This chapter presents a motion planner that enables a humanoid robot to push an object to a desired location on a cluttered table. To reduce reliance on visual feedback, we restrict the robot to use a class of stable pushes that move the object predictably, such that a plan can be executed precisely with infrequent sensing. The motion of the robot-object system lies in a space with a multi-modal structure, where the motion switches between walking, reaching, and pushing modes. Each mode imposes mode-specific constraints (e.g., dynamic constraints, kinematic limits, obstacle avoidance) such that motion is restricted to a lower dimensional sub-space. The multi-modal planner must choose a discrete sequence of mode switches to reach the goal, while performing continuous motion planning to move between them. To address the problem of selecting modes, we present the Random-MMP algorithm, which randomly samples mode transitions to distribute a sparse number of modes across configuration space. The resulting planner solves problems that require several carefully chosen pushes in minutes. Results are presented in simulation and on the Honda ASIMO robot.
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