Gait Sequence Optimization of Quadruped Robot Locomotion

Abstract

Optimizing contact sequences for legged robots is critical for various locomotion tasks and effective disturbance adaptation. The discrete nature of this problem prevents differentiability and renders search-based algorithms essential for actively exploring gait sequences. This paper constructs a decision tree for the contact sequence backward in time via a backward gait tree (BGT). The approach employs a relaxed dynamics model to bound the cost-to-here, and enforces rigid contact when computing the cost-to-go, both resolved through a continuous Differential Dynamic Programming (DDP) solver. The framework uses a hybrid search algorithm combining depth-first and A*-search, using the lower bound from the BGT to identify promising gait sequences. When growing the search tree, the relaxed model can be projected to any contact mode for efficient warm starting. Implemented in a receding horizon manner, our method balances performance and computational speed, requiring roughly 25 DDP sub-problem evaluations per iteration. Simulations demonstrate that our approach generates emergent contact sequences that adapt well to speed changes and external disturbances.