The principal objective of this thesis is the development of trajectory-planning optimization techniques for the coordinated motion of two robots. Both contact and non-contact manufacturing operations are considered. Contact operations require the tool to maintain contact with the workpiece during the operation execution. These operations include deburring. Non-contact operations, on the other hand, require the tool to move relative to the workpiece without coming in contact with it. These operations include arc-welding. 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 relative to the workpiece. The original tool-trajectory is thus resolved into a pair of conjugate trajectories, specified in task space relative to an inertial frame, describing the motions of the two robots. Since two robots often form a kinematically redundant system, the trajectory resolution yields an infinite number of solutions. An optimization can then be utilized to select the best solution based on a given choice of objective function.

Each robot in the two-robot system can be a single-arm manipulator or a two-arm cooperative robot. The motion is planned in an optimal manner, taking into consideration the dynamics of the robots and their payloads, capacity limits for the joint actuators, as well as contact forces in the case of contact operations. The motion planning, which also considers the optimal placement of the robots in the workcell, is facilitated in this thesis by developing a dynamic time-scaling technique, and adapting it to the problems at hand.

Two techniques are developed for the optimal trajectory resolution:​ the first technique is based on sub-dividing the tool-trajectory into a number of segments and then resolving the motion corresponding to each segment separately. This technique yields a near-optimal "local" solution. The second technique is based on the use of polynomial function parameterizations for the conjugate trajectories. The parameterization coefficients, which govern the entire motion, are then optimized yielding a global solution.