Navigation of Robot-Formation via Overlap-Induced Equilibrium Points in Uncertain Environments

Abstract

We propose a novel reactive algorithm for a multi-robot formation navigating from its starting point to its destination in geometrically changing non-convex environments containing dynamic obstacles that move stochastically. Taking formation’s buffer into consideration, the proposed algorithm estimates the optimal velocity by means of minimizing collision threats from obstacles to the formation. It considers the obstacles in pairs so that the formation crosses the gap between every involved pair of obstacles. At every time step, this algorithm is executed in four phases: 1) optimal velocity estimation using a probabilistic model; 2) topological trajectory decision; 3) optimal waypoint (crossing point) determination; and 4) real-time optimal velocity determination. Compared to existing algorithms, the simulation shows that our algorithm is robust and has significant improvement. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This paper was motivated by the problem of formation navigation in places containing a large number of moving objects such as human beings and other vehicles. Existing approaches either do not forecast the probability of collision, or do not explicitly consider a certain comfort or safety distance to maintain. This paper quantifies the expectation of objects getting “too close” to the formation before collision as a numerical collision forecast, where the future motions of objects are unknown: this allows a formation to navigate by acquiring least environment information. From this expectation, by considering the formation to be moving between pairs of these objects, the optimal path to the destination for the formation is computed. Our approach is proved by the simulation to have significant improvement compared to the existing approaches. In future research, we will consider more ways to avoid obstacles such as formation rotation and waiting.