In this paper, we evaluate theoretical aspects of a distributed system of noncooperative robots controlled by a distributed model predictive control scheme, which operates in a shared space. Here, for collision avoidance, the future predicted state trajectories are projected on a grid and exchanged via discrete cell indexes to reduce the communication burden. The predicted trajectories are obtained locally by each robot and carried out in the continuous space. Therefore, the quantisation does not impose the quality of the solution. We derive sufficient conditions to show convergence and practical stability for the distributed control system by using an idea of a temporary roundabout derived from crossing patterns of street traffic rules, which is established in a fixed and flexible circle size. Furthermore, a condition for the sufficient prediction horizon length to recognise necessary detours is presented, which is adapted for the occupancy grid. The theoretical results match with the trajectory patterns from former numerical simulations, showing that this pattern is naturally chosen as an overall solution.
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