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.