RRT is a motion-planning algorithm that finds a path through complex, high-dimensional spaces by randomly growing a tree of reachable states — the go-to planner for robot arms and self-driving cars where grid search can't cope.
RRT explores by throwing random points into the space and growing a branching tree toward them, quickly reaching into every corner. When the tree touches the goal, you trace back a path — great for arms and cars where a simple grid won't work.
A* is perfect for a 2D grid. But how do you plan a collision-free motion for a 7-joint arm, where the space of configurations has seven dimensions and no natural grid? You sample it — with a Rapidly-exploring Random Tree.
How it grows
RRT builds a tree outward from the start configuration:
Sample a random point in the configuration space.
Find the nearest existing tree node to it.
Extend a small step from that node toward the sample (if the step is collision-free).
Repeat. When the tree reaches the goal region, trace back the branch — that's your path.
The RRT growth loop
Because samples are uniform, the tree is pulled toward large unexplored regions — it 'rapidly explores' the whole space, then connects to the goal.
The magic is a Voronoi bias: random sampling naturally pulls the tree toward the biggest unexplored gaps, so it spreads to fill the space quickly rather than clustering.
Why robots rely on it
RRT scales to high-dimensional, continuous spaces where grid methods explode — robot arms, humanoids, and car-like vehicles with motion constraints. It only needs a collision checker and a way to step between states, not an explicit map of every obstacle. It's the backbone of libraries like OMPL and planners inside MoveIt-style manipulation stacks.
The trade-offs and the sequel
Plain RRT finds a path, not the shortest — the route often looks jagged and needs smoothing. RRT* fixes this: it rewires the tree as it grows and provably converges toward the optimal path, at more compute cost. Variants add goal-biasing, bidirectional search (RRT-Connect), and kinodynamic steering for vehicles that can't move in any direction.
Why it matters
RRT is how robots plan motion when the world is too high-dimensional to enumerate. It, and its optimal cousin RRT*, are the default sampling-based planners in modern robotics.
