In the past, ship steering systems were based on gyrocompass measurements to control ship heading. As new measurements become available, as well as the knowledge of advanced nonlinear control techniques, it became possible to perform much more complicated maneuvers by automatic control. This has increased the functionality and reliability of commercially available automatic ship navigation systems. Maneuvering a ship along a desired path is the present challenge.

Ship Steering Systems

Maneuvering a craft, vehicle or vessel means that there are two coupled tasks to be performed to achieve the desired motion. The first is a geometric task stated in terms of a desired curve or path to be followed; the second is a dynamic task given as a desired

speed or, perhaps, acceleration along the path. For a ship in transit, the desired path will be some feasible curve connecting the departure point and the destination. This must be coupled to a dynamic objective which, perhaps, is to keep a constant desired cruise speed or, more advanced, a speed profile along the path constructed by optimizing fuel economy versus time constraints.

History of Automatic Ship Steering

Automatic steering of ships started with the invention of the gyrocompass. Based on the earlier developed gyroscope, Dr. Anschutz-Kaempfe patented the first north-seeking gyrocompass in 1908. This work attracted considerable attention from engineers around the world. In the same year, Elmer Sperry introduced the first ballistic gyrocompass, which was patented in 1911.1,2,3 Soon thereafter, Sperry designed an automatic pilot, the gyropilot, for automatic steering of ships. This was first commercially available in 1922. It had been christened "Metal Mike" by the officers of the ship Moffett. The performance of Metal-Mike seemed uncanny to many because it seemed to have had built into it the intuition of an experienced helmsman.2

The gyropilot, today known as a conventional autopilot, is a single-- input, single-output (SISO) control system where the heading, measured by the gyrocompass, is regulated to a desired heading by corrective action of the rudder. In spite of the relatively simple ship model the autopilot controller is based on, it has had great success for many years. However, the introduction of new measurement systems, in particular the global positioning system (GPS), and the need to perform more advanced maneuvers with a ship, motivated creative thinking that opened new possibilities and directions of research. Preeminently, this resulted in dynamic positioning (DP) systems, which were first designed in the 1960s by three decoupled proportional-integral-derivative (PID) controllers.

A DP system is a multiple-input, multiple-output (MIMO) control system where three degrees of freedom (3DOF)-surge, sway and yaw-are controlled by a number of azimuth and tunnel thrusters. The model-based DP controller uses an advanced nonlinear hydrodynamic ship model, derived from first principles, which is simplified to a linear model for almost zero speed applications. Building on the extensive theory generated by the DP research community, the research on ship steering is now going in the direction of high-- speed tracking of desired moving position.9 This leads to the theory of maneuvering that, as briefly explained, incorporates a desired feasible path to be followed and a desired speed along it.4,5,6,7

Maneuvering a Ship

In a conventional waypoint tracking system, only the heading is controlled to take the ship from one waypoint to the next, perhaps using a line-of-sight (LOS) algorithm. The easiest way to make this problem into a path following problem is to connect the straightline segments between the waypoints by inscribed circles. Indeed, as pointed out by numerous authors, the shortest distance connecting two points consists of only straight lines and circular arc segments. However, such a path is not feasible for a ship, since at the point where the path switches from a straight line to a circular segment, the desired yaw rate would jump from zero to a non-zero constant. A feasible path (and perhaps optimal in some sense) between two points must be a curve that, in mathematical terms, is at least twice differentiable.

Feasibility of the path is a property of each ship, its minimum turning radius and its dynamic response. Excluding the shape of the path, in the process of control design, the objective in the maneuvering problem is:7

* a geometric task, forcing the ship to converge to and follow the desired path

* a dynamic task, making the ship move at a desired velocity, either determined by a speed profile along the path, or by inputs from the pilot. The desired heading will ideally be pointed along the tangent vector of the path, but it can also be adjusted by an offset to compensate for ocean currents or weather forces in order to facilitate weather optimal maneuvering.

speed or, perhaps, acceleration along the path. For a ship in transit, the desired path will be some feasible curve connecting the departure point and the destination. This must be coupled to a dynamic objective which, perhaps, is to keep a constant desired cruise speed or, more advanced, a speed profile along the path constructed by optimizing fuel economy versus time constraints.

History of Automatic Ship Steering

Automatic steering of ships started with the invention of the gyrocompass. Based on the earlier developed gyroscope, Dr. Anschutz-Kaempfe patented the first north-seeking gyrocompass in 1908. This work attracted considerable attention from engineers around the world. In the same year, Elmer Sperry introduced the first ballistic gyrocompass, which was patented in 1911.1,2,3 Soon thereafter, Sperry designed an automatic pilot, the gyropilot, for automatic steering of ships. This was first commercially available in 1922. It had been christened "Metal Mike" by the officers of the ship Moffett. The performance of Metal-Mike seemed uncanny to many because it seemed to have had built into it the intuition of an experienced helmsman.2

The gyropilot, today known as a conventional autopilot, is a single-- input, single-output (SISO) control system where the heading, measured by the gyrocompass, is regulated to a desired heading by corrective action of the rudder. In spite of the relatively simple ship model the autopilot controller is based on, it has had great success for many years. However, the introduction of new measurement systems, in particular the global positioning system (GPS), and the need to perform more advanced maneuvers with a ship, motivated creative thinking that opened new possibilities and directions of research. Preeminently, this resulted in dynamic positioning (DP) systems, which were first designed in the 1960s by three decoupled proportional-integral-derivative (PID) controllers.

A DP system is a multiple-input, multiple-output (MIMO) control system where three degrees of freedom (3DOF)-surge, sway and yaw-are controlled by a number of azimuth and tunnel thrusters. The model-based DP controller uses an advanced nonlinear hydrodynamic ship model, derived from first principles, which is simplified to a linear model for almost zero speed applications. Building on the extensive theory generated by the DP research community, the research on ship steering is now going in the direction of high-- speed tracking of desired moving position.9 This leads to the theory of maneuvering that, as briefly explained, incorporates a desired feasible path to be followed and a desired speed along it.4,5,6,7

Maneuvering a Ship

In a conventional waypoint tracking system, only the heading is controlled to take the ship from one waypoint to the next, perhaps using a line-of-sight (LOS) algorithm. The easiest way to make this problem into a path following problem is to connect the straightline segments between the waypoints by inscribed circles. Indeed, as pointed out by numerous authors, the shortest distance connecting two points consists of only straight lines and circular arc segments. However, such a path is not feasible for a ship, since at the point where the path switches from a straight line to a circular segment, the desired yaw rate would jump from zero to a non-zero constant. A feasible path (and perhaps optimal in some sense) between two points must be a curve that, in mathematical terms, is at least twice differentiable.

Feasibility of the path is a property of each ship, its minimum turning radius and its dynamic response. Excluding the shape of the path, in the process of control design, the objective in the maneuvering problem is:7

* a geometric task, forcing the ship to converge to and follow the desired path

* a dynamic task, making the ship move at a desired velocity, either determined by a speed profile along the path, or by inputs from the pilot. The desired heading will ideally be pointed along the tangent vector of the path, but it can also be adjusted by an offset to compensate for ocean currents or weather forces in order to facilitate weather optimal maneuvering.

Numerous applications arise in this setup: cruising, docking or formation (fleet) maneuvering, to name a few.

Model-Based Control

Since maneuvering means controlling both position and heading (3DOF), present control theory requires that at least three actuators produce force/moment in all degrees of freedom. However, by decomposing the position vectors in the Serret-- Frenet frame,4 it is possible to use only the rudder to eliminate the cross-track deviation from the path, as well as to keep the desired heading. The main propeller will independently ensure a desired surge velocity along the path.

Dynamic Ship Model

Model-Based Control

Since maneuvering means controlling both position and heading (3DOF), present control theory requires that at least three actuators produce force/moment in all degrees of freedom. However, by decomposing the position vectors in the Serret-- Frenet frame,4 it is possible to use only the rudder to eliminate the cross-track deviation from the path, as well as to keep the desired heading. The main propeller will independently ensure a desired surge velocity along the path.

Dynamic Ship Model

In autopilot designs, usually a linear first or second order Nomoto model1 relating the rudder command to the yaw mode is used with a PID controller to regulate the heading to a reference. In maneuvering applications, the position should also be controlled, and this necessitates a more complex nonlinear model since, as opposed to DP, the simplification to a linear hydrodynamic model of the ship is not valid at higher speeds (except for the special case where the heading and cruise speed are kept constant). In fact, the maneuvering model will include both Coriolis and centripetal forces and nonlinear damping terms.

A general ship model" consists of a kinematics equation and a dynamic equation derived from rigid-body dynamics and hydrodynamic forces. The main complications of this model in high speed are:

* The system inertia matrix is non-- symmetrical and depends, among others, on the wave dynamics and frequency of encounter.

* No unified representation of the damping forces has been agreed upon. It is also unclear how to represent shallow water and close boundary effects with respect to this model.

* The mapping between the actuators, that is, the propeller revolutions and pitch angle, the rudder angle, etc., and the forces/moment they produce is special to each ship. Hence, control allocation on a case-by-case basis is necessary.

In addition to these complications, the components form equations given by the kinematics and dynamic equations that are very messy and, therefore, make component form analysis very hard.

If for each desired force/moment vector in surge, sway and yaw there exists an actuator setting that will produce that vector value, then the ship is fully actuated. On the other hand, if there exist force/moment values (within a neighborhood of the operating point) that cannot be produced by the actuator system, then the ship is under actuated. For 3DOF maneuvering, we say, for simplicity, that the ship is fully actuated if it has three or more controls and under-actuated if there are fewer.

Some Proposed Methods

A good method for solving the maneuvering problem for fully actuated ships and vessels has recently been proposed.6 Research on using the same method for under-actuated ships is currently in progress.10 However, solving the maneuvering problem by applying the Serret-Frenet equations11 is also a promising method and has been demonstrated.4,5

A general ship model" consists of a kinematics equation and a dynamic equation derived from rigid-body dynamics and hydrodynamic forces. The main complications of this model in high speed are:

* The system inertia matrix is non-- symmetrical and depends, among others, on the wave dynamics and frequency of encounter.

* No unified representation of the damping forces has been agreed upon. It is also unclear how to represent shallow water and close boundary effects with respect to this model.

* The mapping between the actuators, that is, the propeller revolutions and pitch angle, the rudder angle, etc., and the forces/moment they produce is special to each ship. Hence, control allocation on a case-by-case basis is necessary.

In addition to these complications, the components form equations given by the kinematics and dynamic equations that are very messy and, therefore, make component form analysis very hard.

If for each desired force/moment vector in surge, sway and yaw there exists an actuator setting that will produce that vector value, then the ship is fully actuated. On the other hand, if there exist force/moment values (within a neighborhood of the operating point) that cannot be produced by the actuator system, then the ship is under actuated. For 3DOF maneuvering, we say, for simplicity, that the ship is fully actuated if it has three or more controls and under-actuated if there are fewer.

Some Proposed Methods

A good method for solving the maneuvering problem for fully actuated ships and vessels has recently been proposed.6 Research on using the same method for under-actuated ships is currently in progress.10 However, solving the maneuvering problem by applying the Serret-Frenet equations11 is also a promising method and has been demonstrated.4,5

A reasonable assumption on the dynamic model is that the ship is portstarboard symmetric, which implies that the surge mode is decoupled from the sway and yaw modes. In this case, an independent control system can keep the ship at a constant desired surge velocity by using the main propeller. This implies that the state (velocity) can be treated as a constant in the sway and yaw modes, which is under the assumption that some terms in the mathematics are small compared to others, thus the model becomes a linear parametrically varying (LPV) model. This is the basis for the design in reference 4 (nonlinear maneuvering and control), where the LPV maneuvering model of Davidson and Schiff represents the sway/yaw dynamics. Therefore, the setup is given a desired feasible path, the cross-track and heading deviations are decomposed in the Serret-Frenet frame. Then, the objectives are that the surge velocity is kept constant by some decoupled control system, and the rudder is used to regulate the cross-track deviation to zero while keeping the ship at the desired heading along the path.

The result is that the under-actuated ship moves along the path with its preferred speed.

In reference 6, the authors presented a nonlinear control design for the second objective, which included an estimator to deal with ocean currents. The model they used was not the Davidson and Schiff model, which was the basis for the design in reference 5. Here, the authors had to resort to both acceleration feedback and output redefinition to solve the same objective. In spite of the preliminary nature of these designs, they both indicate promising ideas towards the goal of a good, robust and reliable maneuvering controller that can be implemented industrially.

Future Challenge

Offshore operators have recently expressed a need for ship and vessel control systems which make it possible to do offshore operations in extreme weather situations. Examples are station-keeping in higher sea states, helicopter landing on ship decks in extreme weather, ROV operations in large waves and robust maneuvering systems in extreme weather. This work must be rooted in both physical modeling, preferably based on first principles, control design and an extensive experimental testing to validate the models and the closed-loop maneuvering performance.12

At present, work is underway to identify and understand the hydrodynamic phenomena that occur in the ship model as sea state increases. Once sufficient ship models have been established and agreed upon, the control engineers need to design robust maneuvering systems that can handle such extreme conditions. Presently, knowledge, we are maneuvering ourselves on the path toward this goal. /st/

In reference 6, the authors presented a nonlinear control design for the second objective, which included an estimator to deal with ocean currents. The model they used was not the Davidson and Schiff model, which was the basis for the design in reference 5. Here, the authors had to resort to both acceleration feedback and output redefinition to solve the same objective. In spite of the preliminary nature of these designs, they both indicate promising ideas towards the goal of a good, robust and reliable maneuvering controller that can be implemented industrially.

Future Challenge

Offshore operators have recently expressed a need for ship and vessel control systems which make it possible to do offshore operations in extreme weather situations. Examples are station-keeping in higher sea states, helicopter landing on ship decks in extreme weather, ROV operations in large waves and robust maneuvering systems in extreme weather. This work must be rooted in both physical modeling, preferably based on first principles, control design and an extensive experimental testing to validate the models and the closed-loop maneuvering performance.12

At present, work is underway to identify and understand the hydrodynamic phenomena that occur in the ship model as sea state increases. Once sufficient ship models have been established and agreed upon, the control engineers need to design robust maneuvering systems that can handle such extreme conditions. Presently, knowledge, we are maneuvering ourselves on the path toward this goal. /st/

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