A non-periodic planning and control framework of dynamic legged locomotion

This study proposes an integrated planning and control framework for achieving three-dimensional robust and dynamic legged locomotion over uneven terrain. The proposed framework is composed of three hierarchical layers. The high-level layer is a state-space motion planner designing highly dynamic locomotion behaviors based on a reduced-order robot model. This motion planner incorporates two robust bundles, named as invariant and recoverability bundles, which quantify analytical state-space deviations for robust planning design. The low-level layer is a model-based trajectory tracking controller capable of robustly realizing the planned locomotion behaviors. This controller is synthesized based on full-order hybrid dynamic modeling, model-based state feedback control, and Lyapunov stability analysis. The planning and control layers are concatenated by a middle-level trajectory generator that produces nominal behaviors for a full-order robot model. The proposed framework is validated through flat and uneven terrain walking simulations of a three-dimensional bipedal robot.

[1]  Ye Zhao,et al.  A three dimensional foot placement planner for locomotion in very rough terrains , 2012, 2012 12th IEEE-RAS International Conference on Humanoid Robots (Humanoids 2012).

[2]  Arthur D Kuo,et al.  Energetics of actively powered locomotion using the simplest walking model. , 2002, Journal of biomechanical engineering.

[3]  Xingye Da,et al.  Combining trajectory optimization, supervised machine learning, and model structure for mitigating the curse of dimensionality in the control of bipedal robots , 2017, Int. J. Robotics Res..

[4]  Koushil Sreenath,et al.  Dynamic Walking on Randomly-Varying Discrete Terrain with One-step Preview , 2017, Robotics: Science and Systems.

[5]  David A. Winter,et al.  Human balance and posture control during standing and walking , 1995 .

[6]  Kazuhito Yokoi,et al.  Biped walking pattern generation by using preview control of zero-moment point , 2003, 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422).

[7]  Ye Zhao,et al.  Robust Bipedal Locomotion Based on a Hierarchical Control Structure , 2019, Robotica.

[8]  M. Tomizuka,et al.  High performance robust motion control of machine tools: an adaptive robust control approach and comparative experiments , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

[9]  Twan Koolen,et al.  Capturability-based analysis and control of legged locomotion, Part 1: Theory and application to three simple gait models , 2011, Int. J. Robotics Res..

[10]  J. Corriou Chapter 12 – Nonlinear Control , 2017 .

[11]  Twan Koolen,et al.  Capturability-based analysis and control of legged locomotion, Part 2: Application to M2V2, a lower-body humanoid , 2012, Int. J. Robotics Res..

[12]  Laura Menini,et al.  Robust Trajectory Tracking for a Class of Hybrid Systems: An Internal Model Principle Approach , 2012, IEEE Transactions on Automatic Control.

[13]  Franck Plestan,et al.  Asymptotically stable walking for biped robots: analysis via systems with impulse effects , 2001, IEEE Trans. Autom. Control..

[14]  Alin Albu-Schäffer,et al.  Three-Dimensional Bipedal Walking Control Based on Divergent Component of Motion , 2015, IEEE Transactions on Robotics.

[15]  Nathan van de Wouw,et al.  Sensitivity analysis of hybrid systems with state jumps with application to trajectory tracking , 2014, 53rd IEEE Conference on Decision and Control.

[16]  Alfred A. Rizzi,et al.  Physically Variable Compliance in Running , 2005 .

[17]  E. Feron,et al.  Robust hybrid control for autonomous vehicle motion planning , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[18]  Jonathan P. How,et al.  Robust motion planning using a maneuver automation with built-in uncertainties , 2003, Proceedings of the 2003 American Control Conference, 2003..

[19]  Timothy Bretl,et al.  Motion Planning for Legged Robots on Varied Terrain , 2008, Int. J. Robotics Res..

[20]  Ufuk Topcu,et al.  High-level planner synthesis for whole-body locomotion in unstructured environments , 2016, 2016 IEEE 55th Conference on Decision and Control (CDC).

[21]  Aaron D. Ames,et al.  Human-Inspired Control of Bipedal Walking Robots , 2014, IEEE Transactions on Automatic Control.

[22]  Anirudha Majumdar,et al.  Robust online motion planning with reachable sets , 2013 .

[23]  Evangelos Theodorou,et al.  Hierarchical optimization for Whole-Body Control of Wheeled Inverted Pendulum Humanoids , 2019, 2019 International Conference on Robotics and Automation (ICRA).

[24]  A. Tornambe,et al.  Asymptotic tracking of periodic trajectories for a simple mechanical system subject to nonsmooth impacts , 2001, IEEE Trans. Autom. Control..

[25]  V. Borkar,et al.  A unified framework for hybrid control: model and optimal control theory , 1998, IEEE Trans. Autom. Control..

[26]  Marko B. Popovic,et al.  Angular momentum in human walking , 2008, Journal of Experimental Biology.

[27]  Kris Hauser,et al.  Generalizations of the capture point to nonlinear center of mass paths and uneven terrain , 2015, 2015 IEEE-RAS 15th International Conference on Humanoid Robots (Humanoids).

[28]  Twan Koolen,et al.  Balance control using center of mass height variation: Limitations imposed by unilateral contact , 2016, 2016 IEEE-RAS 16th International Conference on Humanoid Robots (Humanoids).

[29]  M. Branicky Multiple Lyapunov functions and other analysis tools for switched and hybrid systems , 1998, IEEE Trans. Autom. Control..

[30]  Christine Chevallereau,et al.  Asymptotically Stable Walking of a Five-Link Underactuated 3-D Bipedal Robot , 2009, IEEE Transactions on Robotics.

[31]  Ye Zhao,et al.  Robust optimal planning and control of non-periodic bipedal locomotion with a centroidal momentum model , 2017, Int. J. Robotics Res..

[32]  Christopher G. Atkeson,et al.  Optimization‐based Full Body Control for the DARPA Robotics Challenge , 2015, J. Field Robotics.

[33]  Bin Yao,et al.  Straight-Line Contouring Control of Fully Actuated 3-D Bipedal Robotic Walking , 2018, 2018 Annual American Control Conference (ACC).

[34]  Russ Tedrake,et al.  Whole-body motion planning with centroidal dynamics and full kinematics , 2014, 2014 IEEE-RAS International Conference on Humanoid Robots.

[35]  Jessy W. Grizzle,et al.  Hybrid Invariant Manifolds in Systems With Impulse Effects With Application to Periodic Locomotion in Bipedal Robots , 2009, IEEE Transactions on Automatic Control.

[36]  Luca Zaccarian,et al.  Follow the Bouncing Ball: Global Results on Tracking and State Estimation With Impacts , 2013, IEEE Transactions on Automatic Control.

[37]  John Lygeros,et al.  Hybrid Systems: Modeling, Analysis and Control , 2008 .

[38]  Dennis W. Hong,et al.  Compliant locomotion using whole-body control and Divergent Component of Motion tracking , 2015, 2015 IEEE International Conference on Robotics and Automation (ICRA).

[39]  Bin Yao,et al.  Bipedal gait recharacterization and walking encoding generalization for stable dynamic walking , 2016, 2016 IEEE International Conference on Robotics and Automation (ICRA).

[40]  Christine Chevallereau,et al.  Models, feedback control, and open problems of 3D bipedal robotic walking , 2014, Autom..

[41]  Jonas Buchli,et al.  An efficient optimal planning and control framework for quadrupedal locomotion , 2016, 2017 IEEE International Conference on Robotics and Automation (ICRA).

[42]  Takeo Kanade,et al.  Footstep Planning for the Honda ASIMO Humanoid , 2005, Proceedings of the 2005 IEEE International Conference on Robotics and Automation.

[43]  F E Zajac,et al.  Human standing posture: multi-joint movement strategies based on biomechanical constraints. , 1993, Progress in brain research.

[44]  Daniel E. Koditschek,et al.  Hybrid zero dynamics of planar biped walkers , 2003, IEEE Trans. Autom. Control..

[45]  Nathan van de Wouw,et al.  Tracking Control for Hybrid Systems With State-Triggered Jumps , 2013, IEEE Transactions on Automatic Control.

[46]  Ufuk Topcu,et al.  Synthesis of Reactive Switching Protocols From Temporal Logic Specifications , 2013, IEEE Transactions on Automatic Control.