CONTENTS
The olden days in Robotic field, robot progmming is normally done by either teach-pendant method or robot programming language. But nowadays the more recent technique called Task level programming is used. Here the objective is to plan a path to move a part from a given source position and orientation s to a desired goal position and orientation g in the presence of other parts which are regarded as obstacles.In its general form,the path-planning requires a search in six-dimensional space,because a moving part has three translationlal plus three rotational degrees of freedom.
A fundametal analytical tool for solving motion-planning problems in general is the configuration-space framework.
DEF: Given a mobile part A and an obstacle B, the Configuration Space of A w.r.t. B is the set of all possible configurations of A w.r.t. B.
CONSTRAINTS: Here we restricted ourself to two dimensional objects and translation of mobile part only.
In the above figure triangle A is the mobile robot and rectangle B is an obstacle. We already mentioned in intorduction that A can translate but not rotate. Given a mobile robot A,we choose a reference point r somewhere on the part. To convert to configuration space ,we then shrink the mobile part to its refrence point r while simultaneously growing the obstacles to compensate. In the case of pure translation of the mobile part A,the growth is achieved by sliding part A along the boundary of the obstacle B and tracing out the locus of points traversed by the refrence point r as shown in the following fig.
As triangle A is shrunk to its reference pointr,rectangle B grows intofive sided polygon, C. The enlarged obstacle is called configuration-space obstacle induced by A. When the original polygonal scene in fig1 is redrawn in the configuration space generated by triangel A, the result is shown in the below fig.The robot workspace can be regarded as a hole in a large obstacle . Hence the walls of the workspace have grown inwardby an amount which corresponds to sliding triangle A along the workspace boundary.
The important point to be noted here is that as long as the refrence point of triangle A will not collide with obstacle B.Moreover A and B be the convex polygon convex polygon and C be the configuration-space obstacle generated by Ausing refrence pont r.if nA,nBand nC denote the number of vertices of A,B,and C respectively,then
Steps involved in our algo are as follows.
We have already shown the results of simple example i.e both the polygon inputs are convex in the algorithm itself. Normally Minkowski's Sumis used for finding the config.space, but this works only if the inputs are convex polygons. The primary aim of our project is to find the config.space whatever be the inputs either convex or non convex. The case for non convex also shown in the following figs and also compared with the procedure.
The above fig shows the input (i.e mobile and obstacle) of non convex polygon. /P>
The above fig shows the configuration space for the input of non convex polygon.
DONE BY K.SANTHOSH KUMAR & V.JEYAKUMAR