Another way to utilize the approximate path is to use iterative pushing. The basic idea is to first solve a simpler version of the original problem (one may do this, for example, by shrinking the robot), and then use the resulting solution path as an `approximate path' input for the harder problem. The process can be applied iteratively until the original version of the problem is solved. This approach can potentially take much less time, since at each iteration, the input approximate path is very close to a valid solution path. That is, since only small penetrations occur the pushing methods described above should be able to quickly and easily push the path to the free space.
The initial input path could be haptically generated, or simply one found by an automatic planner. However, the success of this approach depends very much on the quality of the input path, which must be continuously deformable to a valid path for the original problem. It is here where the user's insight is crucial, and is another reason that we believe incorporating the strengths of both a human operator and an automatic planner is useful.
This approach is similar to the idea of building a roadmap in a dilated freespace [11]. The main difference is that we concentrate only on a select path, which is close (or at least hopefully deformable) to a valid path for the original problem. That is, we are focused exclusively on the important regions of the free space.