Instrumentos para la recogida de información

The solution developed in the previous section requires the robots to make very complex motions – motions that are not possible for non-holonomic members of the robot team. In addressing this issue, we first observe that the robots are capable of moving in line abreast formation, and this formation maximizes the coverage of the fleet’s sensors in terms of the BCD algorithm. If we maintain line abreast formation but require the robots to move in their preferred direction, then the resulting motion of the robots within the fleet would be as depicted in Figure3.8. Note that here we have not imposed non-holonomic constraints on any of the robots.

As the mother robot moves the child robots adjust their positions so that their relative position with respect to the mother robots remains unchanged. In this approach, the sensor footprint

f (a) Rc Rc Rm f (b) (c) (d) (e) (f)

Figure 3.8: Line abreast approach without non-holonomic constraint. (a) depicts the fleet

coverage path. (b)depicts the fleet members and their formation (a mother robot in the middle

and two child robots in two sides of mother robot). Dotted circles denote the sensing area of

each robots. (c)-(f)depict the mother and child robots motions in turns considering all robots

a holonomic robot.

does not change as a function of time. In the BCD algorithm, individual cells are swept using back-and-forth motions of the sensor. For forward motions, the combined fleet sweeps out a complex region that is 2nRc + 2Rm wide. Assuming that individual elements of the fleet are holonomic, the process of executing the turning maneuver at the end of a pass is a simple matter

(a) (b)

(c) (d)

Figure 3.9: Fleet coverage with holonomic robots. (a)Boustrophedon cellular decomposition,

the boustrophedon motion in each cell, and the fleet formation. (b)-(d) area covered in grey

by traversing fleet following Eulerian order and path provided in each cell. The boundaries of the environment are dilated such that the robots can move to the absolute boundary of the swept space. Small “holes” may appear at the boundary of obstacles due to the large physical footprint of the combined fleet. Such holes are predictable and identifiable and can be covered

by the mother robot operating in isolation or through some other method.

of moving the entire fleet over one sensor width and then moving down the next row, which is shown are Figure 3.8(c)-(f).

The basic sweep algorithm assumes that the sensor provides a single line of sensory information perpendicular to the direction of travel. Under this model the entire fleet must move to the actual boundary of the space being swept out. Practically, we dilate the boundaries of the environment slightly so that the robots can move to the absolute boundary of the “swept space”. Figure3.9shows a couple of snapshots of the fleet providing coverage of a polygon environment without considering non-holonomic constraints. Figure3.9(a)depicts the BCD, the path should be covered by fleet in each cell, and the primary line abreast formation of the mother and child robots. Here the mother robot is located in the middle as the leader and two child robots are located on either side of the mother robot. In Figure3.9(b)-(d), the area that has been covered

x y (a) x y (b) x y (c)

Figure 3.10: Three potential strategies for steering the non-holonomic child robots along the

ideal path (shown in red). (a)is not desirable in that it will be difficult to ensure good coverage

at the beginning and end of the motion along the y direction to the x direction. (b) has a

similar issue but along the x direction and then along the y direction as the robot moves down

the next leg of the path. Motion like(c)avoids both of these problems although it does require

that there be free space for the robot to move in outside of the region being scanned.

by fleet is painted in grey. Due to the nature of the combined sensor footprint some slight over scanning of some areas is required in order to provide full coverage. Furthermore, if the cells are trapezoidal like the second cell, some other areas are missed as shown in Figure3.9(c). Such regions are easily identified and can be covered later by the mother robot operating on its own. Although the motions presented in Figure3.8and Figure3.9are possible for the mother robot, and this configuration is straightforward in terms of the BCD algorithm as the sweep region remains constant, it is problematic for the child robots. Specifically, it can cause elements of the fleet to execute motions that violate their non-holonomic constraints. As is the case with the mother robot, the child robots are non-holonomic. Unfortunately, unlike the mother robot, the child robots cannot change orientation independently of position. Therefore, an optimized and smooth continuous control trajectory for the child robots is required that takes into account the dynamic constraints of the child robots. Three potential strategies for steering the non-holonomic child robots along the ideal path are shown in Figure 3.10. Figure 3.10(a)

is not desirable in that it will be difficult to ensure good coverage while navigating from along the y direction to the x direction (and vice versa). The strategy described in Figure 3.10(b)

has a similar issue as the robot moves down the next leg of the path. Motion plans like that illustrated in Figure 3.10(c) avoid these problems although it does require that there be free space for the robot to move in outside of the region being scanned. Figure 3.11 illustrates this type of maneuver if we assume the child robots are non-holonomic and the mother robot is capable of holonomic motion. Figure 3.11(b) depicts the fleet members and their formation. Figure 3.11(c)-(f) depicts the mother and child robot motions during turns considering the

f (a) Rc Rc Rm f (b) (c) (d) (e) (f)

Figure 3.11: Line abreast approach with non-holonomic constraints. (a) depicts the fleet

coverage path. (b) depicts the fleet members and their formation (a mother robot in middle

and two child robots in two sides of the mother robot). Dotted circles denote the sensing area of

each robots. (c)-(f)depict the mother and child robots motions in turns considering the mother

D

D

(a) (b)

(c) (d)

Figure 3.12: Fleet coverage with nonholonomic robots. (a)Boustrophedon cellular decompo-

sition, the boustrophedon motion in each cell, and the fleet formation. (b)-(d)area covered in

grey by traversing the fleet following Eulerian order and the path provided in each cell.

mother robot can change orientation independently of position and the child robots as a non- holonomic devices that must move in order to change direction

Using the full turn strategy for the child robots in turning motions requires the presence of a safe area around boundaries and obstacles which its size is determined from the child robot’s safe turning diameter (D). Practically this means that the regions around obstacles and boundaries must be dilated so as to provide sufficient space for the fleet to maneuver. Figure3.12 provides of snapshots of the fleet providing coverage of a polygon environment while incorporating the considering non-holonomic motion constraints associated with the child robots and D = 2Rc. The regions around obstacles have been dilated so as to provide sufficient space for the fleet to maneuver. Figure3.12(a) depicts the BCD, the path that is to be covered by fleet in each cell, and the primary line abreast formation of the mother and child robots. In Figure 3.12(b)-(d), the area that have been covered by fleet are coloured in grey.

One final issue involves insuring that the motion of the mother robot does not intersect the motion of the child robots. If the mother robot executes the same motion trajectory as the child robots then this will be straightforward. Such an approach will also ensure that the fleet remains in close proximity to each other. Another approach is to have the mother robot execute simple rotation/straight line motions while the child robots execute their curved trajectories. The mother robot can then adjust its velocity along its straight line motion paths so that it remains away from the child robots. This is the approach followed in the experiments reported here, but either approach would be appropriate.