Regulating a Formation of a Large Number of Vehicles

Various control algorithms have been developed for fleets of autonomous vehicles. Many of the successful control algorithms in practice are behavior-based control or nonlinear control algorithms, which makes analyzing their stability difficult. At the same time, many system theoretic approaches for controlling a fleet of vehicles have also been developed. These approaches usually use very simple vehicle models such as particles or point-mass systems and have only one coordinate system which allows stability to be proven. Since most of the practical vehicle models are six-degree-of-freedom systems defined relative to a body-fixed coordinate system, it is difficult to apply these algorithms in practice. In this paper, we consider a formation regulation problem as opposed to a formation control problem. In a formation control problem, convergence of a formation from random positions and orientations is considered, and it may need a scheme to integrate multiple moving coordinates. On the contrary, in a formation regulation problem, it is not necessary since small perturbations from the nominal condition, in which the vehicles are in formation, are considered. A common origin is also not necessary if the relative distance to neighbors or a leader is used for regulation. Under these circumstances, the system theoretic control algorithms are applicable to a formation regulation problem where the vehicle models have six degrees of freedom. We will use a realistic six-degree-of-freedom model and investigate stability of a fleet using results from decentralized control theory. We will show that the leader-follower control algorithm does not have any unstable fixed modes if the followers are able to measure distance to the leader. We also show that the leader-follower control algorithm has fixed modes at the origin, indicating that the formation is marginally stable, when the relative distance measurements are not available. Multi-vehicle simulations are performed using a hybrid leader-follower control algorithm where each vehicle is given a desired trajectory to follow and adjusts its velocity to maintain a prescribed distance to the leader. Each vehicle is modeled as a three-degree-of-freedom system to investigate the vehicle’s motion in a horizontal plane. The examples show efficacy of the analysis.