Safe, Delta-v-Efficient Spacecraft Swarm Reconfiguration Using Lyapunov Stability and Artificial Potentials

Spacecraft swarms can achieve mission objectives otherwise impossible by monolithic satellites. To this end, swarms need to autonomously reconfigure their relative motion while complying with spacecraft constraints. Convex optimization provides safety and efficiency for arbitrary reconfigurations at high computational cost. Comparatively, closed-form solutions are computationally efficient but do not guarantee optimality and compliance to constraints in general cases. This work proposes a novel control architecture with Lyapunov functions and artificial potentials based on relative orbit elements that promise the numerical efficiency of closed-form solutions and the general applicability of convex optimization solvers. The novel Lyapunov functions are designed using analytical lower bounds calculated using the current control tracking errors. When the functions are used with a feedback control scheme modeled after the optimal, closed-form solutions for binary system reconfiguration, the resulting controller is both computationally and efficient. To address safety and state constraints in general, reference governors based on artificial potential functions enable computationally efficient collision avoidance using only neighbor state information. The controllers are validated in example mission simulations representative of Starling-1 and the Van Allen Swarm. In these missions, the controllers demonstrate safe, -efficient, and computationally tractable swarm reconfiguration, enabling future swarming missions.