用序列凸优化解决接触隐式运动规划，无需复杂初始化也能稳定求解。
On the Surprising Robustness of Sequential Convex Optimization for Contact-Implicit Motion Planning
- 基于原始问题的序列凸规划，避开传统对偶算法陷阱。
- 在全零初始条件下仍能求解多个接触隐式规划问题。
- 适合机器人运动规划中需要自动发现新接触模式的场景。
接触隐式运动规划将接触顺序作为隐式互补约束嵌入，有望利用连续优化在线发现新的接触模式。然而，此类优化属于带互补约束的数学规划，不满足经典约束资格条件，导致主流数值求解器难以收敛。本文提出一种基于序列凸规划的鲁棒求解方法CRISP，其不采用传统的原-对偶框架，仅关注原始问题。CRISP在每轮迭代中求解一个带自适应信任域半径的凸二次规划，通过加权惩罚构造的代价函数评估收敛性。我们（i）给出了CRISP收敛至代价函数一阶驻点的充分条件；（ii）发布了具有通用非线性规划接口的高性能C++实现；（iii）展示了CRISP在使用简单初始化时的惊人鲁棒性。事实上，CRISP可在全零初始化下成功求解多个接触隐式规划问题。
原文摘要 · Abstract (English)
Contact-implicit motion planning-embedding contact sequencing as implicit complementarity constraints-holds the promise of leveraging continuous optimization to discover new contact patterns online. Nevertheless, the resulting optimization, being an instance of Mathematical Programming with Complementary Constraints, fails the classical constraint qualifications that are crucial for the convergence of popular numerical solvers. We present robust contact-implicit motion planning with sequential convex programming (CRISP), a solver that departs from the usual primal-dual algorithmic framework but instead only focuses on the primal problem. CRISP solves a convex quadratic program with an adaptive trust region radius at each iteration, and its convergence is evaluated by a merit function using weighted penalty. We (i) provide sufficient conditions on CRISP's convergence to first-order stationary points of the merit function; (ii) release a high-performance C++ implementation of CRISP with a generic nonlinear programming interface; and (iii) demonstrate CRISP's surprising robustness in solving contact-implicit planning with naive initialization. In fact, CRISP solves several contact-implicit problems with all-zero initialization.
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