RRT* is the optimal version of the RRT motion planner — it rewires its search tree as it grows so the path it finds converges toward the shortest one, combining sampling-based flexibility with quality.
RRT* is a smarter version of RRT. Plain RRT finds *a* path; RRT* keeps improving it as it explores, reconnecting branches so the route gets shorter and smoother, converging toward the best possible path.
Plain RRT is great at finding a path through complex, high-dimensional spaces — but the path it finds is often jagged and far from shortest. RRT* fixes that, keeping RRT's flexibility while converging toward the optimal path.
What it adds
RRT* grows a tree by random sampling just like RRT, but adds a crucial rewiring step every time it adds a node:
Sample and extend toward a new point (as in RRT).
Choose the best parent — connect the new node to whichever nearby node gives it the lowest cost-to-reach, not just the nearest.
Rewire — check nearby existing nodes and, if routing them through the new node would be cheaper, reconnect them.
Over time this constant local improvement makes the whole tree's paths shorter and smoother.
Grow, then rewire for quality
The extra 'choose best parent + rewire' steps continually shorten paths, so RRT*'s solution improves toward optimal the longer it runs.
Asymptotic optimality
The key property: RRT* is asymptotically optimal — given enough samples, its path converges to the true shortest path. Plain RRT has no such guarantee; it just finds some feasible path. This makes RRT* the go-to when path quality matters, not just feasibility.
The trade-off
More computation. The rewiring and best-parent search cost more per sample than RRT, so RRT* is slower to a first solution.
Anytime behavior. But it's an anytime planner — it returns a valid path quickly and keeps improving it if given more time, which suits many robots (act on the current best, refine as you go).
Variants (Informed RRT*, RRT#, BIT*) speed up convergence by focusing sampling where it helps.
Where it fits
RRT — fast, feasible-path planning in high dimensions (arms, cars).
RRT* — when you also want a good (near-optimal) path.
A* — optimal on discrete grids/graphs; RRT* is its spirit for continuous, high-dimensional spaces.
PRM — sampling-based, better for repeated queries in a fixed space.
Why it matters
RRT* answered a key question in motion planning: can sampling-based planners give optimal paths, not just feasible ones? Its rewiring idea and asymptotic optimality made it a foundational algorithm for high-quality motion planning of arms, drones, and vehicles in complex spaces.
