AUV guidance system

A typical AUV chemical plume tracing system includes an adaptive mission planner (AMP) that rapidly responds to the sensor inputs to generate a trajectory for the AUV to trace the plume. Because the AUV has velocity (<2 m/ sec) and heading rate (<10 degree/sec) constraints and the vehicle navigation system has navigation fixes (The vehicle is performing dead-reckoning based on acoustic Doppler data with periodic navigation updates based on data from a long baseline acoustic buoy transponder system. The position updates to the dead-reckoned position based on the LBL data are referred to as navigation fixes), a guidance system is necessary for the AUV to generate heading and speed commands within the constraints to achieve the trajectory desired by the AMP. "Guidance is the action of determining the course, attitude and speed of the vehicle, relative to some reference frame, to be followed by the vehicle" (Fossen, 1994). For the chemical signal guided AUV, the guidance system combined with the AMP decides the best trajectory to be followed by the AUV based on the chemical information and vehicle capability. Although many guidance systems exist for use on the land and air vehicles, there are few, if any systems designed for AUVs (Naeem et al., 2003).

The AUV guidance system is divided into four guidance modes: Go To Point mode, Follow Line mode, Go To Point with Heading mode, and Cage mode. The Go To Point mode is used to drive the AUV from its present location to a destination, without regard to the heading at the destination location. The Follow Line mode is used to track a straight line. The Go To Point with Heading mode is to drive the AUV from a start position and orientation angle to a destination position and orientation angle with the constraint that desired trajectory cannot violate a prespecified minimum turning circle. The Cage mode prevents the vehicle from leaving the operating area or return the vehicle to the operating area if it has left the operating area. To ensure the outputs of the guidance system do not violate the heading rate constraint, the heading commands are filtered before they are sent to the vehicle control unit. In any of these modes, the guidance function will output depth/altitude and earth relative velocity (geographic heading and speed) commands that are within the velocity and heading rate constraints of the AUV. For accurate implementation of the desired trajectory, the guidance system should compensate these commands for the flow vector to produce water relative speed uc and ground relative heading commands :

where Vf = (uf, vf, Wf) is the water relative AUV velocity, Vg is the ground relative AUV velocity, and Fg is the ground relative flow vector. A superscript indicates a coordinate frame: "t" for geodetic tangent frame or "b" for body frame. The components of vector V'

4.1 Go to point

This mode is used to drive the vehicle from its present location to a destination, without regard to the heading at the destination location, e.g., initialize the plume search from a desired point, go to next search region after the vehicle finish searching in the current region, or return to home location after the vehicle finish its mission.

When the guidance system is in Go To Point mode, the output of the system is the geographic heading command

and a constant speed command

where (x(t), y(t)) is the current vehicle position, (xd yd) is the destination location, and v is a predefined constant speed. Note, the heading angle ^ e [0, 360] is defined in degrees and goes clockwise. When the vehicle is within a radius R of the destination location,

where R is a predefine value, it is considered to have arrived at the destination location and the guidance system will exit from the Go To Point mode.

This mode is the most robust mode in our guidance system. Because unlike the other modes in our guidance system, the vehicle does not try to follow a precalculated trajectory, instead it calculates its trajectory based on the real time vehicle location information. Therefore, when we have navigation fixes and curvature constrains during the vehicle traveling, the vehicle trajectory is modified accordingly.

4.2 Follow line

Sometimes the vehicle needs to track a straight line, e.g. the vehicle doing a lawn mower search, or the vehicle doing a side scan maneuver after it declares the source location. Given two locations (xs, ys) and (xd, yd) in the OpArea, we can get a line segment Lsd which starts from point (xs, ys) and ends at point (xd yd). The Follow Line mode will generate a set of heading and speed commands which will make the vehicle follow the line Lsd. The first step to achieve follow line mode is to drive the vehicle to approach the start point (xs, ys) while ensuring that the vehicle heading f upon arrival at the start of the line is about the same as the line orientation angle, ad = arctanf yd ~ y* 1 . (7)

xd xs

Here we cannot use Go To Point mode, because it cannot satisfy the heading condition. So we design a new mode Go To Point with Heading to achieve this work. This mode will be discussed later. When the vehicle is within radius R of the start point and within heading angle 0of osa, the vehicle will begin to follow the line. The corresponding heading command is asd +K x d d < d! (8)

where d is the signed distance between the vehicle current position P(t) = (x(t), y(t)) and the line Lsd, K is a predefined gain, di = 45/K, and the sign function is defined f 1 x > 0 (9)

Note, the distance d is positive when the vehicle is on the left side of the line Lsd (when looking from the start point (xs, ys) to the destination point (xd, yd)), and negative when the vehicle is on the right side of the line.

The exit condition for this mode is different from Go To Point mode. In Go To Point mode, we exit the mode when the vehicle is within a radius R of the destination location. Here in the Follow Line mode, we can still use this condition. However, since there are some navigation fixes during the vehicle traveling, the vehicle trajectory is not continuous; it contains some jumps in the trajectory. These jumps may happen near the destination point, therefore the vehicle may jump over the destination point without being within radius R, and it will continue following the line until it hits the edge of the OpArea. To prevent this, we need to add one additional exit condition for this mode. When the vehicle pass the destination point in the direction of the line for more than RL meters we suppose that the vehicle has finished the follow line mode and it exits from this mode. That is, if

where vector V = [x-xd, y-yd], and h = [cos(asd); sin(asd)] is a unit vector in the direction of the line, then we exit from the follow line mode.

Fig. 3 shows an example of follow line mode. The vehicle is start from position Pi(xj, y1). Go To Point with Heading function drives the vehicle to the position P2(xs, ys), which is within a radius R of the start position (xs, ys) with heading error less than 15 degrees. Then, the vehicle will follow the line based on the heading command defined in equation (8) until either condition (6) or condition (10) is satisfied.

4.3 Go to point with heading

The goal of this mode is to drive the AUV from a start position and orientation angle to a destination position and orientation angle with the constraint that desired trajectory cannot violate a prespecified minimum turning circle. This guidance mode is significantly more complicated than it first appears. It was proved by Dubins (Dubins, 1957) that this trajectory consists of exactly three path segments. It is either a sequence of CCC or CSC, where C (circle) is an arc of minimal turning radius Rm and S (straight line) is a line segment. In our application, we only use the CSC trajectory. Even though the CSC trajectory sometimes is not the shortest path, it is easy to generate this trajectory, thereby saving computation resources.

(XsTys)

Fig. 3. Definition of variables for the Follow Line mode.

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