loaded inverted pendulum. IEEE Transactions on Robotics, 2016, 32(5): 1178–1195

[13] Yu H, Li M, Wang P, Approximate perturbation stance map of the slip runner and application to locomotion control. Journal of Bionics Engineering, 2012, 9(4): 411–422

[14] Hutter M, Remy C D, Höpflinger A, SLIP running with an articulated robotic leg. In: Proceedings of 2010 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). Taipei: IEEE, 2010, 4934–4939

[15] Piovan G, Byl K. Approximation and control of the SLIP model dynamics via partial feedback linearization and two-element leg actuation strategy. IEEE Transactions on Robotics, 2016, 32(2): 399–412

[16] Seyfarth A, Geyer H, Herr H. Swing-leg retraction: A simple control model for stable running. Journal of Experimental Biology, 2003, 206(15): 2547–2555

[17] Karseen J G D, Haberland M, Wisse M, The optimal swing-leg retraction rate for running. In: Proceedings of 2011 IEEE International Conference on Robotics and Automation (ICRA). Shanghai: IEEE, 2011, 4000–4006

[18] Yu J, Hong D, Haberland M. Energetic efficiency of a compositional controller on a monoped with an articulated leg and SLIP dynamics. In: Proceedings of 2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). Madrid: IEEE, 2018, 2221–2228

[19] Rustchmann M, Satzinger B, Byl M, Nonlinear model predictive control for rough-terrain robot hopping. In: Proceedings of 2012 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). Vilamoura: IEEE, 2012, 1859–1864

[20] Garofalo O C, Albu-Schäffer A. Walking control of fully actuated robots based on the Bipedal SLIP model. In: Proceedings of 2012 International Conference on Robotics and Automation (ICRA). Saint Paul: IEEE, 2012, 1456–1463

[21] Wensing P M, Orin D E. High-speed humanoid running through control with a 3D-SLIP model. In: Proceedings of 2013 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). Tokyo: IEEE, 2013, 5134–5140

[22] Wensing P M, Orin D E. 3D-SLIP steering for high-speed humanoid turns. In: Proceedings of 2014 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). Chicago: IEEE, 2014, 4008–4013

[23] Ernst M, Geyer H, Blickhan R. Extension and customization of self-stability control in compliant legged systems. Bioinspiration & Biomimetics, 2012, 7(4): 046002

[24] Khatib O. A unified approach for motion and force control of robot manipulators: The operational space formulation. IEEE Journal on Robotics and Automation, 1987, 3(1): 43–53

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 51605115), State Key Laboratory of Robotics and System (Self-Planned Task No. SKLRS201719A), Heilongjiang Postdoctoral Financial Assistance (Grant No. LBH-Z16083), and Natural Science Foundation of Heilongjiang Province (Grant No. QC2017052).

Open Access

This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.ƒThe images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.ƒTo view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

RIGHTS & PERMISSIONS

2020 The Author(s) 2020. This article is published with open access at link.springer.com and journal.hep.com.cn