Induction couplers exploit eddy-current effects to create force and torque on a target without mechanical contact. Nearly all spacecraft structures include conductive material, so induction couplers may be the closest realizable technology to science fiction's tractor beam: a device that generates contactless force on an uncooperative target. Contactless forces can potentially enable on-orbit servicing missions that are currently infeasible because they are too dangerous and expensive. On-oribt servicing enables tasks we take for granted on earth but are difficult in space like maintenence, repair, and disposal. Relative movement between two uncooperative spacecraft traditionally requires either mechanical grapplers or thrusters. Contactless actuators can act in the place of mechanical grapplers in many situations, reducing the risks associated with mechanical contact and sudden non-compliant dynamics coupling. Induction couplers reduce or eliminate the need for thrusters while maneuvering near a larger object - increasing lifetimes, reducing costs, and eliminating risks from plume impingement. Contactless actuation technology asks three major questions: • How do you model and characterize dynamic eddy-current interactions? • How can an inspector use induction couplers to move in six degrees of freedom? • How do you design an inspection system that can successfully control itself with induction couplers? This thesis describes solutions to each of these challenges, laying the groundwork for safe and practical on-orbit servicing.Induction couplers can produce millinewton actuation forces with a lower specific power than other contactless actuators. The inspector can move in six degrees of freedom by following trajectories composed of four motion primitives, each with two possible control laws. Finally, a new algorithm based on the idea of controllable volumes informs the inspector's physical layout so that it can maximize the use of its induction couplers.