Thor I. Fossen

Passive nonlinear observer design for ships using lyapunov methods: full-scale experiments with a supply vessel

Dynamic positioning (DP) and tracking systems for ships are usually designed under the assumption that the kinematic equations can be linearized about a set of predefined constant yaw angles, typically 36 operating points in steps of 10^o, to cover the whole heading envelope. This is necessary when applying linear (Kalman filter)theory and gain scheduling techniques. However, global exponential stability (GES) cannot be guaranteed if linear theory is used. In this paper a nonlinear observer is derived. The observer is proven to be passive and GES. The number of tuning parameters is reduced to a minimum by using passivity theory. This results in a simple and intuitive tuning procedure. The proposed observer includes features like estimation of both the low-frequency position and velocity of the ship from noisy position measurements, bias state estimation (environmental disturbances) and wave filtering. The nonlinear passive observer has been simulated on a computer model of a supply vessel and implemented on full-scale ships with excellent results.

Control allocation—A survey

Abstract The control algorithm hierarchy of motion control for over-actuated mechanical systems with a redundant set of effectors and actuators commonly includes three levels. First, a high-level motion control algorithm commands a vector of virtual control efforts (i.e. forces and moments) in order to meet the overall motion control objectives. Second, a control allocation algorithm coordinates the different effectors such that they together produce the desired virtual control efforts, if possible. Third, low-level control algorithms may be used to control each individual effector via its actuators. Control allocation offers the advantage of a modular design where the high-level motion control algorithm can be designed without detailed knowledge about the effectors and actuators. Important issues such as input saturation and rate constraints, actuator and effector fault tolerance, and meeting secondary objectives such as power efficiency and tear-and-wear minimization are handled within the control allocation algorithm. The objective of the present paper is to survey control allocation algorithms, motivated by the rapidly growing range of applications that have expanded from the aerospace and maritime industries, where control allocation has its roots, to automotive, mechatronics, and other industries. The survey classifies the different algorithms according to two main classes based on the use of linear or nonlinear models, respectively. The presence of physical constraints (e.g input saturation and rate constraints), operational constraints and secondary objectives makes optimization-based design a powerful approach. The simplest formulations allow explicit solutions to be computed using numerical linear algebra in combination with some logic and engineering solutions, while the more challenging formulations with nonlinear models or complex constraints and objectives call for iterative numerical optimization procedures. Experiences using the different methods in aerospace, maritime, automotive and other application areas are discussed. The paper ends with some perspectives on new applications and theoretical challenges.

Robust output maneuvering for a class of nonlinear systems

The output maneuvering problem involves two tasks. The first, called the geometric task, is to force the system output to converge to a desired path parametrized by a continuous scalar variable @q. The second task, called the dynamic task, is to satisfy a desired dynamic behavior along the path. This dynamic behavior is further specified via a time, speed, or acceleration assignment. While the main concern is to satisfy the geometric task, the dynamic task ensures that the system output follows the path with the desired speed. A robust recursive design technique is developed for uncertain nonlinear plants in vectorial strict feedback form. First the geometric part of the problem is solved. Then an update law is constructed that bridges the geometric design with the speed assignment. The design procedure is illustrated through several examples.

Nonlinear output feedback control of dynamically positioned ships using vectorial observer backstepping

Dynamic positioning (DP) systems for ships are usually designed under the assumption that the kinematic equations be linearized about a constant yaw angle such that linear and gain scheduling techniques can be applied. This paper proposes a globally exponentially stable (GES) nonlinear control where this assumption is removed. A nonlinear observer is included in the design such that only position measurements are required. GES is proven by applying the backstepping design methodology and Lyapunov stability theory. The control law is simulated on two thruster-controlled ships.

Constrained nonlinear control allocation with singularity avoidance using sequential quadratic programming

Control allocation problems can be formulated as optimization problems, where the objective is typically to minimize the use of control effort (or power) subject to actuator rate and position constraints, and other operational constraints. Here we consider the additional objective of singularity avoidance, which is essential to avoid loss of controllability in some applications, leading to a nonconvex nonlinear program. We suggest a sequential quadratic programming approach, solving at each sample a convex quadratic program approximating the nonlinear program. The method is illustrated by simulated maneuvers for a marine vessel equipped with azimuth thrusters. The example indicates reduced power consumption and increased maneuverability as a consequence of the singularity-avoidance.

Line-of-Sight Path Following of Underactuated Marine Craft

Abstract A 3 degrees of freedom (surge, sway, and yaw) nonlinear controller for path following of marine craft using only two controls is derived using nonlinear control theory. Path following is achieved by a geometric assignment based on a line-of-sight projection algorithm for minimization of the cross-track error to the path. The desired speed along the path can be specified independently. The control laws in surge and yaw are derived using backstepping. This results in a dynamic feedback controller where the dynamics of the uncontrolled sway mode enters the yaw control law. UGAS is proven for the tracking error dynamics in surge and yaw while the controller dynamics is bounded. A case study involving an experiment with a model ship is included to demonstrate the performance of the controller and guidance systems.

Adaptive maneuvering, with experiments, for a model ship in a marine control laboratory

The maneuvering problem involves two tasks. The first, called the geometric task, is to force the system output to converge to a desired path continuously parametrized by a scalar @q. The second task, called the dynamic task, is to satisfy a desired dynamic behavior along the path. In this paper, this dynamic behavior is further specified as a speed assignment for @q(t). While the main concern is to satisfy the geometric task, the dynamic task ensures that the system output follows the path with the desired speed. An adaptive recursive design technique is developed for a parametrically uncertain nonlinear plant describing the dynamics of a ship. First the geometric part of the problem is solved. Then an update law is constructed that bridges the geometric design with the dynamic task. The design procedure is performed and tested by several experiments for a model ship in a marine control laboratory.

DESIGN OF A DYNAMIC POSITIONING SYSTEM USING MODEL-BASED CONTROL

Abstract A dynamic positioning (DP) system includes different control functions for the automatic positioning and guidance of marine vessels by means of thruster and propeller actions. This paper describes the control functions which provide station-keeping and tracking. The DP controller is a model-based control design, where a new modified LQG feedback controller and a model reference feedforward controller are applied. A reference model calculates appropriate reference trajectories. Since it is not desirable, nor even possible, to counteract the wave-frequency movement caused by first-order wave loads, the control action of the propulsion system should be produced by the low-frequency part of the vessel movement caused by current, wind and second-order mean and slowly varying wave loads. A Kalman-filter-based state estimator and a Luenberger observer are used to compute the low-frequency feedback and feedforward control signals. Full-scale experiments with a multipurpose supply ship demonstrate the performance of the proposed controller.

Vehicle velocity estimation using nonlinear observers

Nonlinear observers for estimation of lateral and longitudinal velocity of automotive vehicles are proposed. The observers are based on a sensor suite that is standard in many new cars, consisting of acceleration and yaw rate measurements in addition to wheel speed and steering angle measurements. Two approaches are considered: first, a modular approach where the estimated longitudinal velocity is used as input to the observer for lateral velocity, and second, a combined approach where all states are estimated in the same observer. Both approaches use a tire-road friction model, which is assumed to be known. It is also assumed that the road is flat. Stability of the observers is proven in the form of input-to-state stability of the observer error dynamics, under a structural assumption on the friction model. The assumption on the friction model is discussed in detail, and the observers are validated on experimental data from cars.

Passivity-based designs for synchronized path-following

We consider a formation control system where individual systems are controlled by a path-following design and the path variables are to be synchronized. We first show a passivity property for the path following system and, next, combine this with a passivity-based synchronization algorithm developed in Arcak, M. (2006), The passivity approach expands the classes of synchronization schemes available to the designer. This generality offers the possibility to optimize controllers to, e.g., improve robustness and performance. Two designs are developed in the proposed passivity framework: The first employs the path error information in the synchronization loop, while the second only uses synchronization errors. A sampled-data design, where the path variables are updated in discrete-time and the path following controllers are updated in continuous time, is also developed