Orbital debris in Earth orbit poses a threat to the future of spaceflight. To combat this issue, this thesis proposes a novel robotic mechanism for non-cooperative capture and active servicing missions on non-cooperative targets. Specifically, a tendon-driven manipulator designed to employ a synthetic gecko adhesive on the contact interface is proposed. Since the cable-sheath transmission mechanism is a non-linear time varying hysteretic system, two separate adaptive control strategies were compared against the uncontrolled and PID controlled performance of the closed-loop gripper. Specifically, an indirect control method (denoted AB controller in this work) and a direct L1 controller were employed. Both the simulations and experiments demonstrate that the adaptive controllers show better tracking performance of a joint trajectory over the PID and uncontrolled cases. The experimental results show that the L1 controller performs best under dynamic conditions, while the AB controller performs best in steady state.