Physically-Feasible Reactive Synthesis for Terrain-Adaptive Locomotion via Trajectory Optimization and Symbolic Repair

We propose an integrated planning framework for quadrupedal locomotion over dynamically changing, unforeseen terrains. Existing approaches either rely on heuristics for instantaneous foothold selection--compromising safety and versatility--or solve expensive trajectory optimization problems with complex terrain features and long time horizons. In contrast, our framework leverages reactive synthesis to generate correct-by-construction controllers at the symbolic level, and mixed-integer convex programming (MICP) for dynamic and physically feasible footstep planning for each symbolic transition. We use a high-level manager to reduce the large state space in synthesis by incorporating local environment information, improving synthesis scalability. To handle specifications that cannot be met due to dynamic infeasibility, and to minimize costly MICP solves, we leverage a symbolic repair process to generate only necessary symbolic transitions. During online execution, re-running the MICP with real-world terrain data, along with runtime symbolic repair, bridges the gap between offline synthesis and online execution. We demonstrate, in simulation, our framework's capabilities to discover missing locomotion skills and react promptly in safety-critical environments, such as scattered stepping stones and rebars.