In this dissertation a framework for planning and control of cooperative autonomous systems is presented, which allows a group of Unmanned Vehicle Systems (UxSs) to generate and follow desired trajectories, while coordinating along them in order to satisfy relative temporal constraints. The described methodology is based on two key results. First, a centralized optimal motion planning algorithm produces a set of feasible and flyable trajectories, which guarantee inter-vehicle safety, while satisfying specific temporal mission requirements, as well as dynamic constraints of the vehicles. Then, a distributed coordinated tracking controller ensures that the vehicles follow the trajectories while coordinating along them in order to arrive at the final destination at the same time, or with a predefined temporal separation, according to the mission requirements.
The optimal motion planning problem is formulated as a continuous-time optimal control problem, which is then approximated by a discrete-time formulation using Bernstein polynomials. Using the convergence properties of Bernstein polynomial approximation, the thesis provides a rigorous analysis that shows that the solution to the discrete-time approximation converges to the solution to the continuous-time problem. The motivation behind this approach lies in the fact that Bernstein polynomials possess favorable geometric properties that allow for efficient computation of various constraints along the entire trajectory, and are particularly convenient for generating trajectories for safe operation of multiple vehicles in complex environments.
The coordinated tracking algorithm relies on the presence of a virtual target tracking controller which guarantees that the distance between each vehicle and its assigned virtual target running along the desired trajectory remains bounded throughout the mission. Then, the speed of the virtual target is adjusted in order to satisfy the temporal constraints and achieve coordination. The coordination problem is formulated as a consensus problem, with the objective of regulating a suitably defined set of coordination variables to zero. Conditions are derived under which the consensus algorithm proposed solves the coordination problem in the presence of faulty communications and switching topologies
