Chance constrained model predictive control for multi-agent systems with coupling constraints

We consider stochastic model predictive control of a multi-agent systems with constraints on the probabilities of inter-agent collisions. First, we discuss a method based on sample average approximation of the collision probabilities to make the stochastic control problem computationally tractable. Empirical results indicate that the complexity of the resulting optimization problem can be too high to be solved under realtime requirements. To reduce the computational burden we propose a second approach. It employs probabilistic bounds to determine regions of increased probability of presence for each agent and introduce constraints for the control problem prohibiting overlap of these regions. We prove that the resulting problem is conservative for the original problem, i.e., every control strategy that is feasible under our new constraints will automatically be feasible for the true original problem. Furthermore, we present simulations demonstrating improved run-time performance of our second approach and compare our stochastic method to robust control.