ASYMPTOTIC METHODS IN PROBLEMS OF SUPERVISORY CONTROL OF AUTONOMOUS UNDERWATER ROBOTS

Abstract

The work is devoted to the relevant problem of control synthesis for autonomous underwater vehicles
(AUVs). Since AUVs must perform actions in accordance with a given program under conditions
of a volatile predictable environment, it is necessary to provide working tools, the use of which, together
with the AUV position and orientation control requires, along with continuous local stabilization means,
implementation of supervising and coordinated control algorithms at the upper level. Such a two-level
control scheme, which can be called supervisory, is proposed in this paper to be implemented using two
types of asymptotic methods: to separate movements into fast and slow, an apparatus for analyzing singularly perturbed differential equations is used, and the upper level control is based on the principle
of large deviations. The general synthesis task is to control slow movements and stabilize fast movements.
At the same time, in the stochastic problem formulation, it is assumed that there is a random
perturbation in fast movements. Given that fast movements are stabilized, it is high probable that the
noise influence averaged and does not significantly affect the behavior of slow variables. However, with
sufficiently long observation it is possible to find a situation where at some period the perturbation values
are not only uncompensated, but, on the contrary, line up in a sequence as specially intended to
form an apparent deviation of the slow sub-vector from equilibrium. It is known from the theory of large
deviations that such a trajectory is the only and most likely of all those leading to a certain critical event.
At the same time, the phase of this process can be used to judge the critical event proximity. For this
reason, the large deviations theory usage makes it possible to organize the control of deviations from a
iven object’ t jecto y, capable of giving estimates on the probability of the controlled deviations
critical values. As a result, it is shown that if accelerations are formed by fast subsystems, then in slow
subsystems it is possible not only to achieve acceptable quality and accuracy at a fixed interval, but also
to ensure this regardless of the disturbances. The validity of the proposed approach to synthesis, based
on the separation of movements and the large deviations theory, is shown on the example of an autonomous
underwater vehicle with two rudders (fore and aft) in the task of controlling longitudinal motion at
a given depth. Simulation results and their discussion are presented.