Random Finite Set Theory and Optimal Control for Large Spacecraft Swarms

Controlling large swarms of robotic agents has many challenges including, but not limited to, computational complexity due to the number of agents, uncertainty in the functionality of each agent in the swarm, and uncertainty in the swarm's configuration. This work generalizes the swarm state using Random Finite Set (RFS) theory and solves the control problem using model predictive control (MPC) which naturally handles the challenges. To determine more computationally efficient solutions, iterative linear quadratic regulator (ILQR) is also explored. This work uses information divergence to define the distance between swarm RFS and a desired distribution. A stochastic optimal control problem is formulated using a modified L2^2 distance. Simulation results using MPC and ILQR show that swarm intensities converge to a target destination, and the RFS control formulation can vary in the number of target destinations. ILQR also provides a more computationally efficient solution to the RFS swarm problem when compared to the MPC solution. Lastly, the RFS control solution is applied to the spacecraft relative motion problem showing the viability for this real-world scenario.

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