State-of-the-art approaches to footstep planning assume reduced-order dynamics when solving the combinatorial problem of selecting contact surfaces in real time. However, in exchange for computational efficiency, these approaches ignore joint torque limits and limb dynamics. In this work, we address these limitations by presenting a topology-based approach that enables model predictive control (MPC) to simultaneously plan full-body motions, torque commands, footstep placements, and contact surfaces in real time. To determine if a robot's foot is inside a contact surface, we borrow the winding number concept from topology. We then use this winding number and potential field to create a contact-surface penalty function. By using this penalty function, MPC can select a contact surface from all candidate surfaces in the vicinity and determine footstep placements within it. We demonstrate the benefits of our approach by showing the impact of considering full-body dynamics, which includes joint torque limits and limb dynamics, on the selection of footstep placements and contact surfaces. Furthermore, we validate the feasibility of deploying our topology-based approach in an MPC scheme and explore its potential capabilities through a series of experimental and simulation trials.

翻译：最先进的落脚点规划方法在实时求解接触面组合选择问题时，通常假设降阶动力学模型。然而，为换取计算效率，这类方法忽略了关节力矩限制与肢体动力学。本文针对这些局限，提出一种基于拓扑的方法，使模型预测控制（MPC）能够同时实时规划全身运动、力矩指令、落脚点位置及接触面选择。为判定机器人足部是否位于接触面内，我们借用了拓扑学中的缠绕数概念，并利用该缠绕数与势场构建接触面惩罚函数。通过该惩罚函数，MPC可从邻近所有候选接触面中选择目标表面，并确定其内部的落脚点位置。我们通过展示考虑包含关节力矩限制与肢体动力学的全身动力学对落脚点与接触面选择的影响，论证了本方法的优势。此外，通过系列实验与仿真试验，我们验证了将所提拓扑方法部署于MPC框架的可行性，并探索了其潜在能力。