Complex dexterous manipulations require switching between prehensile and non-prehensile grasps, and sliding and pivoting the object against the environment. This paper presents a manipulation planner that is able to reason about diverse changes of contacts to discover such plans. It implements a hybrid approach that performs contact-implicit trajectory optimization for pivoting and sliding manipulation primitives and sampling-based planning to change between manipulation primitives and target object poses. The optimization method, simultaneous trajectory optimization and contact selection (STOCS), introduces an infinite programming framework to dynamically select from contact points and support forces between the object and environment during a manipulation primitive. To sequence manipulation primitives, a sampling-based tree-growing planner uses STOCS to construct a manipulation tree. We show that by using a powerful trajectory optimizer, the proposed planner can discover multi-modal manipulation trajectories involving grasping, sliding, and pivoting within a few dozen samples. The resulting trajectories are verified to enable a 6 DoF manipulator to manipulate physical objects successfully.

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