Real-time Coupled Centroidal Motion and Footstep Planning for Biped Robots

TL;DR

This paper introduces a fast algorithm for real-time centroidal motion and footstep planning in bipedal robots, enabling quick and automatic gait discovery through a novel dynamic environment representation.

Contribution

The paper presents a novel formulation using $l_1$-norm minimization and quadratic programming to significantly accelerate footstep and motion planning for bipeds.

Findings

Achieves 10x faster planning than existing methods

Successfully plans in 142 ms for a 2 s horizon with multiple surfaces

Demonstrates versatility across various simulated environments

Abstract

This paper presents an algorithm that finds a centroidal motion and footstep plan for a Spring-Loaded Inverted Pendulum (SLIP)-like bipedal robot model substantially faster than real-time. This is achieved with a novel representation of the dynamic footstep planning problem, where each point in the environment is considered a potential foothold that can apply a force to the center of mass to keep it on a desired trajectory. For a biped, up to two such footholds per time step must be selected, and we approximate this cardinality constraint with an iteratively reweighted $l_1$-norm minimization. Along with a linearizing approximation of an angular momentum constraint, this results in a quadratic program can be solved for a contact schedule and center of mass trajectory with automatic gait discovery. A 2 s planning horizon with 13 time steps and 20 surfaces available at each time is solved in 142 ms, roughly ten times faster than comparable existing methods in the literature. We demonstrate the versatility of this program in a variety of simulated environments.