We now move from discrete to continuous environments but continue to use nondeterministic uncertainty. First, several bug algorithms [504,667,505] are presented, which represent a family of motion plans that solve planning problems using ideas that are related in many ways to the maze exploration ideas of Section 12.3.1. In addition to bug algorithms, the concept of competitive ratios is also briefly covered.
The following model will be used for bug algorithms. Suppose that a point robot is placed into an unknown 2D environment that may contain any finite number of bounded obstacles. It is assumed that the boundary of each obstacle and the outer boundary (if it exists) are piecewise-analytic (here, analytic implies that each piece is smooth and switches its curvature sign only a finite number of times). Thus, the obstacles could be polygons, smooth curves, or some combination of curved and linear parts. The set of possible environments is overwhelming, but it will be managed by avoiding its explicit construction. The robot configuration is characterized by its position and orientation.
There are two main sensors:^{12.2}
Some strategies will now be considered for the robot. Each of these can be considered as an information-feedback plan on a nondeterministic I-space.