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One of the main challenges of planning legged locomotion in complexenvironments is the combinatorial contact selection problem. Recentcontributions propose to use integer variables to represent which contactsurface is selected, and then to rely on modern mixed-integer (MI) optimizationsolvers to handle this combinatorial issue. To reduce the computational cost ofMI, we exploit the sparsity properties of L1 norm minimization techniques torelax the contact planning problem into a feasibility linear program. Ourapproach accounts for kinematic reachability of the center of mass (COM) and ofthe contact effectors. We ensure the existence of a quasi-static COM trajectoryby restricting our plan to quasi-flat contacts. For planning 10 steps with lessthan 10 potential contact surfaces for each phase, our approach is 50 to 100times faster that its MI counterpart, which suggests potential applications foronline contact re-planning. The method is demonstrated in simulation with thehumanoid robots HRP-2 and Talos over various scenarios.

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