SL1M: Sparse L1-norm Minimization for contact planning on uneven terrain

TL;DR

This paper introduces SL1M, a novel contact planning method for legged robots on uneven terrain that leverages L1-norm sparsity to significantly reduce computation time compared to traditional mixed-integer approaches.

Contribution

SL1M relaxes the contact planning problem into a linear feasibility program using L1-norm sparsity, enabling faster and potentially real-time planning for complex terrains.

Findings

SL1M is 50 to 100 times faster than mixed-integer methods.

The approach successfully plans 10-step sequences on uneven terrain.

Demonstrated on humanoid robots HRP-2 and Talos in simulation.

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.