Path Tracking Error Analysis for Underwater Glider Navigation in a Spatially and Temporally Varying Flow Field

In this paper, we presented path tracking error comparison between two navigation schemes for underwater glider that combine path planning and a path tracking controller. Path planning is performed with the time-averaged flow field for both schemes, while path tracking is performed with the instantaneous or the time-averaged flow field. Mathematical analysis and numerical simulation show that performing path tracking control with instantaneous flow results in smaller path tracking error when the strength of spatially varying flow is small compared to glider speed, while it leads to larger path tracking error if spatially varying flow is the same order as the glider speed. Performing path tracking control with instantaneous flow leads to less path tracking error when the spatially varying flow is of relatively high frequency, but it produces larger path tracking error if the spatially varying flow is of low frequency. Simulated experiments near Cape Hatteras, NC show that in this specific region, performing path tracking control with instantaneous flow results in less path tracking error, which is consistent with the analytical result.

I. Introduction

Underwater gliders are moving robotic sensing platforms [1] that are able to perform persistent surveying missions in the ocean for data collection [2] –[4]. They take advantage of buoyancy and attitude to move through the water column [5] –[8], surfacing at defined intervals to communicate with the onshore dockserver to receive mission updates and commands. Control and navigation of underwater gliders can be achieved through a combined path planning and path tracking control scheme. Path planning designs an optimal path connecting the glider’s current position with the destination position. Then, a path tracking controller computes a series of steering angle that drives the glider to follow the designed optimal path. Flow canceling strategy was introduced in [9] to track, or follow, the path. It computes the steering angle to cancel the flow component orthogonal to the heading direction, such that at each timestep, the addition of glider speed and flow velocity coincides with the predefined heading direction.