Time-Optimal Path Following for Robotic Manipulation of Loosely Placed Objects: Modeling and Experiment

Abstract

A consistent method is presented for solving the so-called general waiter problem, which resembles the general task of manipulating several objects that are loosely placed on a robot, rather than grasped or fixed otherwise. The waiter problem consists of moving a tray (mounted at the end-effector of a robot) with a number of cups, from one pose to another as fast as possible such that the cups do not slide at any time. The geometric path of the tray motion is prescribed while the attitude of the tray must vary. The basis for any optimization and realtime control is a reliable dynamic model of the robot. Therefore a parameter identification is performed using optimized persistent excitation trajectories. The optimization problem is solved with a multiple shooting method which determines the robot trajectory. For the considered wrist-partitioned robot, the motion is described by the joint coordinates of the translation part and the angles describing the orientation of the tray. This combination of joint and task space coordinates is beneficial for solving the optimal control problem (convergence is increased). The optimization accounts for the technical limitations of the robot as well as the limiting friction of the cups. Experimental results with 4 cups for a time-optimal motion are shown. A crucial aspect is the use of a model-based control strategy, along with the identified parameters.