Abstract:

A method based on a virtual spring-damper mesh is proposed for formation control of spacecraft swarms. Spacecrafts are interconnected virtually by spring-damper pairs. The natural lengths of the springs are set according to the geometrical requirements for the desired formation. The control input to each spacecraft is the resultant of the forces generated by the virtual spring-damper pairs connected to the spacecraft. Under the assumption of linear translational dynamics and that the mesh topology is fixed and connected, the stability condition of the virtual spring-damper mesh controlled closed-loop relative motion system are derived by using the algebraic graph theory. Simulations of a lattice formation of 100 spacecrafts and an elliptical, time-varying formation of 20 spacecrafts are presented. Orbit perturbations are included in the simulation. The results show that the desired formations can autonomously evolve from random initial states and that the formation-keeping errors are in the order of centimeter. The method won’t change the mass center of the swarm, and only small control accelerations are required. The distributed nature of the interactions makes the method desirable for formation control of large swarms.

Key words: Spacecraft swarms, Formation flight, Formation control, Spring-dampers