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This work investigates the problem of robotic arm control with the goal of achieving given performance requirements by solving for the optimal joint trajectories and corresponding controls for tasks, such as point-to-point positioning. The resulting optimal control problem is highly nonlinear and constrained due to the nonlinearities in the robotic arm dynamics and kinodynamic constraints including limits on joint velocities and actuator torques. This thesis illustrates the applicability of pseudospectral methods to solve the optimal path planning problem for a system of multi-link, multi-degree of freedom robotic arms. The optimal control problem is defined in standard form and solved using the software package DIDO. Pontryagin's Minimum Principle is used to verify that the proposed solution satisfies the necessary conditions for optimality. A particularly challenging aspect that is explored is the optimal motion of multiple arms conducting independent tasks with the risk of collision. Collision avoidance can be achieved by modeling appropriate path constraints. The processes for optimal trajectory planning are developed for a single two degree-of-freedom manipulator conducting point-to-point positioning and extended to include dual three degree-of-freedom manipulator maneuvers employing collision avoidance. The results demonstrate the suitability of pseudospectral techniques to solving the minimum time and minimum control maneuvers for robotic arms. The employment of collision avoidance techniques will facilitate continued research in autonomous robotic motion planning using optimal control criteria in multiple arm systems. http://archive.org/details/optimalpathplann109453687 Approved for public release; distribution is unlimited.