An industrialized On-Orbit Servicing (OOS) mission architecture is proposed in this thesis which signifies the role of space manipulators in performing OOS missions. This mission architecture summarizes a procedure for OOS mission design based on a series of multi-objective optimization problems. To enhance proximity operations, it is concluded that the existence of an output tracking control system for space manipulators is beneficial. This thesis develops an output tracking controller to control the end-effector pose of an N-link free-floating space manipulator, with non-zero momentum. We employ feedback linearization on the Lie algebra of the Special Euclidean group SE(3) to remove the nonlinear influence from the system’s dynamics and momentum in the controlled end-effector motion. Space manipulators are modelled as open-chain rigid multi-body systems, connected by either single or multi degree of freedom joints. The dynamics and kinematics of free-floating space manipulators are formulated on SE(3) using the exponential parameterization of screw motions. Multi-degree of freedom joints are modelled as the combination of the joints’ individual exponential screw motion mappings to describe their motions as homogeneous transformations. The free-floating systems’ equations of motion are obtained through an Euler-Lagrange derivation and decoupled into the base and manipulator motions. The conservation of linear and angular momentum is then considered as an affine nonholonomic constraint to the system, allowing for the dynamic reduction of a space manipulator system with conserved non-zero momentum. Due to the system’s free-floating nature, the equations of motion are restricted to the manipulator’s joint space which defines the region of controlled states.

Two control cases are considered in this thesis, the first involving control over the output’s linear motion and the second considering control over the end-effector pose. The first control case performs feedback linearization on ℝ³ where the resulting linear end-effector motion is controlled by a classical PID controller defined to impart a critically damped response in the error dynamics. For full pose control, feedback linearization is employed on se(3) for subsequent control using a modified feedforward, feedback PID control structure involving a coordinate-free pose error function. An associated transfer map is used to define the corresponding velocity error on the Lie algebra se(3). Using a Lyapunov candidate predicated on the total energy of the error dynamics, the developed full pose output tracking controller is proven to stabilize the end-effector pose to a feasible desired trajectory. The singularity-robust inverse derived from the damped least squares method is implemented in both the linear and full pose workspace controllers to avoid impractical joint torques in the region of kinematic/dynamic singularities.

A free-floating space manipulator simulation platform is developed in Python to analyze the performance of the linear and full pose output tracking controllers. The simulation is carefully structured to maximize computational efficiency such that a fast model propagation is achieved. A validation procedure is performed using an equivalent space manipulator model in Simscape to confirm the accuracy of the implemented kinematics and dynamics models in Python. In both control cases, the output responses are observed under trapezoidal trajectories involving systems containing zero and non-zero momentum. In the case of strictly linear output control, both a circular trajectory and a trajectory approaching a singular configuration are tested to demonstrate the controlled system’s dexterity and singularity accommodation ability, respectively. Model uncertainty is also introduced in the space manipulator’s mass to assess the controllers’ robustness. All testing scenarios demonstrate accurate trajectory followings, and successful mitigation of large control torques in the neighbourhood of singularities.