Relaxed Collision Constraints Based on Interval Superposition Principle in a DMPC Scheme

Within this paper, we consider a group of mobile robots in a shared operation space controlled by a distributed model predictive control scheme, where each robot is assigned with individual start and target positions. Each robot solves an Optimal Control Problem, based on information about the predictions of the other robots, to calculate an optimal trajectory over a fixed horizon length. The information exchange among the robots is quantised by projecting the trajectory onto a grid. To reduce the communication overhead, the interval superposition principle is used by transmitting only the minimum and maximum coordinates of the trajectory, yielding a static interval of reserved cells. To attenuate the effect of many reserved cells, the dynamics and directional movement of the robot is incorporated to determine, which of the reserved cells are not needed by this robot anymore. This additional information can be transmitted without necessary overhead. Furthermore, the time instant can be excluded from the communicated cells. To this end, numerical simulations based on holonomic dynamics of mobile robots are presented and compared with the conservative approach.