Question

When using RRT* for path planning, what feature allows the algorithm to converge toward an optimal path rather than just finding any feasible path?

Accepted Answer

The feature that allows RRT* to converge toward an optimal path is the rewiring process, which is complemented by the neighborhood search mechanism. In standard RRT, once a new node is added to the tree, it remains connected to its parent permanently. RRT* improves on this by performing two distinct steps whenever a new node is added. First, it identifies a set of nearby nodes within a specific radius, called the neighborhood, and selects the parent that provides the lowest cumulative cost from the start to the new node. This is known as the optimal parent selection. Second, RRT* evaluates whether the new node can serve as a more efficient parent for any of its existing neighbors. If connecting a neighbor through the new node results in a lower cost path from the start, RRT* updates that neighbor&#x27;s parent to the new node. This act of changing existing connections to reduce path cost is the rewiring process. By continuously searching for better parents and updating connections throughout the growth of the tree, RRT* ensures that the cumulative cost of paths steadily decreases, eventually converging to the mathematically optimal path as the number of nodes approaches infinity.

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When using RRT* for path planning, what feature allows the algorithm to converge toward an optimal path rather than just finding any feasible path?