Cooperative Control of Formations of Underwater Vehicles
Doctoral thesis
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https://hdl.handle.net/11250/3100735Utgivelsesdato
2023Metadata
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Sammendrag
This thesis investigates various control algorithms for marine vehicles. Most of the algorithms proposed in the thesis address the formation path-following problem for a fleet of underactuated autonomous underwater vehicles, although other types of vehicles, such as autonomous surface vehicles and differential drive robots, and other types of control problems, such as collision avoidance, trajectory tracking, and path following, are also considered. The thesis is divided into three parts.
In the first part, we develop a collision avoidance algorithm for overactuated vehicles. The vehicles must reach a desired position while maintaining some minimum safety distance from each other. To solve this problem, we propose an optimizationbased control allocation scheme augmented with control barrier functions. Control allocation is a collection of methods for finding an actuator configuration that satisfies a given goal (e.g., reaching a desired position), while control barrier functions allow us to enforce constraints on dynamical systems (e.g., keeping a minimum safety distance). By combining control allocation with control barrier functions, we can create a controller that satisfies a given goal while avoiding collisions. The proposed controller is tested in numerical simulations on two types of autonomous surface vehicles: the milliAmpere ferry, and the Inocean Cat I drillship.
The second part addresses the formation path-following problem. We propose to solve the problem using the null-space-behavioral method. This method allows us to decompose the problem into several tasks. Then, by combining these tasks in a hierarchic manner, we can achieve the desired behavior. To solve the formation path-following problem, we define three tasks: collision avoidance, formation keeping, and path following. In this thesis, we develop and analyze three different null-space-behavioral algorithms for the formation path-following problem. The first algorithm uses a model of an autonomous underwater vehicle with five degrees of freedom. Using Lyapunov analysis, we show that the path-following task is uniformly semiglobally exponentially stable. Numerical simulations then validate this result. The second algorithm uses a six-degree-of-freedom model. Compared to the previous method, this algorithm does not suffer from numerical singularities. This algorithm also contains additional tasks, namely obstacle avoidance and depth limiting. Moreover, we prove that both the path-following and the formation-keeping tasks are uniformly semiglobally exponentially stable. These theoretical results are then validated in numerical simulations. One issue with null-space-behavioral algorithms is that they are centralized. In many applications, centralized algorithms are difficult to implement, as they require a central node or an agent that can communicate and coordinate with other agents in real-time. To solve this issue, the third algorithm combines the null-space-behavioral method with consensus, resulting in a fully distributed controller. We propose two types of consensus algorithms. First, we propose a continuous-time consensus algorithm and prove its stability using Lyapunov analysis. Then, we present a modified discrete-time version of the algorithm based on event-triggered control. The effectiveness of both the continuous- and discrete-time algorithms is demonstrated in numerical simulations. Furthermore, the discrete-time version is also tested in field experiments.
The third part of the thesis extends the hand position approach to underactuated underwater vehicles moving in three dimensions. This approach was originally developed to stabilize nonholonomic vehicles. By treating the hand position of the vehicle as the output of the system, we can use input-output feedback linearization to transform the underactuated highly nonlinear vehicle model into a system with linear external dynamics and nonlinear internal dynamics. We analyze the closed-loop behavior of a generic hand position-based controller and present four applications of the hand position approach. First, we use this approach to solve the trajectory-tracking and path-following problems. We propose simple PID-based controllers to solve these problems and show that using these controllers renders the external states globally exponentially stable, while the internal states remain bounded. The theoretical results are validated in numerical simulations as well as field experiments. Next, we present a spline-based model predictive control method for solving the formation path-following problem. The proposed method is not restricted to the hand position approach only. In fact, the method is applicable to any vehicle with a differentially flat model. To demonstrate this, we present two case studies: underwater vehicles with the hand position controller, and differential drive robots. Next, we use the hand position concept to solve the tracking-in-formation problem for a fleet of autonomous underwater vehicles. The proposed method combines consensus with barrier Lyapunov functions, allowing the fleet to reach the desired formation while avoiding collisions and maintaining connectivity. We show that the closed-loop system is almost-everywhere uniformly asymptotically stable and that the output error dynamics converge to the origin exponentially fast while satisfying the constraints. The theoretical results are verified in numerical simulations. Finally, we combine the hand position approach with null-space-behavioral control. Specifically, we extend the null-spacebehavioral algorithm, which was originally developed for first-order kinematic systems, to second-order systems. Similarly to our previous work, we then design the path-following, formation-keeping, and collision-avoidance tasks, so that the fleet can follow a given path in a formation while avoiding collisions. We prove the stability of the control scheme using Lyapunov analysis and verify its effectiveness in simulations.