Guidance and control for underactuated autonomous underwater vehicles

The main focus of this paper is on the motion planning problem for an under-actuated, submerged, Omni-directional autonomous vehicle. Underactuation is extremely important to consider in ocean research and exploration. Battery failure, actuator malfunction and electronic shorts are a few reasons that may cause the vehicle to lose direct control of one or more degrees-of-freedom. Underactuation is also critical to understand when designing vehicles for specific tasks, such as torpedo-shaped vehicles. An under-actuated vehicle is less controllable, and hence, the motion planning problem is more difficult. Here, we present techniques based on geometric control to provide solutions to the under-actuated motion planning problem for a submerged underwater vehicle. Our results are validated with experiments.

Calculus of variations. Supplementary notes and exercises to 1945-1946 notes, at New York University.

Reproduced from typewritten copy.

Calculus of Variations with Classical and Fractional Derivatives

MSC 2010: 49K05, 26A33

Delay distribution based robust H∞ control of networked control systems with uncertainties

Network induced delay in networked control systems (NCS) is inherently non-uniformly distributed and behaves with multifractal nature. However, such network characteristics have not been well considered in NCS analysis and synthesis. Making use of the information of the statistical distribution of NCS network induced delay, a delay distribution based stochastic model is adopted to link Quality-of-Control and network Quality-of-Service for NCS with uncertainties. From this model together with a tighter bounding technology for cross terms, H∞ NCS analysis is carried out with significantly improved stability results. Furthermore, a memoryless H∞ controller is designed to stabilize the NCS and to achieve the prescribed disturbance attenuation level. Numerical examples are given to demonstrate the effectiveness of the proposed method.

Optimization problems for controlled mechanical systems : bridging the gap between theory and application

Mechanical control systems have become a part of our everyday life. Systems such as automobiles, robot manipulators, mobile robots, satellites, buildings with active vibration controllers and air conditioning systems, make life easier and safer, as well as help us explore the world we live in and exploit it’s available resources. In this chapter, we examine a specific example of a mechanical control system; the Autonomous Underwater Vehicle (AUV). Our contribution to the advancement of AUV research is in the area of guidance and control. We present innovative techniques to design and implement control strategies that consider the optimization of time and/or energy consumption. Recent advances in robotics, control theory, portable energy sources and automation increase our ability to create more intelligent robots, and allows us to conduct more explorations by use of autonomous vehicles. This facilitates access to higher risk areas, longer time underwater, and more efficient exploration as compared to human occupied vehicles. The use of underwater vehicles is expanding in every area of ocean science. Such vehicles are used by oceanographers, archaeologists, geologists, ocean engineers, and many others. These vehicles are designed to be agile, versatile and robust, and thus, their usage has gone from novelty to necessity for any ocean expedition.

A first extension of geometric control theory to underwater vehicles

This paper serves as a first study on the implementation of control strategies developed using a kinematic reduction onto test bed autonomous underwater vehicles (AUVs). The equations of motion are presented in the framework of differential geometry, including external dissipative forces, as a forced affine connection control system. We show that the hydrodynamic drag forces can be included in the affine connection, resulting in an affine connection control system. The definitions of kinematic reduction and decoupling vector field are thus extended from the ideal fluid scenario. Control strategies are computed using this new extension and are reformulated for implementation onto a test-bed AUV. We compare these geometrically computed controls to time and energy optimal controls for the same trajectory which are computed using a previously developed algorithm. Through this comparison we are able to validate our theoretical results based on the experiments conducted using the time and energy efficient strategies.

Geometric Control Theory and its Application to Underwater Vehicles

This dissertation is based on theoretical study and experiments which extend geometric control theory to practical applications within the field of ocean engineering. We present a method for path planning and control design for underwater vehicles by use of the architecture of differential geometry. In addition to the theoretical design of the trajectory and control strategy, we demonstrate the effectiveness of the method via the implementation onto a test-bed autonomous underwater vehicle. Bridging the gap between theory and application is the ultimate goal of control theory. Major developments have occurred recently in the field of geometric control which narrow this gap and which promote research linking theory and application. In particular, Riemannian and affine differential geometry have proven to be a very effective approach to the modeling of mechanical systems such as underwater vehicles. In this framework, the application of a kinematic reduction allows us to calculate control strategies for fully and under-actuated vehicles via kinematic decoupled motion planning. However, this method has not yet been extended to account for external forces such as dissipative viscous drag and buoyancy induced potentials acting on a submerged vehicle. To fully bridge the gap between theory and application, this dissertation addresses the extension of this geometric control design method to include such forces. We incorporate the hydrodynamic drag experienced by the vehicle by modifying the Levi-Civita affine connection and demonstrate a method for the compensation of potential forces experienced during a prescribed motion. We present the design method for multiple different missions and include experimental results which validate both the extension of the theory and the ability to implement control strategies designed through the use of geometric techniques. By use of the extension presented in this dissertation, the underwater vehicle application successfully demonstrates the applicability of geometric methods to design implementable motion planning solutions for complex mechanical systems having equal or fewer input forces than available degrees of freedom. Thus, we provide another tool with which to further increase the autonomy of underwater vehicles.

Delay-dependent robust H-infinity control for uncertain systems with time-varying delay

This paper proposes a new approach for delay-dependent robust H-infinity stability analysis and control synthesis of uncertain systems with time-varying delay. The key features of the approach include the introduction of a new Lyapunov–Krasovskii functional, the construction of an augmented matrix with uncorrelated terms, and the employment of a tighter bounding technique. As a result, significant performance improvement is achieved in system analysis and synthesis without using either free weighting matrices or model transformation. Examples are given to demonstrate the effectiveness of the proposed approach.

New Approach on Robust Delay-Dependent H∞ Control for Uncertain T-S Fuzzy Systems With Interval Time-Varying Delay

This paper investigates the robust H∞ control for Takagi-Sugeno (T-S) fuzzy systems with interval time-varying delay. By employing a new and tighter integral inequality and constructing an appropriate type of Lyapunov functional, delay-dependent stability criteria are derived for the control problem. Because neither any model transformation nor free weighting matrices are employed in our theoretical derivation, the developed stability criteria significantly improve and simplify the existing stability conditions. Also, the maximum allowable upper delay bound and controller feedback gains can be obtained simultaneously from the developed approach by solving a constrained convex optimization problem. Numerical examples are given to demonstrate the effectiveness of the proposed methods.

Robust tracking control of autonomous underwater vehicles in the presence of disturbance inputs

An autonomous underwater vehicle (AUV) is expected to operate in an ocean in the presence of poorly known disturbance forces and moments. The uncertainties of the environment makes it difficult to apply open-loop control scheme for the motion planning of the vehicle. The objective of this paper is to develop a robust feedback trajectory tracking control scheme for an AUV that can track a prescribed trajectory amidst such disturbances. We solve a general problem of feedback trajectory tracking of an AUV in SE(3). The feedback control scheme is derived using Lyapunov-type analysis. The results obtained from numerical simulations confirm the asymptotic tracking properties of the feedback control law. We apply the feedback control scheme to different mission scenarios, with the disturbances being initial errors in the state of the AUV.

Autonomous underwater vehicles: development and implementation of time and energy efficient trajectories

Autonomous underwater vehicles (AUVs) are increasingly used, both in military and civilian applications. These vehicles are limited mainly by the intelligence we give them and the life of their batteries. Research is active to extend vehicle autonomy in both aspects. Our intent is to give the vehicle the ability to adapt its behavior under different mission scenarios (emergency maneuvers versus long duration monitoring). This involves a search for optimal trajectories minimizing time, energy or a combination of both. Despite some success stories in AUV control, optimal control is still a very underdeveloped area. Adaptive control research has contributed to cost minimization problems, but vehicle design has been the driving force for advancement in optimal control research. We look to advance the development of optimal control theory by expanding the motions along which AUVs travel. Traditionally, AUVs have taken the role of performing the long data gathering mission in the open ocean with little to no interaction with their surroundings, MacIver et al. (2004). The AUV is used to find the shipwreck, and the remotely operated vehicle (ROV) handles the exploration up close. AUV mission profiles of this sort are best suited through the use of a torpedo shaped AUV, Bertram and Alvarez (2006), since straight lines and minimal (0 deg - 30 deg) angular displacements are all that are necessary to perform the transects and grid lines for these applications. However, the torpedo shape AUV lacks the ability to perform low-speed maneuvers in cluttered environments, such as autonomous exploration close to the seabed and around obstacles, MacIver et al. (2004). Thus, we consider an agile vehicle capable of movement in six degrees of freedom without any preference of direction.

Efficient control of an autonomous underwater vehicle while accounting for thruster failure

This paper is concerned with the design and implementation of control strategies onto a test-bed vehicle with six degrees-of-freedom. We design our trajectories to be efficient in time and in power consumption. Moreover, we also consider cases when actuator failure can arise and discuss alternate control strategies in this situation. Our calculations are supplemented by experimental results.

Design and implementation of time efficient trajectories for an underwater vehicle

This paper discusses control strategies adapted for practical implementation and efficient motion of underwater vehicles. These trajectories are piecewise constant thrust arcs with few actuator switchings. We provide the numerical algorithm which computes the time efficient trajectories parameterized by the switching times. We discuss both the theoretical analysis and experimental implementation results.

Optimal-stopping control for airborne collision avoidance and return-to-course flight

This paper considers an aircraft collision avoidance design problem that also incorporates design of the aircraft’s return-to-course flight. This control design problem is formulated as a non-linear optimal-stopping control problem; a formulation that does not require a prior knowledge of time taken to perform the avoidance and return-to-course manoeuvre. A dynamic programming solution to the avoidance and return-to-course problem is presented, before a Markov chain numerical approximation technique is described. Simulation results are presented that illustrate the proposed collision avoidance and return-to-course flight approach.

Reducing Actuator Switchings for Motion Control of Autonomous Underwater Vehicles

A priority when designing control strategies for autonomous underwater vehicles is to emphasize their cost of implementation on a real vehicle. Indeed, due to the vehicles' design and the actuation modes usually under consideration for underwater plateforms the number of actuator switchings must be kept to a small value to insure feasibility and precision. This is the main objective of the algorithm presented in this paper. The theory is illustrated on two examples, one is a fully actuated underwater vehicle capable of motion in six-degrees-of freedom and one is minimally actuated with control motions in the vertical plane only.