Solving Footstep Planning as a Feasibility Problem Using L1-Norm Minimization

One challenge of legged locomotion on uneven terrains is to deal with both the discrete problem selecting a contact surface for each footstep and continuous placing selected surface. Consequently, planning can be addressed Mixed Integer Program (MIP), an elegant but computationally-demanding method, which make it unsuitable online planning. We reformulate MIP into cardinality problem, then approximate as computationally efficient l1-norm minimisation, called SL1M. Moreover, we improve performance convergence SL1M by combining sampling-based root trajectory planner prune irrelevant candidates. Our tests humanoid Talos in four representative scenarios show that always converges faster than MIP. For when combinatorial complexity small (< 10 surfaces per step), at least two times no need pruning. In more complex cases, up 100 help pruning also computation time. The versatility framework shown additional quadruped robot ANYmal.