Adaptive collision-free formation control for under-actuated spacecraft

This paper proposes an adaptive collision-free formation control strategy for a team of under-actuated spacecraft subject to parametric uncertainties. The objective is to drive follower spacecraft to form a prescribed shape around a leader, while collision avoidance is achieved among different spacecraft. To explore the under-actuated nature of the studied spacecraft, a hierarchical inner-outer loop strategy is adopted. First, in the outer position loop, a virtual force is synthesized by introducing negative gradients of novel potential functions with respect to the distances between spacecraft such that the collision-free formation objective is completed. Based on the synthesized virtual force, an applied thrust and a command attitude are extracted. Then, in the inner attitude loop, an applied torque is designed for each individual spacecraft to track the command attitude. Moreover, during the virtual force and applied torque syntheses, adaptive laws are developed to estimate and compensate the uncertain inertial parameters. In terms of Lyapunov theory, it is shown that the spacecraft trajectories driven by the proposed controller ultimately converges to a neighborhood of the desired formation. Finally, illustrative simulations are performed to verify the proposed theoretical results.