SL1M: Sparse L1-norm Minimization for contact planning on uneven terrain
This work addresses the computational bottleneck in contact planning for humanoid robots on uneven terrain, offering a faster solution that could enable online re-planning, though it is incremental as it builds on existing optimization methods.
The paper tackles the combinatorial contact selection problem in legged locomotion planning by relaxing it into a feasibility linear program using L1-norm minimization, achieving a 50 to 100 times speedup compared to mixed-integer optimization for planning 10 steps with under 10 potential contact surfaces per phase.
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.