Model Predictive Control of Vehicle Formations

We propose a two-layer scheme to control a set of vehicles moving in a formation. The first; layer, file trajectory controller, is a nonlinear controller since most vehicles are nonholonomic systems and require a nonlinear, even discontinuous, feedback to stabilize them. The trajectory controller, a model predictive controller, computes centrally a bang-bang control law and only a small set of parameters need to be transmitted to each vehicle at each iteration. The second layer, the formation controller, aims to compensate for small changes around a nominal trajectory maintaining the relative positions between vehicles. We argue that; the formation control call be, in most; cases, adequately carried out, by a linear model predictive controller accommodating input, and state constraints. This has the advantage that the control laws for each vehicle are simple piecewise affine feedback laws that, call be pre-computed off-line and implemented in a, distributed way in each vehicle. Although several optimization problems have to be solved, the control strategy proposed results in a simple and efficient; implementation where no optimization problem needs to be solved in real-time at each vehicle.