In this thesis, solutions to the first two of three phases associated with on-orbit debris removal are proposed. The first phase concerns the development of optimal space robot manipulator deployment manoeuvres which ensure zero-attitude displacement by the end of the trajectory. Three common pseudospectral optimal control tools are used to develop the trajectories, and the optimality of each solution is assessed using well-established validation techniques. The second phase addresses the compliant capture of a cooperative target using a nonlinear disturbance observer coupled with an impedance controller, and the observer is shown to be asymptotically stable for the case of a free-flying space robot. The performance of the techniques proposed for each phase are first verified in simulation, then through an experimental validation campaign using Carleton University's Spacecraft Robotics and Control Laboratory.