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.

翻译：许多现实世界中的行走场景包含障碍物和不安全地面区域（例如湿滑或杂乱区域），仅留下可建模为类踏脚石区域的不连续允许立足点集合。我们提出一种机载感知式混合整数模型预测控制框架，该框架利用步间发散运动分量（DCM）动力学联合规划足部放置与步态时长。以自我为中心的深度图像被融合为概率化局部高度图，从中提取出凸可踏区域的并集。区域隶属关系通过混合整数二次规划（MIQP）中的二元变量进行约束。为在保证安全性的同时保持优化可解性，我们在DCM空间中嵌入可捕获性边界：侧向单步条件（防止腿部交叉）与限制不稳定增长的矢状面无限步边界。我们进一步通过反向传播测量的瞬时DCM来更新初始DCM，实现步态周期内的重规划，从而提升对模型失配和外部干扰的鲁棒性。我们在Digit仿真平台上通过随机踏脚石场地（含外部推力）评估该方法。该规划器能以毫秒级求解时间生成具有地形感知能力、动力学一致的自适应时序足步序列。