A Stochastic Optimal Enhancement of Feedback Control for Unicycle Formations

摘要

We consider an optimal feedback control approach for multiple nonholo-nomic vehicles to achieve a distance-based formation with their neighbors using only local observations. Beginning with a non-optimal feedback formation control, each agent determines an additive correction term to its non-optimal control based on an elliptic Hamilton-Jacobi-Bellman equation so that its actions are optimal and robust to uncertainty. In order to avoid offline spatial discretization of the stationary, high-dimensional cost-to-go function, we exploit the stochasticity of the distributed nature of the problem to develop an equivalent estimation problem in a continuous state space using a path integral representation. Consequently, each agent independently computes its optimal feedback control using a discrete-time Unscented Kalman smoother. Our approach is illustrated by a numerical example in which five agents achieve a pentagon with aligned and equal velocities.