Abstract

One of the main challenges of planning legged locomotion in complex environments is the combinatorial contact selection problem. Recent contributions propose to use integer variables to represent which contact surface is selected, and then to rely on modern mixed-integer (MI) optimization solvers to handle this combinatorial issue. To reduce the computational cost of MI, we exploit the sparsity properties of L1 norm minimization techniques to relax the contact planning problem into a feasibility linear program. Our approach accounts for kinematic reachability of the center of mass (COM) and of the contact effectors. We ensure the existence of a quasi-static COM trajectory by restricting our plan to quasi-flat contacts. For planning 10 steps with less than 10 potential contact surfaces for each phase, our approach is 50 to 100 times faster that its MI counterpart, which suggests potential applications for online contact re-planning. The method is demonstrated in simulation with the humanoid robots HRP-2 and Talos over various scenarios.


Bibtex

IEEE ICRA 2020:

@INPROCEEDINGS{9197371,
  author={S. {Tonneau} and D. {Song} and P. {Fernbach} and N. {Mansard} and M. {Taïx} and A. {Del Prete}},
  booktitle={2020 IEEE International Conference on Robotics and Automation (ICRA)},
  title={SL1M: Sparse L1-norm Minimization for contact planning on uneven terrain},
  year={2020},
  volume={},
  number={},
  pages={6604-6610},
  doi={10.1109/ICRA40945.2020.9197371}}

Extended version, “Solving Footstep Planning as a Feasibility Problem using L1-norm Minimization”:

@misc{song2020solving,
      title={Solving Footstep Planning as a Feasibility Problem using L1-norm Minimization},
      author={Daeun Song and Pierre Fernbach and Thomas Flayols and Andrea Del Prete and Nicolas Mansard and Steve Tonneau and Young J. Kim},
      year={2020},
      eprint={2011.09772},
      archivePrefix={arXiv},
      primaryClass={cs.RO}}