The Rendezvous Problem: Fixed Neighbours

Imagine a group of rovers on Mars, distributed over a large area and without any global positioning system. During the day each robot carries out scientific experiments. When the day comes to an end, robots are to convene at a point that is not established a priori. To do so, the robots may rely only on their on-board cameras to see each other. There are peaks and valleys so each robot will normally see only a subset of the others. This so-called rendezvous problem is the subject of this chapter. We present solutions when the robots are modelled as integrator points and kinematic unicycles. The analysis is conducted under the assumption that the visibility graph is fixed. In the next chapter we present the case of proximity-based visibility graphs.