Probabilistic Guidance of Swarms using Sequential Convex Programming∗

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.