Probabilistic guidance of distributed systems using sequential convex programming

In this paper, we integrate, implement, and validate formation flying algorithms for a large number of agents using probabilistic guidance of distributed systems 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 iteration in a statistically independent manner while the distributed system converges to the desired formation. Moreover, the distributed system is robust to external disturbances or damages to the formation. Once the target positions are assigned, 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, collision-free trajectories and model predictive control is implemented to update these trajectories as new state information becomes available. Finally, we validate the probabilistic guidance of distributed systems and model predictive control algorithms using the formation flying testbed.