CASSR: Continuous A-Star Search through Reachability for real time footstep planning

TL;DR

CASSR introduces a continuous, reachability-based A* search framework for real-time footstep planning that significantly outperforms traditional methods in speed and reliability.

Contribution

The paper presents CASSR, a novel recursive convex formulation integrated with A* for efficient, continuous reachability-based footstep planning in biped robots.

Findings

Plans up to 30 footsteps in under 125 ms

Outperforms traditional discretised A* by up to 100x

Surpasses commercial MIP solver in speed and reliability

Abstract

Footstep planning involves a challenging combinatorial search. Traditional A* approaches require discretising reachability constraints, while Mixed-Integer Programming (MIP) supports continuous formulations but quickly becomes intractable, especially when rotations are included. We present CASSR, a novel framework that recursively propagates convex, continuous formulations of a robot's kinematic constraints within an A* search. Combined with a new cost-to-go heuristic based on the EPA algorithm, CASSR efficiently plans contact sequences of up to 30 footsteps in under 125 ms. Experiments on biped locomotion tasks demonstrate that CASSR outperforms traditional discretised A* by up to a factor of 100, while also surpassing a commercial MIP solver. These results show that CASSR enables fast, reliable, and real-time footstep planning for biped robots.