Adaptive Vectored Thrust Deorbiting of Space Debris

A novel but simple deorbiting control system is proposed for cleaning up space debris in a low Earth orbit. The method consists of employing a low-thrust spacecraft tug with a continuously varying thrust direction for collecting and decelerating debris items at a given orbital radius. A time-linear thrust-direction profile is the outcome of the nominal, two-point boundary-value problem for deceleration by a given velocity magnitude. Three simple model reference adaptive control strategies are proposed for driving the velocity error from nominal to zero in the presence of uncertain debris mass and rocket thrust variation. Although linear time-varying control with velocity feedback and a dead-zone is sufficient to minimize tracking error in most cases, it is improved significantly by a Lyapunov-based controller that guarantees asymptotic stability in the presence of a random but bounded acceleration disturbance. A nonlinear feedback adaptation law based upon the MIT rule achieves the fastest error decay rate error of the three techniques and is seen to have a logarithmic relationship between the steady-state value of controller parameter and adaptation gain.