A Decentralized Kernel Density Estimation Approach to Distributed Robot Path Planning

This paper presents a decentralized kernel density estimation (KDE) technique for computing the actual positional density of the robots in a distributed network, which constitutes the feedback in the robot’s control law. The goal of the feedback control law is to plan the paths of a distributed robot network in order to follow a known, optimal time-varying robot distribution or probability density function (PDF). Thus, knowledge of the actual positional density of the robots is needed to compute the robot feedback control law, such that the optimal PDF is achieved over time by the network. The optimal PDF is computed using a distributed optimal control (DOC) approach that guarantees the robots avoid collisions with obstacles, while minimizing the energy required to meet a goal distribution. This novel approach generates a potential function, and corresponding control law, for each robot through the decentralized computation of the robots’ probability density function (PDF) obtained from the individual states of the robots. The methodology is demonstrated through a numerical simulation of a large distributed network of robots navigating an obstacle-populated region of interest.