The technology of hydrodynamic modeling and marine craft motion control systems has progressed greatly in recent years. This timely survey includes the latest tools for analysis and design of advanced guidance, navigation and control systems and presents new material on underwater vehicles and surface vessels. Each section presents numerous case studies and applications, providing a practical understanding of how model-based motion control systems are designed.

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Handbook of Marine Craft Hydrodynamics and Motion Control: Fossen/Handbook of Marine Craft Hydrodynamics and Motion Control

WITH the ever-widening scope of modern mathematical analysis and its many ramifications, it is quite impossible to include, in a single volume of reasonable size, an adequate and exhaustive discussion of the calculus in its more advanced stages. It therefore becomes necessary, in planning a thoroughly sound course in the subject, to consider several important aspects of the vast field confronting a modern writer. The limitation of space renders the selection of subject-matter fundamentally dependent upon the aim of the course, which may or may not be related to the content of specific examination syllabuses. Logical development, too, may lead to the inclusion of many topics which, at present, may only be of academic interest, while others, of greater practical value, may have to be omitted. The experience and training of the writer may also have, more or less, a bearing on both these considerations.Advanced CalculusBy Dr. C. A. Stewart. Pp. xviii + 523. (London: Methuen and Co., Ltd., 1940.) 25s.

Advanced Calculus I

This talk will outline a comprehensive set of modeling, analysis and design techniques for a class of mechanical systems. We concern ourselves with simple mechanical control systems, that is, systems whose Lagrangian is kinetic energy minus potential energy. Example devices include robotic manipulators, aerospace and underwater vehicles, and mechanisms that locomote exploiting nonholonomic constraints. Borrowing techniques from nonlinear control and geometric mechanics, we propose a coordinateinvariant control theory for this class of systems. First, we take a Riemannian geometric approach to modeling systems dened on smooth manifolds, subject to nonholonomic constraints, external forces and control forces. We also model mechanical systems on groups and symmetries. Second, we analyze some control-theoretic properties of this class of systems, including controllability, averaged response to oscillatory controls, and kinematic reductions. Finally, we exploit the modeling and analysis results to tackle control design problems. Starting from controllability and kinematic reduction assumptions we propose some algorithms for generating and tracking trajectories.

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Geometric control of mechanical systems

We consider the application of a formulation of passivity-based control (PBC), known as interconnection and damping assignment (IDA) to the problem of stabilization of underactuated mechanical systems, which requires the modification of both the potential and the kinetic energies. Our main contribution is the characterization of a class of systems for which IDA-PBC yields a smooth asymptotically stabilizing controller with a guaranteed domain of attraction. The class is given in terms of solvability of certain partial differential equations. One important feature of IDA-PBC, stemming from its Hamiltonian formulation, is that it provides new degrees of freedom for the solution of these equations. Using this additional freedom, we are able to show that the method of "controlled Lagrangians"-in its original formulation-may be viewed as a special case of our approach. As illustrations we design asymptotically stabilizing IDA-PBCs for the classical ball and beam system and a novel inertia wheel pendulum.

Stabilization of a class of underactuated mechanical systems via interconnection and damping assignment

This is the first of a two-part paper that investigates the stability properties of a system of multiple mobile agents with double integrator dynamics In this first part we generate stable flocking motion for the group using a coordination control scheme which gives rise to smooth control laws for the agents These control laws are a combination of attractive/repulsive and alignment forces, ensuring collision avoidance and cohesion of the group and an aggregate motion along a common heading direction In this control scheme the topology of the control interconnections is fixed and time invariant The control policy ensures that all agents eventually align with each other and have a common heading direction while at the same time avoid collisions and group into a tight formation

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Stable flocking of mobile agents, part I: fixed topology

The purpose of this paper is to show that the method of controlled Lagrangians and
its Hamiltonian counterpart (based on the notion of passivity) are equivalent under rather general
hypotheses. We study the particular case of simple mechanical control systems (where the underlying
Lagrangian is kinetic minus potential energy) subject to controls and external forces in some detail.
The equivalence makes use of almost Poisson structures (Poisson brackets that may fail to satisfy the
Jacobi identity) on the Hamiltonian side, which is the Hamiltonian counterpart of a class of gyroscopic
forces on the Lagrangian side.

https://www.esaim-cocv.org/articles/cocv/pdf/2002/02/Chang.pdf

The equivalence of controlled lagrangian and controlled hamiltonian systems

This paper is concerned with time-optimal path planning for a constant-speed unmanned aerial vehicle flying at constant altitude in steady uniform winds. The unmanned aerial vehicle is modeled as a particle moving at a constant air-relative speed and with symmetric bounds on turn rate. It is known from the necessary conditions for optimality that extremal paths comprise only straight segments and maximum-rate turns. An essential observation is that maximum-rate turns correspond to trochoidal path segments, as observed from an Earth-fixed inertial frame. The path-planning problem therefore reduces to identifying the switching points at which straight and trochoidal path segments join to form a feasible path and choosing the true minimum-time solution from the resulting set of candidate extremals. The paper's primary contribution is a simple analytical solution for a subset of candidate extremal paths: those for which an initial maximum-rate turn is followed by a straight segment and then a second maximum-rate turn in the same direction as the first. The solution is easy to compute and is suitable for real-time implementation onboard an unmanned aerial vehicle with limited computational power. The remaining candidate extremal paths may be found using a simple numerical root-finding routine. The paper also shows that, for some candidate extremal paths, no corresponding Dubins path exists in the (moving) air-relative frame.

Minimum-Time Path Planning for Unmanned Aerial Vehicles in Steady Uniform Winds

This paper describes planar motion modeling for an unmanned surface vehicle (USV), including a comparative evaluation of several experimentally identified models over a wide range of speeds and planing conditions. The modeling and identification objective is to determine a model that is sufficiently rich to enable effective model-based control design and trajectory optimization, sufficiently simple to allow parameter identification, and sufficiently general to describe a variety of hullforms and actuator configurations. We focus, however, on a specific platform: a modified rigid hull inflatable boat with automated throttle and steering. Analysis of experimental results for this vessel indicates that Nomoto's first-order steering model provides the best compromise between simplicity and fidelity at higher speeds. At low speeds, it is helpful to include a first-order lag model for sideslip. Accordingly, we adopt a multiple model approach in which the model structure and parameter values are scheduled based on the nominal forward speed. The speed-scheduled planar motion model may be used to generate dynamically feasible trajectories and to develop trajectory tracking control laws. The paper describes the development, analysis, and experimental implementation of two trajectory tracking control algorithms: a cascade of proportional-derivative controllers and a nonlinear controller obtained through backstepping. Experimental results indicate that the backstepping controller is much more effective at tracking trajectories with highly variable speed and course angle. © 2013 Wiley Periodicals, Inc.

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Modeling, Identification, and Control of an Unmanned Surface Vehicle

This paper describes analysis of steady motions for underwater gliders, a type of highly efficient underwater vehicle which uses gravity for propulsion. Underwater gliders are winged underwater vehicles which locomote by modulating their buoyancy and their attitude. Several underwater gliders have been developed and have proven their worth as efficient long-distance, long-duration ocean sampling platforms. Underwater gliders are so efficient because they spend much of their flight time in stable, steady motion. Wings-level gliding flight for underwater gliders has been well studied, but analysis of steady turning flight is more subtle. This paper presents an approximate analytical expression for steady turning motion for a realistic underwater glider model. The problem is formulated in terms of regular perturbation theory, with the vehicle turn rate as the perturbation parameter. The resulting solution exhibits a special structure that suggests an efficient approach to motion control as well as a planning strategy for energy efficient paths.

Approximate Analytical Turning Conditions for Underwater Gliders: Implications for Motion Control and Path Planning

This paper describes an underwater glider motion control system intended to enhance locomotive efficiency by reducing the energy expended by vehicle guidance. In previous work, the authors derived an approximate analytical expression for steady turning motion by applying regular perturbation theory to a realistic vehicle model. The analysis results suggested the use of a well-known time-optimal path planning procedure developed for the Dubins car, an often-used model of a wheeled mobile robot. For underwater gliders operating at their most efficient flight condition, time-optimal glide paths correspond to energy-optimal glide paths. Thus, an analytically informed strategy for energy-efficient locomotion is to generate sequences of steady wings-level and turning motions according to the Dubins path planning procedure. Because the turning motion results are only approximate, however, and to compensate for model and environmental uncertainty, one must incorporate feedback to ensure convergent path following. This paper describes the dynamic modelling of the complete multi-body control system and the development and numerical implementation of a motion control system. The control system can be combined with a higher level guidance strategy involving Dubins-like paths to achieve energy-efficient locomotion.

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Craig A. Woolsey

Papers

The equivalence of controlled lagrangian and controlled hamiltonian systems

Minimum-Time Path Planning for Unmanned Aerial Vehicles in Steady Uniform Winds

Modeling, Identification, and Control of an Unmanned Surface Vehicle

Approximate Analytical Turning Conditions for Underwater Gliders: Implications for Motion Control and Path Planning

Underwater glider motion control