提出新算法提升接触隐式轨迹优化求解速度与鲁棒性
ContactIPM: A Structure-Exploiting Interior-Point Solver for Contact-Implicit Trajectory Optimization
- 结合内点法与最优控制结构，处理接触互补约束
- 比现有方法快2.17至8.87倍，尤其在推箱与推塔任务中表现更好
- 适合需要高可靠性的机器人运动规划场景
接触隐式轨迹优化无需预设接触序列，但会产生带有互补约束的数学规划问题（MPCC），其退化特性挑战传统原始-对偶求解器。现有接触专用方法虽增强对退化的鲁棒性，却未利用分阶段最优控制分解与原始-对偶一致性；而结构化最优控制求解器又未针对互补约束设计。本文展示可将这些能力融合于单一原始-对偶方法中。ContactIPM识别互补不等式对，通过屏障耦合弹性内部松弛嵌入，分阶段消除松弛变量与对偶变量，并使用Riccati递推求解约化牛顿系统。采用固定多阶段MPCC恢复调度，提供四次连续与重启尝试，从初始猜测开始；终止条件由未松弛的物理互补残差决定。在四个与CRISP匹配的基准案例上，接触隐式轨迹优化比较显示：20次配对重复测试中，ContactIPM速度提升2.17–8.87倍，且在推箱与推塔鲁棒性套件中成功率更高。与IMPACT对比，在推塔任务上快2.96倍，小车运输任务上快4.91倍，但在推箱任务上慢4.46倍。50次闭环推箱滚动测试覆盖模型失配、测量噪声、初始位姿误差与状态重置。
原文摘要 · Abstract (English)
Contact-implicit trajectory optimization avoids prescribing contact sequences, but yields mathematical programs with complementarity constraints (MPCCs) whose degeneracy challenges conventional primal--dual solvers. Existing contact-specific methods improve robustness to this degeneracy but do not leverage a stagewise optimal-control factorization and primal--dual consistency, while structure-exploiting optimal-control solvers are not designed for complementarity constraints. We show that these capabilities can be combined in a single primal--dual method. ContactIPM identifies complementary inequality pairs, embeds them through a barrier-coupled elastic interior relaxation, eliminates slack and dual variables stagewise, and solves the reduced Newton system using a Riccati recursion. A fixed multi-phase MPCC recovery schedule provides four continuation and restart attempts from naive initializations, while termination is gated by the unrelaxed physical complementarity residual. We compare ContactIPM with two contact-specific MPCC solvers, CRISP and IMPACT, using matched benchmark conditions and common post-solve acceptance criteria. On four fixed CRISP benchmark cases, ContactIPM is $2.17$--$8.87\times$ faster over 20 paired timing repetitions per case and achieves higher success on the Push Box and Push-T robustness suites. Against IMPACT, ContactIPM is \(2.96\times\) faster on Push T and \(4.91\times\) faster on Cart Transport, but \(4.46\times\) slower on Push Box. In 50 closed-loop Push Box rollouts spanning model mismatch, measurement noise, initial-pose errors, and state resets,
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