# Tutorial Review on Space Manipulators for Space Debris Mitigation
## 4 Space debris Mitigation
During capture, an active compliance control law is given by:  
\[e=\theta_{i}^{d}-\theta_{i}=-\frac{1}{I_{i}}\int\int(\tau_{i}-b_{i}\dot{\theta} _{i}-k_{i}\theta_{i})ddt^{\prime} \tag{5}\]  
where \(I_{i}=\) joint \(i\) inertia, \(\tau_{i}=\) measured joint torque, \(b_{i}=\) joint viscosity coefficient. It has been determined that for handling and stabilising upper stages during de-orbit, the appropriate clamping points are at the payload fairing adaptor ring, which is designed to tolerate clamping forces and torques [55]. Two or three manipulators permit distribution of grappling forces/torques equally around the ring. For example, the DLR arm can capture a 7-tonne satellite spinning at 4\({}^{\circ}\)/s without exceeding its maximum torque limit of 120 Nm. Post-capture detumbling can exploit the kinematic redundancy of the spacecraft-mounted manipulator [56]. Active de-orbiting of debris requires propulsive capabilities attached to the target to ensure disposal. Re-entry may be controlled or passive--controlled direct re-entry is more efficient than passive uncontrolled re-entry, but the latter is simpler. Controlled de-orbiting is essential to remove larger pieces of debris \(\sim\)500-1000 kg which could potentially survive re-entry. Nominally, this requires robotic attachment of a propulsion stage to the debris to de-orbit it. Contactless methods of disposing of debris include ion beam shepherding. This involves generating a beam of ions from two sets of ion engines along the same axis by pointing in opposite directions. The chaser directs one ion beam onto the debris to generate thrust on it. The reaction thrust on the chaser is cancelled by the other engine, generating an opposing thrust to maintain a constant distance to the debris. Solar concentrators have been proposed to deflect asteroids by inducing thrust from ablated material, a technique that may be adapted to active debris disposal [57] but requires dynamic stability. Electrodynamic propulsion offers a potentially propellantless option for debris transport [58]. A 1-5 km long conducting electrodynamic tether which mounts solar panels rotating at 6-8 times every orbit generates current which interacts with the Earth's magnetic field. Electrodynamic thrust is generated when current flows through a conductor in the Earth's geomagnetic field. The conductor must close the current loop through the ambient plasma by electron emission through hollow cathodes and electron collection to the bare conducting cable. The tether is attached to the debris and uses electrodynamic drag generated by Lorentz JxB forces to remove debris from low Earth orbit [59]. Lorenz forces allow it to manoeuvre by altering the current to match the orbit of the target to be captured by a robotic hand or net. ElectroDynamic Debris Eliminator (EDDE) uses a long conducting tether to manoeuvre in the Earth's magnetic field powered by solar arrays but consuming no propellant. Small nets at either end of the tether with solar arrays attached at the middle catch debris in the nets and release them at lower altitude to increase the rate of orbital decay. A dozen 100 kg electrodynamic debris eliminators (EDDE) mounted onto one launch adaptor ring can remove 80% of all 2 kg + objects in LEO (concentrating on 71-74\({}^{\circ}\), 81-83\({}^{\circ}\) and sun synchronous orbits) in 7 years (1000 tonnes in total). The electrodynamic tether linking the chaser and the target debris captured by a compliant grappling end effector at the end of the tether is a variation on the concept [60]. However, electrodynamic tethers are still subject to a significant probability of being severed by debris, though this be can partially obviated through double line tethers [61]. A deployable large-area drag-sail or ballute may be used to de-orbit debris from LEO below 1000 km altitude [62]. SSTL's TechDemo-Sat-1 was launched in 2014 fitted with a deployable de-orbit sail acting as a drag brake to orient the satellite target for de-orbiting and re-entry disposal.