Road Map Approach Based on Visibility Graph The road map approach is one of the earliest path-planning methods.. In the visibility graph, The coarse line represents one of these paths..
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© 1999 by CRC Press LLC
The abstract model of the path-planning problem can take different forms depending on the application characteristics It can be in two dimensions or in three dimensions The concern can be the end effector alone or the entire robot arm The end effector can be considered as a solid body or an infinitesimal point Different considerations can have significant implications on the solution methodology and complexity In this handbook, we will only discuss the simplest cases in which a point end effector in two-dimensional space is concerned The readers are referred to Latombe (1991) for more complex procedures
Road Map Approach Based on Visibility Graph
The road map approach is one of the earliest path-planning methods The obstacles are modeled as
polygons, the initial point and the goal point The links of the graphs are straight-line segments that connect a pair of nodes without intersecting with any obstacles A reduced visibility graph for the example
links in terms of distance The elliptical obstacle is approximated by a hexagon In the visibility graph,
The coarse line represents one of these paths The use of the term “semicollision free” is due to the fact the path may actually contact an obstacle It is clear that the path is not unique In the example the
possible paths can be Cinit ACgoal, Cinit BCgoal, or Cinit CDgoal Some offer shorter travel distances while others offer smoother paths This method can be extended to include circular end effector and obstacles which have lines and arcs as boundaries
Road Map Approach Based on Voronoi Diagram
segments of the obstacles and the working envelope and use this graph to generate a collision-free path
A Voronoi diagram is a diagram that consists of lines having equal distance from the adjacent objects Obviously, the Voronoi diagram does not touch the obstacles and can provide collision-free paths A Voronoi diagram in a polygonal space with polygonal obstacles is composed of straight line segments and parabolas When both adjacent object segments are straight lines or vertices, the segment of the Voronoi diagram is a straight line When one object segment is a point while the other is a line segment, the segment of Voronoi diagram is a parabola Two additional links need to be created to connect the
Cinit and Cgoal to the Voronoi diagram Any set of links that connects Cinit and Cgoal through the diagram
represents a collision-free path Unlike the road map approach based on visibility graph, this approach tends to maximize the clearance between the robot and the obstacles For the characteristics and creation
of the Voronoi diagrams, the reader is referred to Okabe et al (1992)
FIGURE 14.8.1 Illustration of path-planning problem.