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

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.

Multi-Fidelity Receding Horizon Planning for Multi-Contact Locomotion

“…In our approach, we pre-define the sequence of contact surfaces [44], [49] and the selection of gait pattern (i.e. the sequence in which the feet make and break contacts with the environment) [50].…”

Comparison of Position and Torque Whole-Body Control Schemes on the Humanoid Robot TALOS

“…The trajectories used in the tilted platforms and stairs simulations have been computed using the open-source framework multicontact-locomotion-planning [31]. Given the initial and final poses of the robot, the framework computes a reachability plan and a contacts sequence as in [32]. Then it optimizes the centroidal dynamics (see Section II) using two convex relaxations based on trust regions [33].…”

Learning to steer a locomotion contact planner

“…This category regroups work in which a sequence of discrete contacts can be given by the user [1], [15], retrieved from a database [16] or found using search algorithms or machine learning [4], [10], [17]- [21]. An alternative approach is to use continuous optimization instead of the discrete contact selection problem [22]- [24]. The second strategy is the "motion-before-contact" that first plans a guide path to follow (i.e.…”