让机器人在不连续的踏脚点上自适应规划步态与步时，兼顾安全与动态稳定。
Perceptive Variable-Timing Footstep Planning for Humanoid Locomotion on Disconnected Footholds
- 基于深度图构建局部高程图，提取可踩区域并用二值变量约束
- 联合优化步位与步时，支持毫秒级求解，仿真中抗干扰能力强
- 适合复杂地形行走的类人机器人，尤其适用于有障碍物或滑地场景
许多真实行走场景包含障碍物和不安全地面（如湿滑或杂乱区域），留下一组不连续的可踩踏点，可建模为类似踏石的区域。我们提出一种机载感知的混合整数模型预测控制框架，联合规划足部落点与步长时间，利用步间发散运动分量（DCM）动力学。通过融合以我为中心的深度图像生成概率局部高程图，并从中提取凸形可踩区域。区域归属由混合整数二次规划（MIQP）中的二值变量强制实现。为在保持优化可解性的同时保证安全，我们在DCM空间嵌入捕获性边界：横向单步条件（防止腿交叉）与矢状面无限步边界（限制不稳定增长）。进一步在步内重规划，通过反向传播测量的瞬时DCM更新初始DCM，提升对模型失配和外部扰动的鲁棒性。在模拟中对Digit机器人在随机踏石场地上进行评估，包括外部推力。该规划器生成地形感知、动态一致的步序，具有自适应步时和毫秒级求解时间。
原文摘要 · Abstract (English)
Many real-world walking scenarios contain obstacles and unsafe ground patches (e.g., slippery or cluttered areas), leaving a disconnected set of admissible footholds that can be modeled as stepping-stone-like regions. We propose an onboard, perceptive mixed-integer model predictive control framework that jointly plans foot placement and step duration using step-to-step Divergent Component of Motion (DCM) dynamics. Ego-centric depth images are fused into a probabilistic local heightmap, from which we extract a union of convex steppable regions. Region membership is enforced with binary variables in a mixed-integer quadratic program (MIQP). To keep the optimization tractable while certifying safety, we embed capturability bounds in the DCM space: a lateral one-step condition (preventing leg crossing) and a sagittal infinite-step bound that limits unstable growth. We further re-plan within the step by back-propagating the measured instantaneous DCM to update the initial DCM, improving robustness to model mismatch and external disturbances. We evaluate the approach in simulation on Digit on randomized stepping-stone fields, including external pushes. The planner generates terrain-aware, dynamically consistent footstep sequences with adaptive timing and millisecond-level solve times.
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