We consider stochastic model predictive control of a multi-agent systems with constraints on the probabilities of inter-agent collisions. We first study a sample-based approximation of the collision probabilities and use this approximation to formulate constraints for the stochastic control problem. This approximation will converge as the number of samples goes to infinity, however, the complexity of the resulting control problem is so high that this approach proves unsuitable for control under real-time requirements. To alleviate the computational burden we propose a second approach that uses probabilistic bounds to determine regions with increased probability of presence for each agent and formulate constraints for the control problem that guarantee that these regions will not overlap. We prove that the resulting problem is conservative for the original problem with probabilistic constraints, ie. every control strategy that is feasible under our new constraints will automatically be feasible for the original problem. Furthermore we show in simulations in a UAV path planning scenario that our proposed approach grants significantly better run-time performance compared to a controller with the sample-based approximation with only a small degree of sub-optimality resulting from the conservativeness of our new approach.

Abstract. We present an auction-flavored multi-robot planning mechanism where coordination is to be achieved on the occupation of atomic resources modeled as binary inter-robot constraints. Introducing virtual obstacles, we show how this approach can be combined with particlebased obstacle avoidance methods, offering a decentralized, auction-based alternative to previously established centralized approaches for multirobot open-loop control. We illustrate the effectiveness of our new approach by presenting simulations of typical spatially-continuous multirobot path-planning problems and derive bounds on the collision probability in the presence of uncertainty.

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