Abstract
State-of-the-art approaches to footstep planning assume reduced-order dynamics when solving the combinatorial problem of selecting contact surfaces in real time. However, in exchange for computational efficiency, these approaches ignore limb dynamics and joint torque limits. In this work, we address these limitations by presenting a topology-based approach that enables model predictive control (MPC) to simultaneously plan full-body motions, torque commands, contact surfaces, and footstep placements in real time. To determine if a robot’s foot is inside a polygon, we borrow the winding number concept from topology. Specifically, we use winding number and electric potential to create a contact-surface penalty function that forms a harmonic field. Using our topology-based penalty function, MPC can then select a contact surface from all candidate surfaces in the vicinity and determine footstep placements within it. We highlight the benefits of our approach by showing the impact of considering full-body dynamics, which includes joint torque limits and limb dynamics, in the selection of footstep placements and contact surfaces. Additionally, we demonstrate the feasibility of deploying our topology-based approach in an MPC scheme through a series of experimental and simulation trials.
Turing affiliated authors