Optimal motion coordination of two robots—a polynomial parameterization approach to trajectory resolution

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Abstract
A novel approach is presented for the optimal coordination of two robots performing continuous‐path manufacturing tasks. Two types of operations are considered: contact operations, such as deburring, which require the tool to maintain contact with the workpiece during the operation execution, or non‐contact operations, such as arc‐welding, where the tool moves relative to the workpiece without contact. In both cases, the required tool‐path is specified with respect to the workpiece. A task is performed by mounting the tool on a robot, while a second robot grips the workpiece; the two robots are then coordinated to move simultaneously relative to one another so that the tool follows its prescribed trajectory at a constant speed relative to the workpiece, and provides sufficient contact force in the case of contact operations. The original tool‐trajectory is thus resolved into a pair of conjugate trajectories, specified in task space relative to an inertial frame, describing the motion of the two robots. In cases where the two robots form a kinematically redundant system, the trajectory resolution process can yield an infinity of conjugate‐trajectory pairs corresponding to a given original tool‐trajectory, of which one pair may be chosen based on a specific choice of cost function. This article presents a technique whereby the robot's conjugate trajectories are parameterized using polynomial functions. A method is then developed for optimizing the robot's motion by selecting the optimal pair of conjugate trajectories. The proposed optimal trajectory‐resolution technique is further enhanced by coupling it to a procedure for selecting the optimal relative placement of the two robots, resulting in the best achievable solution. This method of coordinating two robots yields lower cycle‐time values than the corresponding single‐robot operation, as well as reduces the need for complex jigs and fixtures. Numerical simulations are presented to illustrate the proposed technique. © 1994 John Wiley & Sons, Inc.

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