Distributed MPC Formation Path Following for Acoustically Communicating Underwater Vehicles

Abstract

We propose and analyse a model predictive control (MPC) strategy tailored for networks of underwater agents tasked with maintaining formation while following a shared path and using acoustic communication channels. The strategy accommodates both time-division and frequency-division medium access schemes, and addresses the inherent challenges of lossy and broadcast communication over acoustic media. Our approach extends an existing distributed control algorithm originally assuming standard double precision in exchanged data, and designed for synchronous, bidirectional, and reliable communication. Here we introduce adaptations for handling broadcast asynchronous communication, for mitigating packet losses, and for quantising exchanged data. These modifications are general and intended to be applicable to other distributed control schemes that were developed under idealised assumptions. Our goal is thus to help facilitating deployment also of other control schemes in practical field conditions. We provide simulation results that quantify the impact of these adaptations on the performance of the original controller, along with sensitivity analyses on how performance losses are influenced by key hyperparameters. Additionally, we characterise the data rate savings vs. control performance losses that may be achieved through tuning such hyperparameters, showcasing the feasibility of implementing the proposed strategy for practical purposes using commercially available full-duplex or half-duplex modems.

Figures (13)

• Figure 1: Representation of how the channel is divided in the considered MAC protocols. Note that time and frequency gaps may be added so to decrease the chances of packets collisions / interference, trading thus off spectrum efficiency against packet losses probabilities.
• Figure 2: A schematic representation of a lawnmower path, along with its defining parameters. Agents are supposed to follow such a path using a constant speed.
• Figure 3: A graphical visualisation of the information encoded in a packet. The dots along the blue curve correspond to the break points, and thus indirectly give information on the tangential speed that the vehicle is supposed to follow in time. For reference, a straight line would indicate a constant speed along the planned trajectory.
• Figure 4: A graphical comparison of the two extrapolation mechanisms described in Sections \ref{['ssec:naive-extrapolation']} and \ref{['ssec:fitting-extrapolation']}. The markers in the to-be-extended spline are located at the points at which the original spline is sampled for the extrapolating velocity approach. Every other marker is instead a break point for the associated uniform B-spline.
• Figure 5: Comparing the two extrapolation methods against each other around the end of the old time horizon. Extrapolating jerk does not affect the existing forecast, while extrapolating velocity introduces some perturbation towards the end of it.