Nonlinear tracking control for satellite formations

A tracking control design using sliding mode techniques is derived to control a desired satellite formation. Hill's relative motion equations are used to model the follower satellite motion relative to the leader. To minimize fuel usage required to maintain the formation, each satellite is constrained to reside near a natural orbit. Control forces are applied only to maintain the desired relative motion by, correcting for initial offsets and perturbation effects that tend to disperse the formation. These perturbations include effects due to Earth asphericity, atmospheric drag, and third-body effects from the sun and moon. Parametric equations describing the member satellites' relative motion with respect to the leader satellite are essential in this design. The control law is modified to account for discontinuous nature of the control forces available with the satellite propulsive thrusters. Numerical simulations using a high-fidelity, nonlinear model demonstrate the control law performance for the full nonlinear dynamics with high-order perturbations.