Kristin Ytterstad Pettersen

Tracking control of an underactuated ship

In this paper, we address the tracking problem for an underactuated ship using two controls, namely surge force and yaw moment. A simple state-feedback control law is developed and proved to render the tracking error dynamics globally K- exponentially stable. Experimental results are presented where the controller is implemented on a scale model of an offshore supply vessel.

Underactuated ship tracking control : theory and experiments

We consider complete state tracking feedback control of a ship having two controls, namely surge force and yaw moment. The ship model has similarities with chained form systems but cannot directly be transformed in chained form. In particular, the model has a drift vector field as opposed to the drift-free chained form systems. It is shown here that methods developed for tracking control of chained form systems still can be used for developing a tracking control law for the ship. Through a coordinate transformation the model is put in a triangular-like form which makes it possible to use integrator backstepping to develop a tracking control law. The control law steers both the position variables and the course angle of the ship, providing exponential stability of the reference trajectory. Experimental results are presented where the control law is implemented for tracking control of a model of an offshore supply vessel, scale 1:70. In the experiments the ship converges exponentially to a neighbourhood of the reference trajectory, and stays close with errors depending on factors as unmodelled dynamics, parameter uncertainty, measurement noise, thruster saturation, waves, currents and position measurement failures.

Exponential stabilization of an underactuated surface vessel

The paper shows that a large class of underactuated vehicles cannot be asymptotically stabilized by either continuous nor discontinuous state feedback. Furthermore, stabilization of an underactuated surface vessel is considered. Controllability properties of the surface vessel is presented, and a continuous periodic time-varying feedback law is proposed. It is shown that this feedback law exponentially stabilizes the surface vessel to the origin, and this is illustrated by simulations.

Way-point tracking control of ships

The paper considers way-point tracking control of ships using yaw torque control. A full state feedback control law is developed using a cascaded approach, and proved to globally asymptotically stabilize the heading and the cross-track error of the ship. Simulation results are presented.

Snake Robot Obstacle-Aided Locomotion: Modeling, Simulations, and Experiments

Snakes utilize irregularities in the terrain, such as rocks and vegetation, for faster and more efficient locomotion. This motivates the development of snake robots that actively use the terrain for locomotion, i.e., obstacle-aided locomotion. In order to accurately model and understand this phenomenon, this paper presents a novel nonsmooth (hybrid) mathematical model for wheel-less snake robots, which allows the snake robot to push against external obstacles apart from a flat ground. The framework of nonsmooth dynamics and convex analysis allows us to systematically and accurately incorporate both unilateral contact forces (from the obstacles) and isotropic friction forces based on Coulombs law using set-valued force laws. The mathematical model is verified through experiments. In particular, a back-to-back comparison between numerical simulations and experimental results is presented. It is, furthermore, shown that the snake robot is able to move forward faster and more robustly by exploiting obstacles.

A survey on snake robot modeling and locomotion

Snake robots have the potential to make substantial contributions in areas such as rescue missions, firefighting, and maintenance where it may either be too narrow or too dangerous for personnel to operate. During the last 10–15 years, the published literature on snake robots has increased significantly. The purpose of this paper is to give a survey of the various mathematical models and motion patterns presented for snake robots. Both purely kinematic models and models including dynamics are investigated. Moreover, the different approaches to biologically inspired locomotion and artificially generated motion patterns for snake robots are discussed.

Global practical stabilization and tracking for an underactuated ship : a combined averaging and backstepping approach

We solve both the global practical stabilization and tracking problem for an underactuated ship, using a combined integrator backstepping and averaging approach. Exponential convergence to an arbitrarily small neighbourhood of the origin and of the reference trajectory, respectively, is proved. Simulation results are included.

Time-varying exponential stabilization of the position and attitude of an underactuated autonomous underwater vehicle

The paper considers feedback stabilization of the position and attitude of an autonomous underwater vehicle (AUV) with a reduced number of actuators. A nonlinear model describing both the dynamics and the kinematics of an AUV is studied. The paper shows that previous results on attitude stabilization of a spacecraft can be applied to exponentially stabilize both the position and attitude of an AUV using only four, possibly three, actuators. Simulation results are presented.

Straight Line Path Following for Formations of Underactuated Marine Surface Vessels

The problem of formation control and path following for underactuated 3-degrees-of-freedom (3-DOF) marine surface vessels is considered. The proposed decentralized controller makes the vessels asymptotically constitute a desired formation that follows a given straight line path with a given forward speed profile. The controller consists of a cross-track control law, based on line-of-sight guidance, and a nonlinear synchronization control law. The closed-loop dynamics of both the cross-track errors and the synchronization errors are analyzed in detail using nonlinear cascaded systems theory and the overall cascaded system is shown to be both uniformly globally asymptotically stable and uniformly globally exponentially stable under mild assumptions. The proposed control strategy is validated in experiments in both calm water and in waves using a scale model vessel.

Underactuated dynamic positioning of a ship-experimental results

The paper considers the dynamic positioning problem for a ship having only two independent controls, namely surge force and yaw moment. A time-varying feedback control law including integral action is developed and proved to exponentially stabilize both the North and East positions and the orientation of the ship. Experimental results are presented were the controller is implemented on a model ship, scale 1:70, of an offshore supply vessel. The experiments show that the ship converge to a neighborhood of the desired position and orientation, oscillating about stationary errors, and that with integral action in the control law these stationary errors are reduced.