Conservative collision prediction and avoidance for stochastic trajectories in continuous time and space
This addresses collision avoidance in multi-agent systems with continuous-time, stochastic trajectories, which is an incremental improvement over existing discrete-time or deterministic methods.
The paper tackles the problem of predicting and avoiding collisions for continuous, stochastic trajectories by deriving probabilistic bounds and criterion functions, and it demonstrates collision-free trajectories with adjustably high certainty in simulations of feedback controlled plants.
Existing work in multi-agent collision prediction and avoidance typically assumes discrete-time trajectories with Gaussian uncertainty or that are completely deterministic. We propose an approach that allows detection of collisions even between continuous, stochastic trajectories with the only restriction that means and variances can be computed. To this end, we employ probabilistic bounds to derive criterion functions whose negative sign provably is indicative of probable collisions. For criterion functions that are Lipschitz, an algorithm is provided to rapidly find negative values or prove their absence. We propose an iterative policy-search approach that avoids prior discretisations and yields collision-free trajectories with adjustably high certainty. We test our method with both fixed-priority and auction-based protocols for coordinating the iterative planning process. Results are provided in collision-avoidance simulations of feedback controlled plants.