Decentralized path planning for coverage tasks using gradient descent adaptive control

In this paper we propose a new path planning algorithm for coverage tasks in unknown environments that does not rely on recursive search optimization. Given a sensory function that captures the interesting locations in the environment and can be learned, the goal is to compute a set of closed paths that allows a single robot or a multi-robot system to sense/cover the environment according to this function. We present an online adaptive distributed controller, based on gradient descent of a Voronoi-based cost function, that generates these closed paths, which the robots can travel for any coverage task, such as environmental mapping or surveillance. The controller uses local information only, and drives the robots to simultaneously identify the regions of interest and shape their paths online to sense these regions. Lyapunov theory is used to show asymptotic convergence of the system based on a Voronoi-based coverage criterion. Simulated and experimental results, that support the proposed approach, are presented for the single-robot and multi-robot cases in known and unknown environments.