RRT* Motion Planning in 2D — Informed Sampling

RRT and RRT* are sampling-based motion-planning algorithms that solve "find a route from start to goal through obstacles" in continuous space without ever building a grid. This simulator grows the search tree in a flat 2D configuration space scattered with circular obstacles: each iteration samples a random point, connects the tree's nearest node toward it with a fixed step, and rejects the extension if it collides. In RRT* mode two extra passes run every iteration — choosing the cheapest nearby parent for the new node, then rewiring any neighbour that would get cheaper by routing through it — visibly straightening the tree as more iterations run. Because the configuration space is 2D, once a first path exists the planner can restrict further sampling to the Informed-RRT* ellipse — the set of points whose combined distance to start and goal cannot exceed the current best path cost — which is exactly the optimization real 2D path planners for warehouse robots and mobile platforms use to converge fast instead of continuing to waste samples on regions that could never shorten the route.