Roger Skjetne

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.

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.

Nonlinear formation control of marine craft

This paper investigates formation control of a fleet of ships. The control objective for each ship is to maintain its position in the formation while a (virtual) Formation Reference Point (FRP) tracks a predefined path. This is obtained by using vectorial backstepping to solve two subproblems; a geometric task, and a dynamic task. The former guarantees that the FRP, and thus the formation, tracks the path, while the latter ensures accurate speed control along the path. A dynamic guidance system with feedback from the states of all ships ensures that all ships have the same priority (no leader) when moving along the path. Lyapunov stability is proven and robustness to input saturation is demonstrated using computer simulations.

Nonlinear maneuvering and control of ships

We address the problem of maneuvering ships onto curves or paths in the plane. To do this, we introduce the Serret-Frenet equations and show how these fit the scope for control design with 3 degrees-of-freedom (DOF) hydrodynamic ship models in the loop. The Davidson and Schiff (1946) linear parametrically varying ship model is used in the design, and we show how we can manipulate this by introducing acceleration feedback and by moving the body-frame freely. This simplifies the control design in such a way that we do not have to deal with zero-dynamics. Instead we use a 3-step backstepping design and theory for interconnecting subsystems. Real data from a 175 m container ship is used in a computer simulation to validate the design.

Nonlinear formation control of marine craft with experimental results

Decentralized formation control schemes for a fleet of vessels with a small amount of intervessel communication are proposed and investigated. The control objective for each vessel is to maintain its position in the formation relative to a formation reference point, which follows a predefined path. This is done by constructing an individual parametrized path for each vessel so that when the parametrization variables are synchronized, the vessels are in formation. To obtain this, an individual maneuvering problem is solved for each vessel, with an extension of a synchronization feedback function in the dynamic control laws to ensure that the vessels stay assembled in the desired formation. This setup assures that all vessels will have the same priority, i.e. no leader. Performance and theoretical results are validated by experiments for a scaled model ship and a computer simulated ship in a marine control laboratory.

Formation control by synchronizing multiple Maneuvering systems

Abstract This paper investigates formation control of a fleet of vessels with a small amount of intervessel communication. The control objective for each vessel is to maintain its position in the formation. This is obtained by constructing individual parametrized paths for each vessel so that when the parametrization variables are synchronized, the vessels are in formation. Then, vectorial backstepping is used to solve an individual maneuvering problem for each vessel with the extension of a synchronization term in the resulting dynamic controllers to ensure that the vessels keep assembled in the desired formation.

Output maneuvering for a class of nonlinear systems

Abstract The output maneuvering problem involves two tasks. The first, which is the geometric task, is to force the output to converge to a desired path parametrized by a continuous scalar variable θ. The second task is to satisfy a desired speed assignment along the path. The main concern is to satisfy the geometric task. However, the speed assignment will ensure that the output follows the path with sufficient speed. A recursive control design technique is developed for nonlinear plants in vectorial strict feedback form of any relative degree. First the geometric part of the problem is solved. Then an update law is constructed that bridges the geometric design with the speed assignment. An extra degree of freedom is provided for an operator to specify the speed θ. A computer simulation with a marine vessel is performed to illustrate the design.

Particle Filter for Fault Diagnosis and Robust Navigation of Underwater Robot

A particle filter (PF)-based robust navigation with fault diagnosis (FD) is designed for an underwater robot, where 10 failure modes of sensors and thrusters are considered. The nominal underwater robot and its anomaly are described by a switching-mode hidden Markov model. By extensively running a PF on the model, the FD and robust navigation are achieved. Closed-loop full-scale experimental results show that the proposed method is robust, can diagnose faults effectively, and can provide good state estimation even in cases where multiple faults occur. Comparing with other methods, the proposed method can diagnose all faults within a single structure, it can diagnose simultaneous faults, and it is easily implemented.

Nonlinear maneuvering with gradient optimization

The maneuvering problem involves two tasks. The first one, called the geometric task, is to force the system states to converge to a desired parametrized path. The second task, called the dynamic task, is to satisfy a desired dynamic behavior along the path. The desired geometric path /spl xi/ is viewed as a target set /spl Xi/ which is parametrized by a scalar variable /spl theta/. The proposed dynamic controller consists of a stabilization algorithm that drives the state x(t) to the point /spl xi/(/spl theta/(t)), and a smooth dynamic optimization algorithm that selects the point /spl xi/(/spl theta/) in the set /spl Xi/ that minimizes the weighted distance between x and /spl xi/. Choosing a gain /spl mu/ large in the optimization algorithm, induces a two-time scale behavior or a closed-loop plant. In the fast time-scale /spl theta/(t) rapidly converges to the minimizer, and in the slow time-scale x(t) converges to /spl Xi/. Two motivational examples illustrate the design and the achieved performance of the closed-loop.