Perceptive Variable-Timing Footstep Planning for Humanoid Locomotion on Disconnected Footholds

Abstract

Walking over disconnected footholds requires selecting landing regions while adapting step timing to the robot's motion. We present a perceptive model predictive planner that combines discrete region selection, foot placement, and current-step duration in a mixed-integer quadratic program using step-to-step Divergent Component of Motion (DCM) dynamics. Onboard depth data are fused into a probabilistic heightmap in the stance foot frame. Convex steppable regions are extracted and shrunk by margins that increase with estimated height uncertainty. Linear constraints impose capturability-based bounds on DCM evolution and limit swing-foot retargeting using the remaining commanded swing time. Within-step replanning updates the initial DCM from measurements to respond to model mismatch and disturbances. We evaluate the framework on Digit in simulation over randomized footholds and on hardware over separated plates, with mean planner solve times of 11.4~ms and 4.0~ms, respectively.

arXiv comment8 pages, 6 figures, 1 table. Supplemental video at: https://xtificant.github.io/digit_fpp_pub/