This paper presents a distributed, guidance and control algorithm for reconfiguring swarms composed of hundreds to thousands of agents with limited communication and computation capabilities. This algorithm solves both the optimal assignment and collision-free trajectory generation for robotic swarms, in an integrated manner, when given the desired shape of the swarm (without pre-assigned terminal positions). The optimal assignment problem is solved using a distributed auction assignment that can vary the number of target positions in the assignment, and the collision-free trajectories are generated using sequential convex programming. Finally, model predictive control is used to solve the assignment and trajectory generation in real time using a receding horizon. The model predictive control formulation uses current state measurements to resolve for the optimal assignment and trajectory. The implementation of the distributed auction algorithm and sequential convex programming using model predictive control produces the Swarm Assignment and Trajectory Optimization (SATO) algorithm that transfers a swarm of robots or vehicles to a desired shape in a distributed fashion. Once the desired shape is uploaded to the swarm, the algorithm determines where each robot goes and how it should get there in a fuel-efficient, collision-free manner. Results of flight experiments using multiple quadcopters show the effectiveness of the proposed SATO algorithm.

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Abstract-In this paper, we integrate, implement, and validate formation flying algorithms for large number of agents using probabilistic swarm guidance with inhomogeneous Markov chains and model predictive control with sequential convex programming. Using an inhomogeneous Markov chain, each agent determines its target position during each time step in a statistically independent manner while the swarm converges to the desired formation. Moreover, the swarm is robust to external disturbances or damages to the formation. An optimal control problem is formulated to ensure that the agents reach the target positions while avoiding collisions. This problem is solved using sequential convex programming to determine optimal, collisionfree trajectories and model predictive control is implemented to update these trajectories as new state information becomes available. Finally, we validate the probabilistic swarm guidance and model predictive control algorithms using the formation flying testbed.

Small satellites are suitable for formation flying missions where a large number of spacecraft serve as distributed sensors for applications like synthetic aperture radar, interferometry, etc. A survey of existing or proposed small satellite missions concludes that there is a dearth of formation flying missions using four or more spacecraft that require formation maintenance. This paper presents a systems engineering based design of a formation flying technology demonstration mission that requires precise formation maintenance and reconfigurations and highlights the challenges that need to be overcome for its successful implementation. The goal of this paper is to provide directions for future research and development in spacecraft formation flying technologies.