This thesis addresses the robotic manipulator end-effector trajectory control problem during unconstrained and constrained motion. A new controller is proposed for trajectory control during unconstrained motion that is robust to large parameter perturbations caused principally by unknown payloads and unknown joint viscous friction. The controller provides an asymptotic trajectory tracking capability for constant reference input signals in the presence of these dynamic parameter perturbations. If an accurate kinematic model of the manipulator is available, end-effector trajectory control may be accomplished with feedback of the manipulator joint variables, otherwise direct feedback of the position and orientation of the end-effector is necessary. In this thesis, the proposed robust controller is formulated with feedback from either the joint space or task space variables. It is demonstrated that arbitrarily close trajectory tracking is possible for constant reference input trajectories in the presence of large dynamic parameter perturbations. Analytic stability results for both joint space and task space formulations of the new controller are given, guaranteeing the closed-loop stability of the robotic system with this controller applied. Numerical simulation results verify controller performance.

The global asymptotic connective stability of a broad class of nonlinear control laws that approximately compensate for the manipulator nonlinear dynamics is demonstrated. In addition, the stability result is extended to a class of manipulators which, by their construction, exhibit weak coupling amongst the degrees of freedom.

Constrained motion trajectory control, important when the manipulator is in contact with a rigid surface, is considered. Using a dynamic formulation which incorporates the model of the constraint, the control of both the force arising from contact and the position, while in contact, is naturally expressed as an output regulation problem. A solution to this regulation problem is obtained through the use of descriptor variable theory. Considerable physical insight into the nature of the constrained dynamic model is obtained. With the proposed control applied to the robotic manipulator, asymptotic trajectory tracking of both contact force and position, while in contact with the surface, is possible, in the presence of dynamic parameter uncertainty, for constant reference input signals. Numerical simulation results verify the proposed control scheme for constrained manipulator tasks.