This is a typical example in which the RRT planner makes bad choices to extend the tree. In this cases on running the algo's it was found that RRTWeight consistently performs better than both RRT(every run) and RRTGoalBias.one point that was critical in this example was the fact what point was randomly selected at the narrow corridor. If it went into the wrong quadrant(see example for clarity) RRTGoalBias gave a very bad performance.The variation in RRTGoalBias was 58.87 with the worst case taking a time of 63.77. On the other hand RRTWeight had a variation of only 3.08 with the worst case taking a time of 3.91. This example went a long way in convincing me that RRTWeight gives a better performance than RRT and RRTGoalBias. A point worth mentioning here is that intuitively it appears that even RRTWeight should have a case when it gives bad performance on account of going into the 'wrong' quadrent. However,even after repeated runs I was unable to come up with such a case for RRTWeight. This behaviour needs more study.

Given below are the paths computed by the various planners. The paths are nearly the same. What is important is the time taken to arrive at these paths. The edges of the graph given an idea with regards to the time taken to find the path.The edges for the case of RRTWeight and RRTGoalBias have been shown. The average time taken by the various planners was

** RRT-->67.1 RRTGoalBias-->14.39 RRTWeight-->3.35 **

path by RRT

path by RRTGoalBias

edges for RRTGoalBias

path by RRTWeight

edges for RRTWeight