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.

翻译：步态规划涉及一个具有挑战性的组合搜索问题。传统的A*方法需要对可达性约束进行离散化处理，而混合整数规划（MIP）虽然支持连续形式表述，但会迅速变得难以求解，尤其是在包含旋转时。我们提出了CASSR，这是一个新颖的框架，它在A*搜索中递归传播机器人运动学约束的凸连续形式表述。结合基于EPA算法的新型剩余代价启发函数，CASSR能在125毫秒内高效规划多达30步的接触序列。在双足运动任务上的实验表明，CASSR的性能优于传统离散化A*方法高达100倍，同时也超越了商业MIP求解器。这些结果表明，CASSR能够为双足机器人实现快速、可靠且实时的步态规划。