ContactIPM：一种利用结构的接触隐式轨迹优化内点求解器
ContactIPM: A Structure-Exploiting Interior-Point Solver for Contact-Implicit Trajectory Optimization
AI总结：
本文提出ContactIPM，结合接触优化的结构利用与原始-对偶特性，在MPCC基准测试中部分场景速度优于CRISP、IMPACT，提升了接触隐式轨迹优化的求解性能。
AI中文摘要：
接触隐式轨迹优化无需指定接触序列，但会产生具有互补约束的数学规划（MPCCs），其退化特性对传统原始-对偶求解器构成挑战。现有接触专用方法提升了对该退化的鲁棒性，但未利用分段最优控制分解及原始-对偶一致性；而利用结构的最优控制求解器并非为互补约束设计。本文表明可在单一原始-对偶方法中结合这些能力。ContactIPM识别互补不等式对，通过障碍耦合弹性内点松弛嵌入它们，分段消除松弛变量与对偶变量，并用黎卡提递推求解简化的牛顿系统。固定多阶段MPCC恢复方案提供4次从朴素初始值的延续与重启尝试，终止由未松弛的物理互补残差控制。在匹配的基准条件与通用后求解接受准则下，将ContactIPM与两种接触专用MPCC求解器CRISP、IMPACT对比：在4个固定CRISP基准案例中，每个案例经20次配对计时重复，ContactIPM速度提升2.17至8.87倍，且在推箱（Push Box）与推T（Push-T）鲁棒性套件上成功率更高；相较IMPACT，在Push T上快2.96倍，在推车运输（Cart Transport）上快4.91倍，但在Push Box上慢4.46倍。在50次涵盖模型失配、测量噪声、初始位姿误差与状态重置的闭环Push Box滚动实验中，
英文摘要：
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,
