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.

翻译：接触隐式运动规划——将接触序列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，由此产生的优化问题作为带互补约束数学规划的一个实例，无法满足经典约束规范，而这些规范对于常用数值求解器的收敛至关重要。我们提出了基于序列凸规划的鲁棒接触隐式运动规划求解器CRISP，该求解器摒弃了传统的原-对偶算法框架，转而仅聚焦于原问题。CRISP在每次迭代中求解一个具有自适应信赖域半径的凸二次规划，其收敛性通过采用加权惩罚的效益函数进行评估。我们（i）给出了CRISP收敛至效益函数一阶稳定点的充分条件；（ii）发布了具有通用非线性规划接口的高性能C++版CRISP实现；（iii）展示了CRISP在采用朴素初始化时求解接触隐式规划问题的惊人鲁棒性。事实上，CRISP能够以全零初始化成功求解多个接触隐式问题。