Monitoring and Analysis of Large Deviations of Autonomous Underwater Vehicles when Moving in a Group

Abstract

The article is devoted to the issue of constructing the proximity estimation of a pair of autonomous underwater vehicles moving on parallel courses. Two approaches are considered depending on the density of the vehicles in the group: when moving in narrow spaces and when moving on parallel courses for a relatively long time. Exact and approximate methods of constructing such estimates depending on the group density are proposed, since noise manifests itself in fundamentally different ways in these situations. In the case of a dense group, a collision event cannot be considered rare and exact state estimation methods are applied. In the exact method, the equations of dynamics are treated as a conditionally Gaussian system to compute the necessary estimates. For this purpose, the Lipzer-Shiryaev method is used to account for nonlinear dependencies in the equations of the observed variables. In the case of rarefied density (long apparatus movements), coarser approaches in the estimations are allowed. The fact of collision is considered as a rare event, which is led to by the coincidence of factors that form a quite definite sequence in time — the extremal of the optimal control problem. The monitoring problem is formulated as a large deviation control problem. Applying the principle of large deviations, the stochastic problem of collision probability estimation is reduced to a deterministic optimal control problem. A rough estimate of the collision probability for two vehicles is obtained for the limit solution of the averaged system in the paper. As an application of the proposed approach, the problem of motion control of autonomous underwater vehicles moving in the horizontal plane with constant longitudinal velocity at a given depth is considered. Under the condition of nondegeneracy of the diffusion matrix in the equation of observable variables, an algorithm for recovering the transverse coordinates and velocity and calculating the collision risk on this basis is obtained.The paper uses the approach of A. Puchalskii, which requires only controllability of the system by input noise. Knowledge of the extremal allows predicting the collision event, which is used in the paper to estimate the collision risk