Motion Coordination for . . . WITH VISIBILITY SENSORS

The subject of this dissertation is motion coordination for mobile robotic networks with visibility sensors. Such networks consist of robotic agents equipped with sensors that can measure distances to the environment boundary and to other agents within line of sight. We look at two fundamental coordination problems: (i) deploying over an unknown nonconvex environment to achieve complete visibility, and (ii) gathering all agents initially scattered over the environment at a single location. As a special case of problem (i), we first address the problem of optimally locating a single robotic agent in a nonconvex environment. The agent is modeled as a point mass with continuous first-order dynamics. We propose a nonsmooth gradient algorithm for the problem of maximizing the area of the region visible to the observer in a non-self-intersecting nonconvex polygon. First, we show that the visible area is almost everywhere a locally Lipschitz function of the observer location. Second, we provide a novel version of the LaSalle Invariance Principle for discontinuous vector fields and for Lyapunov functions with a finite number of discontinuities. Finally, we establish the asymptotic convergence properties of the nonsmooth gradient algorithm and we illustrate numerically its performance. Second, we address problem (i) by proposing a novel algorithm to the deploy a group of robotic agents in an unknown nonconvex environment to achieve complete visibility. The agents are point masses with discrete-time first-order dynamics. The agents operate asynchronously and two agents can communicate when mutually visible. We also address this deployment problem under the additional constraint that the visibility graph of the final agent locations is connected. We provide distributed algorithms that are guaranteed to solve the two deployment problems if a sufficient number of agents is available. Remarkably, this number is identical to the upper bound established in the famous Art Gallery Problem, i.e., the number of agents sufficient to achieve complete visibility in a known environment through centralized computation. We additionally provide time complexity