Collision Avoidance by Using Space-Time Representations of Motion Processes

This paper handles the problem of collision avoidance in a multi-robot environment. To solve this problem, the motion processes of the mobile robots are modelled in space-time. Since the robots are autonomous and communication is non-deterministic, there is temporal uncertainty in addition to spatial uncertainty. The paper presents a method to model both uncertainty components in a homogeneous way. It is shown, that it is not sufficient to guarantee a spatial security distance between the robots. Distances in space-time and space-time vectors must be considered. The main result of this paper is a straightforward and efficient solution to the problem of collision avoidance between up to three mobile robots by applying a space-time displacement vector. The solution is based on space-time, which is a helpful view onto our world in relativity theory and quantum physics. Space-time methods are also very valuable in Robotics, especially for problems in dynamic environments and for motion coordination of mobile robots. Practical experiments with up to two robots, and simulations of up to three robots have been performed and are reported.