Trajectory optimization problems for legged robots are commonly formulated with fixed contact schedules. These multi-phase Hybrid Trajectory Optimization (HTO) methods result in locally optimal trajectories, but the result depends heavily upon the predefined contact mode sequence. Contact-Implicit Optimization (CIO) offers a potential solution to this issue by allowing the contact mode to be determined throughout the trajectory by the optimization solver. However, CIO suffers from long solve times and convergence issues. This work combines the benefits of these two methods into one algorithm: Staged Contact Optimization (SCO). SCO tightens constraints on contact in stages, eventually fixing them to allow robust and fast convergence to a feasible solution. Results on a planar biped and spatial quadruped demonstrate speed and optimality improvements over CIO and HTO. These properties make SCO well suited for offline trajectory generation or as an effective tool for exploring the dynamic capabilities of a robot.

翻译：腿部机器人的轨迹优化问题通常采用固定接触调度进行建模。此类多阶段混合轨迹优化方法虽能生成局部最优轨迹，但其结果高度依赖于预设的接触模式序列。接触隐式优化通过允许优化求解器在轨迹求解过程中自主确定接触模式，为这一问题提供了潜在解决方案。然而，该技术存在求解耗时长、收敛性欠佳等缺陷。本研究将上述两种方法的优势融合为单一算法：分段接触优化。该算法通过分阶段收紧接触约束，最终将接触模式固定，从而在保证鲁棒性的同时快速收敛至可行解。在平面双足机器人和空间四足机器人上的实验结果表明，相较于接触隐式优化与混合轨迹优化，本方法在求解速度和最优性方面均有显著提升。这些特性使分段接触优化既适用于离线轨迹生成，亦可作为探索机器人动力学能力的有效工具。