PRM
Sample random configurations. Connect to k nearest if collision-free. Query: connect start/goal, run Dijkstra.
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RRT
Tree from start. Repeatedly: random sample, extend tree toward sample by δ. Reach goal.
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RRT*
RRT with rewiring: optimize path length in tree as new samples arrive. Asymptotically optimal.
Complexity
Depends on sample count. Empirically fast in high dimensions where grid-based planners fail.