Footstep Planning for Slippery and Slanted Terrain Using Human-Inspired Models

Energy efficiency and robustness of locomotion to different terrain conditions are important problems for humanoid robots deployed in the real world. In this paper, we propose a footstep-planning algorithm for humanoids that is applicable to flat, slanted, and slippery terrain, which uses simple principles and representations gathered from human gait literature. The planner optimizes a center-of-mass (COM) mechanical work model subject to motion feasibility and ground friction constraints using a hybrid A∗ search and optimization approach. Footstep placements and orientations are discrete states searched with an A∗ algorithm, while other relevant parameters are computed through continuous optimization on state transitions. These parameters are also inspired by human gait literature and include footstep timing (double-support and swing time) and parameterized COM motion using knee flexion angle keypoints. The planner relies on work, the required coefficient of friction (RCOF), and feasibility models that we estimate in a physics simulation. We show through simulation experiments that the proposed planner leads to both low electrical energy consumption and human-like motion on a variety of scenarios. Using the planner, the robot automatically opts between avoiding or (slowly) traversing slippery patches depending on their size and friction, and it chooses energy-optimal stairs and climbing angles in slopes. The obtained motion is also consistent with observations found in human gait literature, such as human-like changes in RCOF, step length and double-support time on slippery terrain, and human-like curved walking on steep slopes. Finally, we compare COM work minimization with other choices of the objective function.