让四足机器人在未知地形上实时自适应行走，兼顾安全与效率。
Physically-Feasible Reactive Synthesis for Terrain-Adaptive Locomotion
- 符号化控制器结合混合整数凸规划，实现动态步态规划。
- 仅在必要时求解优化问题，降低计算负担。
- 适合需要高鲁棒性的野外机器人或救援场景。
我们提出一种集成式规划框架，用于四足机器人在动态变化、未预知地形上的运动控制。现有方法通常依赖启发式规则进行实时落脚点选择，限制了鲁棒性与适应性；或依赖计算量大的轨迹优化，难以应对复杂地形和长时程规划。本方法结合反应式合成生成正确构造的符号级控制器，并利用混合整数凸规划（MICP）在每次符号转换期间实现动态且物理可行的步态规划。为减少对昂贵MICP求解的依赖，并处理因物理不可行而可能违反的约束，我们引入符号修复机制，仅生成必要的符号转换。执行过程中，基于实际地形数据的实时MICP重规划，结合运行时符号修复与延迟感知协调，实现了离线合成与在线操作的无缝衔接。通过大量仿真与硬件实验，验证了该框架在识别缺失运动技能及应对安全关键环境（如散乱石块、钢筋障碍）中的有效性。
原文摘要 · Abstract (English)
We present an integrated planning framework for quadrupedal locomotion over dynamically changing, unforeseen terrains. Existing methods often depend on heuristics for real-time foothold selection-limiting robustness and adaptability-or rely on computationally intensive trajectory optimization across complex terrains and long horizons. In contrast, our approach combines reactive synthesis for generating correct-by-construction symbolic-level controllers with mixed-integer convex programming (MICP) for dynamic and physically feasible footstep planning during each symbolic transition. To reduce the reliance on costly MICP solves and accommodate specifications that may be violated due to physical infeasibility, we adopt a symbolic repair mechanism that selectively generates only the required symbolic transitions. During execution, real-time MICP replanning based on actual terrain data, combined with runtime symbolic repair and delay-aware coordination, enables seamless bridging between offline synthesis and online operation. Through extensive simulation and hardware experiments, we validate the framework's ability to identify missing locomotion skills and respond effectively in safety-critical environments, including scattered stepping stones and rebar scenarios.
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