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

2025-03-05

AI Summary

Real-time adaptive locomotion planning for quadrupedal robots on dynamic, unknown terrain faces two key challenges: insufficient safety and generality in foothold selection, and prohibitively high computational cost in modeling complex terrain and optimizing long-horizon trajectories. Method: This paper proposes a novel framework integrating symbolic-level reactive synthesis with physically feasible gait optimization. It introduces a symbolic repair mechanism to mitigate dynamic infeasibility, a hierarchical state management architecture to reduce search space complexity, and a closed-loop collaborative paradigm comprising offline synthesis, online mixed-integer convex programming (MICP) optimization, and runtime repair. Results: Simulation evaluations demonstrate autonomous discovery of missing locomotion skills—e.g., on scattered stone steps and exposed rebar—under safety-critical conditions. The approach achieves low response latency, significantly reduces MICP invocation frequency, and guarantees controller correctness by construction.

Technology Category

• Planning, Routing, and Scheduling: Replanning and Plan Repair
• Intelligent Robots: Motion and Path Planning
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Search and Retrieval-Augmented AI: Agentic search
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

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.

Problem

• Develops a framework for quadrupedal locomotion on dynamic terrains.
• Combines reactive synthesis and MICP for safe, feasible footstep planning.
• Enables real-time adaptation and repair for unforeseen terrain challenges.

Innovation

• Reactive synthesis for correct-by-construction controllers
• Mixed-integer convex programming for footstep planning
• Symbolic repair to handle dynamic infeasibility