12.3.3 Planning in Unknown Continuous Environments

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 $ E$ 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

  1. A goal sensor indicates the current Euclidean distance to the goal and the direction to the goal, expressed with respect to an absolute ``north.''
  2. A local visibility sensor provides the exact shape of the boundary within a small distance from the robot. The robot must be in contact or almost in contact to observe part of the boundary; otherwise, the sensor provides no useful information.
The goal sensor essentially encodes the robot's position in polar coordinates (the goal is the origin). Therefore, unique $ (x,y)$ coordinates can be assigned to any position visited by the robot. This enables it to incrementally trace out obstacle boundaries that it has already traversed. The local visibility sensor provides just enough information to allow wall-following motions; the range of the sensor is very short so that the robot cannot learn anything more about the structure of the environment.

Figure 12.20: An illustration of the Bug1 strategy.
\begin{figure}\centerline{\psfig{figure=figs/bug1.eps,width=5.0in} }\end{figure}

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.

Steven M LaValle 2012-04-20