Model predictive control: extension to coordinated multi-vehicle formations and real-time implementation

In model predictive control (MPC), the current control action is determined by solving on-line, at each sampling instant, a finite horizon open-loop optimal control problem. Each optimization yields an optimal control sequence and the first control in the sequence is applied to the plant until the next sampling instant. As MPC does not mandate that the control law be pre-computed, it is particularly useful when off-line computation of such a law is difficult or impossible. MPC is not a new approach, and has traditionally been applied to plants where the dynamics are slow enough to permit a sampling rate amenable to optimal input computations between samples, e.g. chemical process plants. These systems are usually also governed by strict constraints on states, inputs and/or combinations of both. With the advent of faster modern computers, it has become possible to extend the MPC approach to systems governed by faster dynamics that warrant this type of solution. In the multi-vehicle realm a general objective it to achieve a formation and perform joint maneuvers in formation. In general, the vehicles are individually governed by nonlinear and constrained dynamics. Interest in the multi-vehicle coordinated control problem has increased in recent years where joint autonomous tasks are of interest, e.g. micro-satellite formations for communications and imaging and unmanned air vehicle (UAV) cooperation in adversarial environments for defense purposes. The objective of this study is to develop a theoretical framework for the application of MPC techniques to the multi-vehicle coordinated control problem. Once the MPC objective is defined in terms of this type of problem, a stability analysis is detailed. Example problems are simulated to study the stability, performance and robustness of the MPC multi-vehicle approach. The simulations are performed using a nonlinear trajectory generation (NTG) software package developed at Caltech. Further, new experimental results are given applying real-time MPC via NTG to the Caltech ducted fan. Future directions, including extension of the MPC multi-vehicle framework to an emerging experimental testbed (MVWT), are also discussed.