The present paper introduces a planning and control strategy for whole-arm manipulation of a slippery polygonal object. Randomized planning methods are first proposed in order to generate contact state transitions, which help not only to reduce the amount of calculation required, but also to handle a hybrid system composed of a continuous system and a discrete system, which has a large search space and complicated constraints. Second, a novel control strategy, which can switch manipulation modes among quasi-static, dynamic, and caging manipulation depending on the situation, is proposed. This strategy not only can cope with changes in the mechanics of the system caused by contact state transitions, but also can increase the manipulation feasibility and reliability. The validity of the proposed methods is verified through simulations and experiments
