Motion planning for maintaining landmarks visibility with a differential drive robot

Abstract

This work studies the interaction of non-holonomic and visibility constraints using a Differential Drive Robot (DDR) that has to keep static landmarks in sight in an environment with obstacles. The robot has a limited sensor, namely, it has a restricted field of view and bounded sensing range (e.g. a video camera). Here, we mean by visibility that a clear line of sight can be thrown between the landmark and the sensor mounted on the DDR. We first determine the necessary and sufficient conditions for the existence of a path such that our system is able to maintain one given landmark visibility in the presence of obstacles. This is done through a recursive, complete algorithm that uses motion primitives exhibiting local optimality, as they are locally shortest-lengths paths. Then, we extend this result to the problem of planning paths guaranteeing visibility among a set of landmarks, e.g. to observe a given sequence of landmarks or to observe at each point of the path at least one element of the landmarks set. We also provide a procedure that computes the robot controls yielding such a path.11A preliminary version of this work has been presented in the 2008 International Workshop on the Algorithmic Foundations of Robotics (WAFR’08) and published in [1].