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Existing work in multi-agent collision prediction and avoidance typicallyassumes discrete-time trajectories with Gaussian uncertainty or that arecompletely deterministic. We propose an approach that allows detection ofcollisions even between continuous, stochastic trajectories with the onlyrestriction that means and variances can be computed. To this end, we employprobabilistic bounds to derive criterion functions whose negative sign provablyis indicative of probable collisions. For criterion functions that areLipschitz, an algorithm is provided to rapidly find negative values or provetheir absence. We propose an iterative policy-search approach that avoids priordiscretisations and yields collision-free trajectories with adjustably highcertainty. We test our method with both fixed-priority and auction-basedprotocols for coordinating the iterative planning process. Results are providedin collision-avoidance simulations of feedback controlled plants.

Conservative collision prediction and avoidance for stochastic trajectories in continuous time and space