We present a reformulation of a contact-implicit optimization (CIO) approach
that computes optimal trajectories for rigid-body systems in contact-rich
settings. A hard-contact model is assumed, and the unilateral constraints are
imposed in the form of complementarity conditions. Newton's impact law is
adopted for enhanced physical correctness. The optimal control problem is
formulated as a multi-staged program through a multiple-shooting scheme. This
problem structure is exploited within the FORCES Pro framework to retrieve
optimal motion plans, contact sequences and control inputs with increased
computational efficiency. We investigate our method on a variety of dynamic
object manipulation tasks, performed by a six degrees of freedom robot. The
dynamic feasibility of the optimal trajectories, as well as the repeatability
and accuracy of the task-satisfaction are verified through simulations and real
hardware experiments on one of the manipulation problems.

本文介绍了一种接触隐式优化方法，利用硬接触模型和互补条件描述单向约束，通过多段程序和多重拍摄机制求解最优控制问题，提高了运动规划、接触顺序和控制输入的计算效率，并通过机器人的多个动态物体操纵任务验证了其优化轨迹的动态可行性，任务完成精度和可重复性。