Safe 3D Bipedal Walking through Linear MPC with 3D Capturability

We propose a linear MPC scheme for online computation of reactive walking motions, necessary for fast interactions such as physical collaboration with humans or collision avoidance in crowds. Unlike other existing schemes, it provides fully adaptable height, adaptable step placement and complete kinematic and dynamic feasibility guarantees, making it possible to walk perfectly safely on a piecewise horizontal ground such as stairs. A linear formulation is proposed, based on efficiently bounding the nonlinear term introduced by vertical motion, considering two linear constraints instead of one nonlinear constraint. Balance and Passive Safety guarantees are secured by enforcing a 3D capturability constraint. Based on a comparison between CoM and CoP trajectories involving exponentials instead of polynomials, this capturability constraint involves a CoM motion stopping along a segment of line, always maintaining complete kinematic and dynamic feasibility.

[1]  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).

[2]  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..

[3]  Pierre-Brice Wieber,et al.  Safe navigation strategies for a biped robot walking in a crowd , 2016, 2016 IEEE-RAS 16th International Conference on Humanoid Robots (Humanoids).

[4]  Mitsuharu Morisawa,et al.  Humanoid robot HRP-4 - Humanoid robotics platform with lightweight and slim body , 2011, 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[5]  Matthias Althoff,et al.  Provably safe motion of mobile robots in human environments , 2017, 2017 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS).

[6]  Pierre-Brice Wieber,et al.  Strong recursive feasibility in model predictive control of biped walking , 2017, 2017 IEEE-RAS 17th International Conference on Humanoid Robotics (Humanoids).

[7]  Shuuji Kajita,et al.  Study of dynamic biped locomotion on rugged terrain-derivation and application of the linear inverted pendulum mode , 1991, Proceedings. 1991 IEEE International Conference on Robotics and Automation.

[8]  Pierre-Brice Wieber,et al.  A Newton method with always feasible iterates for Nonlinear Model Predictive Control of walking in a multi-contact situation , 2016, 2016 IEEE-RAS 16th International Conference on Humanoid Robots (Humanoids).

[9]  Russ Tedrake,et al.  Planning robust walking motion on uneven terrain via convex optimization , 2016, 2016 IEEE-RAS 16th International Conference on Humanoid Robots (Humanoids).

[10]  Pierre-Brice Wieber,et al.  Walking pattern generators designed for physical collaboration , 2016, 2016 IEEE International Conference on Robotics and Automation (ICRA).

[11]  Roland Siegwart,et al.  Towards Safe Vehicle Navigation in Dynamic Urban Scenarios , 2009 .

[12]  Scott Kuindersma,et al.  Modeling and Control of Legged Robots , 2016, Springer Handbook of Robotics, 2nd Ed..

[13]  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).

[14]  Giuseppe Oriolo,et al.  Humanoid Gait Generation on Uneven Ground using Intrinsically Stable MPC ⁎ , 2018, SyRoCo.

[15]  Nicolas Mansard,et al.  Zero Step Capturability for Legged Robots in Multicontact , 2018, IEEE Transactions on Robotics.

[16]  Alexander Leonessa,et al.  Model predictive control for dynamic footstep adjustment using the divergent component of motion , 2016, 2016 IEEE International Conference on Robotics and Automation (ICRA).

[17]  Pierre-Brice Wieber,et al.  A robust linear MPC approach to online generation of 3D biped walking motion , 2015, 2015 IEEE-RAS 15th International Conference on Humanoid Robots (Humanoids).

[18]  Alin Albu-Schäffer,et al.  Three-dimensional bipedal walking control using Divergent Component of Motion , 2013, 2013 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[19]  Adrien Escande,et al.  Capturability-Based Pattern Generation for Walking With Variable Height , 2018, IEEE Transactions on Robotics.

[20]  Alexander Herzog,et al.  A convex model of humanoid momentum dynamics for multi-contact motion generation , 2016, 2016 IEEE-RAS 16th International Conference on Humanoid Robots (Humanoids).