The thesis consists of four independent papers concerning the control of mobile robots in the context of obstacle avoidance and formation keeping.
The first paper describes a new theoretically verifiable approach to obstacle avoidance. It merges the ideas of two previous methods, with complementary properties, using a combined control Lyapunov function (CLF) and model predictive control (MPC) framework.
The second paper investigates the problem of moving a fixed formation of vehicles through a partially known environment with obstacles. Using an input to state (ISS) formulation the concept of configuration space obstacles is generalized to leader follower formations. This generalization then makes it possible to convert the problem into a standard single vehicle obstacle avoidance problem, such as the one considered in the first paper. The properties of goal convergence and safety thus carries over to the formation obstacle avoidance case.
In the third paper, coordination along trajectories of a nonhomogenuos set of vehicles is considered. Using a control Lyapunov function approach, properties such as bounded formation error and finite completion time is shown.
Finally, the fourth paper applies a generalized version of the control in the third paper to translate, rotate and expand a formation. It is furthermore shown how a partial decoupling of formation keeping and formation mission can be achieved. The approach is then applied to a scenario of underwater vehicles climbing gradients in search for specific thermal/biological regions of interest. The sensor data fusion problem for different formation configurations is investigated and an optimal formation geometry is proposed.