Fig 1.
Coordinate systems.
Fig 2.
Motion variables for a marine vessel (SNAME 1950).
Table 1.
The notation of SNAME (1950) for marine vessels.
Fig 3.
AUV body configuration.
Fig 4.
Vessel center point and thrusters allocation.
Fig 5.
Horizontal thrusters geometrical configuration.
Fig 6.
Vertical thrusters geometrical configuration 1.
Fig 7.
Vertical thrusters geometrical configuration 2.
Fig 8.
Gravitational and buoyancy forces acting on center of gravity and center of buoyancy of an underwater vessel.
Fig 9.
Angle of attack and side-slip angle for a marine craft.
Fig 10.
Thruster parts.
Table 2.
DC motor model abbreviations.
Fig 11.
Control system block diagram.
Fig 12.
Continuous-time PID controller block diagram.
Fig 13.
Discrete-time STFPID controller block diagram.
Fig 14.
Fuzzy logic system.
Table 3.
dKp fuzzy rule table.
Table 4.
dKi fuzzy rule table.
Table 5.
dKd fuzzy rule table.
Fig 15.
Inputs membership functions.
Fig 16.
Output membership functions.
Fig 17.
STFPID controller schematic.
Fig 18.
PID.
Fig 19.
Thruster control loop.
Table 6.
System specifications and values used for the simulation.
Table 7.
Velocity controller parameters.
Table 8.
Position controller parameters.
Fig 20.
x-y plan circle trajectory scenario (without disturbances).
The red trajectory is the output from the fuzzy PID controller, the blue trajectory is the output from the PID controller, and the green-dotted line is the reference trajectory.
Fig 21.
x-y plan circle trajectory scenario (with disturbances).
The red line is the output from the fuzzy PID controller, the blue line is the output from the PID controller, and the green-dotted line is the reference.
Fig 22.
Time response of yaw orientation of the x-y plan circle trajectory scenario (without disturbances).
The red line is the fuzzy PID yaw angle output, the blue line is the PID yaw angle output, and the green-dotted line is the reference yaw angle.
Fig 23.
Time response of x-y plan circle trajectory scenario (without disturbances).
The red line is the output from the fuzzy PID controller, the blue line is the output from the PID controller, and the green-dotted line is the reference.
Fig 24.
Time response of x position of the circle trajectory scenario (with disturbances).
The red line is the output from the fuzzy PID controller, the blue line is the output from the PID controller, and the green-dotted line is the reference.
Fig 25.
Disturbance effect in n-frame coordinates.
The sinusoidal blue wave is the noise wave in the current disturbance reference frame. The red waves in the three below figures are the current disturbances in the inertial n-frame axes.
Fig 26.
Disturbance effect in b-frame coordinates.
The disturbances in the body reference frame.
Fig 27.
Attitude control (yaw-pitch-roll sequence).
The red line is the output from the fuzzy PID controller, the blue line is the output from the PID controller, and the green-dotted line is the reference.
Fig 28.
Trajectory following of a Mobius shape trajectory in 3D environment.
The red line is the output from the fuzzy PID controller, the blue line is the output from the PID controller, and the green-dotted line is the reference.
Fig 29.
Time response of the angular velocity about b-frame z-axis in following Mobius trajectory.
The red line is the output from the fuzzy PID controller, the blue line is the output from the PID controller, and the green-dotted line is the reference.
Fig 30.
Time response of the xyz positions of Mobius trajectory.
The red line is the output from the fuzzy PID controller, the blue line is the output from the PID controller, and the green-dotted line is the reference.