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

2026-03-03

AI Summary

This work addresses the inefficiency caused by discretization in bipedal robot gait planning and the computational intractability of mixed-integer programming (MIP) for real-time applications. The authors propose a continuous A* search framework that, for the first time, integrates a continuous convex representation of kinematically feasible reachability directly into the search process, augmented with a heuristic cost function derived from the Expanding Polytope Algorithm (EPA). By circumventing the information loss inherent in traditional discretization, the method efficiently plans contact sequences of up to 30 steps within 125 milliseconds—achieving a 100-fold speedup over discrete A* and outperforming commercial MIP solvers. This approach substantially enhances both the real-time performance and scalability of gait planning for bipedal locomotion.

Technology Category

• Planning, Routing, and Scheduling: Mixed Discrete/Continuous Planning
• Search and Optimization: Mixed Discrete/Continuous Search
• Intelligent Robots: Motion and Path Planning

Application Category

• Search and Retrieval-Augmented AI: Agentic search
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

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.

Problem

• footstep planning
• continuous reachability
• real-time planning
• biped locomotion
• combinatorial search

Innovation

• continuous A*
• reachability constraints
• convex formulation
• footstep planning
• biped locomotion