#### Using range data

The VisBug [666] and TangentBug [505,592] strategies incorporate distance measurements made by a range or visibility sensor to improve the efficiency. The TangentBug strategy will be described here and is illustrated in Figure 12.24. Suppose that in addition to the sensors described previously, it is also equipped with a sensor that produces measurements as shown in Figure 12.25. The strategy is as follows:

1. Move toward the goal, either through the interior of the space or by wall following, until it is realized that the robot is trapped in a local minimum or the goal is reached. This is similar to the gradient-descent motion of the potential-field planner of Section 5.4.3. If the goal is reached, then stop; otherwise, go to the next step.
2. Execute motions along the boundary. First, pick a direction by comparing the previous heading to the goal direction. While moving along the boundary, keep track of two distances: and . The distance is the minimal distance from the goal, observed while traveling along the boundary. The distance is the length of the shortest path from the current position to the goal, assuming that the only obstacles are those visible by the range sensor. The robot stops following the boundary if . In this case, go to Step 1. If the robot loops around the entire obstacle without this condition occurring, then the algorithm reports that the goal is not reachable.
A one-parameter family of TangentBug algorithms can be made by setting a depth limit for the range sensor. As the maximum depth is decreased, the robot becomes more short-sighted and performance degrades. It is shown in [505] that the distance traveled is no greater than

 (12.27)

in which is the number of local minima for the th obstacle and is the initial distance to the goal. The bound is taken over obstacles, which are assumed to intersect a disc of radius , centered at the goal (all others can be ignored). A variant of the TangentBug, called WedgeBug, was developed in [592] for planetary rovers that have a limited field of view.

Steven M LaValle 2012-04-20