MOTION PLANNING FOR MANY DEGREES OF FREEDOM - SEQUENTIAL SEARCH WITH BACKTRACKING

In [7], we presented a sequential framework to develop practical motion planners for manipulator arms with many degrees of freedom. The crux of this framework is to sequentially plan the motion of each link, starting from the base link, thereby solving n single link problems (each of which is solved as a 2-D planning problem) instead of one n-dimensional problem. The solution of each single-link problem is based on the search of a visibility graph (V graph) constructed from a polygonal representation of forbidden regions as seen in successive 2-D t(i) x q(i) spaces. In this paper, we present a backtracking mechanism within this sequential framework to make it more effective in planning collision free paths in cluttered situations. The essence of the backtracking mechanism is based on an edge deletion mechanism that modifies the V graph in t(i-1) x q(i-1) space if no path is found in t(i) x q(i) space. The level of backtracking, b, i.e., the number of links the planner backtracks is an adjustable parameter that can trade off computational speed versus the relative completeness of the planner. Incorporating such a backtracking mechanism has significantly improved the performance of planners developed within this framework. We present extensive experimental results with up to eight degree-of-freedom manipulators in quite cluttered 3-D environments. Although the planner is not complete, our empirical results are very encouraging. These empirical results indicate that b can be chosen small-typically 2 or 3-in over 90% of the cases. These results show that our approach would be useful in practice.