Nonprehensile Manipulation: a Trajectory-Planning Perspective

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Abstract
This paper discusses nonprehensile manipulation of an asymmetric object using a robotic manipulator from a motion planning point of view. Four different aspects of the problem will be analyzed: object stability, motion planning, manipulator control, and experimental validation. Specifically, via an analysis of marginal stability of an object resting on a moving tray, the work establishes the critical accelerations of the manipulator's end-effector, below which the object's stability is guaranteed. These critical accelerations guide the design of the end-effector's motion for successful nonprehensile manipulation of the object. In particular, we propose two methods to formulate polynomial asymmetric s-curve trajectories such that the end- effector completes its motion in minimum time. In one method, the trajectory is divided into segments whose time intervals are then computed via a recursive algorithm. In the other method, we formulate an optimization problem and design the minimum-time trajectory by balancing the trade-off between the travel time and actuator effort. A series of experiments with a robotic arm is designed to validate and compare these motion planning methods in the context of nonprehensile manipulation. In addition, the experimental results demonstrate the advantages of the asymmetric s-curve motion profiles over the traditional symmetric s-curves.

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