Motion planning for maintaining landmarks visibility with a differential drive robot

•Collision-free paths for DDRs keeping landmarks visible during motion are planned.•Convergence proofs and complexity results are given for the recursive approach.•A generalization was proposed to maintain in sight at least one landmark among many.•Simulation examples under uncertain environments support the approach pertinence.•Real experiments were done with a Pioneer robot.

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. 1