Add example visualizing RRT* (#5214)

### What

Adds an python example that visualizes the RRT* pathfinding algorithm.
There isn't a screenshot of the viewer in the `README.md` yet but it
will be added by linking to the image in this pull request.
I have tested the example in the native viewer in and the web viewer but
I'm not sure if that's what "[ ] I have tested the web demo" means.


![rrt-star-screenshot](https://github.com/rerun-io/rerun/assets/28707703/3bea9efc-4c82-4022-9260-cdec630d3005)

### Checklist
* [x] I have read and agree to [Contributor
Guide](https://github.com/rerun-io/rerun/blob/main/CONTRIBUTING.md) and
the [Code of
Conduct](https://github.com/rerun-io/rerun/blob/main/CODE_OF_CONDUCT.md)
* [x] I've included a screenshot or gif (if applicable)
* [x] I have tested the web demo (if applicable):
* [x] The PR title and labels are set such as to maximize their
usefulness for the next release's CHANGELOG

- [PR Build Summary](https://build.rerun.io/pr/5214)
- [Docs
preview](https://rerun.io/preview/48476971401c69710e7c0ffd1a45b97206d2ef9b/docs)
<!--DOCS-PREVIEW-->
- [Examples
preview](https://rerun.io/preview/48476971401c69710e7c0ffd1a45b97206d2ef9b/examples)
<!--EXAMPLES-PREVIEW-->
- [Recent benchmark results](https://build.rerun.io/graphs/crates.html)
- [Wasm size tracking](https://build.rerun.io/graphs/sizes.html)

.vscode/settings.json

@@ -20,9 +20,11 @@
         "emath",
         "flatbuffers",
         "framebuffer",
+        "Frazzoli",
         "hoverable",
         "ilog",
         "jumpflooding",
+        "Karaman",
         "Keypoint",
         "memoffset",
         "nyud",

docs/cspell.json

@@ -118,6 +118,7 @@
     "flamegraphs",
     "flatbuffers",
     "fname",
+    "Frazzoli",
     "frontmatter",
     "gcloud",
     "Georgios",
@@ -153,6 +154,7 @@
     "Joao",
     "jparismorgan",
     "justfile",
+    "Karaman",
     "keypoint",
     "keypointid",
     "keypoints",

examples/python/requirements.txt

@@ -27,6 +27,7 @@
 -r raw_mesh/requirements.txt
 -r rgbd/requirements.txt
 -r ros_node/requirements.txt
+-r rrt-star/requirements.txt
 -r segment_anything_model/requirements.txt
 -r shared_recording/requirements.txt
 -r signed_distance_fields/requirements.txt

examples/python/rrt-star/README.md

@@ -0,0 +1,26 @@
+<!--[metadata]
+title = "RRT*"
+tags = ["2D"]
+description = "Visualization of the path finding algorithm RRT* in a simple environment."
+thumbnail= "https://static.rerun.io/rrt-star/4d4684a24eab7d5def5768b7c1685d8b1cb2c010/full.png"
+thumbnail_dimensions = [480, 360]
+-->
+
+<picture>
+  <img src="https://static.rerun.io/rrt-star/4d4684a24eab7d5def5768b7c1685d8b1cb2c010/full.png" alt="RRT* example screenshot">
+  <source media="(max-width: 480px)" srcset="https://static.rerun.io/rrt-star/4d4684a24eab7d5def5768b7c1685d8b1cb2c010/480w.png">
+  <source media="(max-width: 768px)" srcset="https://static.rerun.io/rrt-star/4d4684a24eab7d5def5768b7c1685d8b1cb2c010/768w.png">
+  <source media="(max-width: 1024px)" srcset="https://static.rerun.io/rrt-star/4d4684a24eab7d5def5768b7c1685d8b1cb2c010/1024w.png">
+  <source media="(max-width: 1200px)" srcset="https://static.rerun.io/rrt-star/4d4684a24eab7d5def5768b7c1685d8b1cb2c010/1200w.png">
+</picture>
+
+This example visualizes the path finding algorithm RRT\* in a simple environment.
+
+A detailed explanation can be found in the original paper
+Karaman, S. Frazzoli, S. 2011. "Sampling-based algorithms for optimal motion planning".
+or in [this medium article](https://theclassytim.medium.com/robotic-path-planning-rrt-and-rrt-212319121378)
+
+```bash
+pip install -r examples/python/rrt-star/requirements.txt
+python examples/python/rrt-star/main.py
+```

examples/python/rrt-star/main.py

@@ -0,0 +1,306 @@
+#!/usr/bin/env python3
+"""
+Visualizes the path finding algorithm RRT* in a simple environment.
+
+The algorithm finds a path between two points by randomly expanding a tree from the start point.
+After it has added a random edge to the tree it looks at nearby nodes to check if it's faster to
+reach them through this new edge instead, and if so it changes the parent of these nodes.
+This ensures that the algorithm will converge to the optimal path given enough time.
+
+A more detailed explanation can be found in the original paper
+Karaman, S. Frazzoli, S. 2011. "Sampling-based algorithms for optimal motion planning".
+or in the following medium article: https://theclassytim.medium.com/robotic-path-planning-rrt-and-rrt-212319121378
+
+Run:
+```bash
+pip install -r examples/python/rrt-star/requirements.txt
+python examples/python/rrt-star/main.py
+```
+"""
+
+from __future__ import annotations
+
+import argparse
+from typing import Annotated, Generator, Literal
+
+import numpy as np
+import numpy.typing as npt
+import rerun as rr
+
+Point2D = Annotated[npt.NDArray[np.float64], Literal[2]]
+
+
+def distance(point0: Point2D, point1: Point2D) -> float:
+    return float(np.linalg.norm(point0 - point1, 2))
+
+
+def segments_intersect(start0: Point2D, end0: Point2D, start1: Point2D, end1: Point2D) -> bool:
+    """Checks if the segments (start0, end0) and (start1, end1) intersect."""
+    dir0 = end0 - start0
+    dir1 = end1 - start1
+    mat = np.stack([dir0, dir1], axis=1)
+    if abs(np.linalg.det(mat)) <= 0.00001:  # They are close to perpendicular
+        return False
+    s, t = np.linalg.solve(mat, start1 - start0)
+    return (0 <= float(s) <= 1) and (0 <= -float(t) <= 1)
+
+
+def steer(start: Point2D, end: Point2D, radius: float) -> Point2D:
+    """Finds the point in a disc around `start` that is closest to `end`."""
+    dist = distance(start, end)
+    if dist < radius:
+        return end
+    else:
+        diff = end - start
+        direction = diff / np.linalg.norm(diff, 2)
+        return direction * radius + start
+
+
+class Node:
+    parent: Node | None
+    pos: Point2D
+    cost: float
+    children: list[Node]
+
+    def __init__(self, parent: Node | None, position: Point2D, cost: float) -> None:
+        self.parent = parent
+        self.pos = position
+        self.cost = cost
+        self.children = []
+
+    def change_cost(self, delta_cost: float) -> None:
+        """Modifies the cost of this node and all child nodes."""
+        self.cost += delta_cost
+        for child_node in self.children:
+            child_node.change_cost(delta_cost)
+
+
+class RRTTree:
+    root: Node
+
+    def __init__(self, root_pos: Point2D) -> None:
+        self.root = Node(None, root_pos, 0)
+
+    def __iter__(self) -> Generator[Node, None, None]:
+        nxt = [self.root]
+        while len(nxt) >= 1:
+            cur = nxt.pop()
+            yield cur
+            for child in cur.children:
+                nxt.append(child)
+
+    def segments(self) -> list[tuple[Point2D, Point2D]]:
+        """Returns all the edges of the tree."""
+        strips = []
+        for node in self:
+            if node.parent is not None:
+                start = node.pos
+                end = node.parent.pos
+                strips.append((start, end))
+        return strips
+
+    def nearest(self, point: Point2D) -> Node:
+        """Finds the point in the tree that is closest to `point`."""
+        min_dist = distance(point, self.root.pos)
+        closest_node = self.root
+        for node in self:
+            dist = distance(point, node.pos)
+            if dist < min_dist:
+                closest_node = node
+                min_dist = dist
+
+        return closest_node
+
+    def add_node(self, parent: Node, node: Node) -> None:
+        parent.children.append(node)
+        node.parent = parent
+
+    def in_neighborhood(self, point: Point2D, radius: float) -> list[Node]:
+        return [node for node in self if distance(node.pos, point) < radius]
+
+
+class Map:
+    obstacles: list[tuple[Point2D, Point2D]]
+
+    def set_default_map(self) -> None:
+        segments = [
+            ((0, 0), (0, 1)),
+            ((0, 1), (2, 1)),
+            ((2, 1), (2, 0)),
+            ((2, 0), (0, 0)),
+            ((1.0, 0.0), (1.0, 0.65)),
+            ((1.5, 1.0), (1.5, 0.2)),
+            ((0.4, 0.2), (0.4, 0.8)),
+        ]
+        for start, end in segments:
+            self.obstacles.append((np.array(start), np.array(end)))
+
+    def log_obstacles(self, path: str) -> None:
+        rr.log(path, rr.LineStrips2D(self.obstacles))
+
+    def __init__(self) -> None:
+        self.obstacles = []  # List of lines as tuples of  (start, end)
+        self.set_default_map()
+
+    def intersects_obstacle(self, start: Point2D, end: Point2D) -> bool:
+        return not all(
+            not segments_intersect(start, end, obs_start, obs_end) for (obs_start, obs_end) in self.obstacles
+        )
+
+
+def path_to_root(node: Node) -> list[Point2D]:
+    path = [node.pos]
+    cur_node = node
+    while cur_node.parent is not None:
+        cur_node = cur_node.parent
+        path.append(cur_node.pos)
+    return path
+
+
+def rrt(
+    mp: Map,
+    start: Point2D,
+    end: Point2D,
+    max_step_size: float,
+    neighborhood_size: float,
+    num_iter: int | None,
+) -> list[tuple[Point2D, Point2D]] | None:
+    tree = RRTTree(start)
+
+    path = None
+    step = 0  # How many iterations of the algorithm we have done.
+    end_node = None
+    step_found = None
+
+    while (num_iter is not None and step < num_iter) or (step_found is None or step < step_found * 3):
+        random_point = np.multiply(np.random.rand(2), [2, 1])
+        closest_node = tree.nearest(random_point)
+        new_point = steer(closest_node.pos, random_point, max_step_size)
+        intersects_obs = mp.intersects_obstacle(closest_node.pos, new_point)
+
+        step += 1
+        rr.set_time_sequence("step", step)
+        rr.log("map/new/close_nodes", rr.Clear(recursive=False))
+        rr.log(
+            "map/tree/edges",
+            rr.LineStrips2D(tree.segments(), radii=0.0005, colors=[0, 0, 255, 128]),
+        )
+        rr.log(
+            "map/tree/vertices",
+            rr.Points2D([node.pos for node in tree], radii=0.002),
+            # So that we can see the cost at a node by hovering over it.
+            rr.AnyValues(cost=[float(node.cost) for node in tree]),
+        )
+        rr.log("map/new/random_point", rr.Points2D([random_point], radii=0.008))
+        rr.log("map/new/closest_node", rr.Points2D([closest_node.pos], radii=0.008))
+        rr.log("map/new/new_point", rr.Points2D([new_point], radii=0.008))
+
+        color = np.array([0, 255, 0, 255]).astype(np.uint8)
+        if intersects_obs:
+            color = np.array([255, 0, 0, 255]).astype(np.uint8)
+        rr.log(
+            "map/new/new_edge",
+            rr.LineStrips2D([(closest_node.pos, new_point)], colors=[color], radii=0.001),
+        )
+
+        if not intersects_obs:
+            # Searches for the point in a neighborhood that would result in the minimal cost (distance from start).
+            close_nodes = tree.in_neighborhood(new_point, neighborhood_size)
+            rr.log("map/new/close_nodes", rr.Points2D([node.pos for node in close_nodes]))
+
+            min_node = min(
+                filter(
+                    lambda node: not mp.intersects_obstacle(node.pos, new_point),
+                    close_nodes + [closest_node],
+                ),
+                key=lambda node: node.cost + distance(node.pos, new_point),
+            )
+
+            cost = distance(min_node.pos, new_point)
+            added_node = Node(min_node, new_point, cost + min_node.cost)
+            tree.add_node(min_node, added_node)
+
+            # Modifies nearby nodes that would be reached faster by going through `added_node`.
+            for node in close_nodes:
+                cost = added_node.cost + distance(added_node.pos, node.pos)
+                if not mp.intersects_obstacle(new_point, node.pos) and cost < node.cost:
+                    parent = node.parent
+                    if parent is not None:
+                        parent.children.remove(node)
+
+                        node.parent = added_node
+                        node.change_cost(cost - node.cost)
+                        added_node.children.append(node)
+
+            if (
+                distance(new_point, end) < max_step_size
+                and not mp.intersects_obstacle(new_point, end)
+                and end_node is None
+            ):
+                end_node = Node(added_node, end, added_node.cost + distance(new_point, end))
+                tree.add_node(added_node, end_node)
+                step_found = step
+
+            if end_node:
+                # Reconstruct shortest path in tree
+                path = path_to_root(end_node)
+                segments = [(path[i], path[i + 1]) for i in range(len(path) - 1)]
+                rr.log(
+                    "map/path",
+                    rr.LineStrips2D(segments, radii=0.002, colors=[0, 255, 255, 255]),
+                )
+
+    return path
+
+
+def main() -> None:
+    parser = argparse.ArgumentParser(description="Visualization of the path finding algorithm RRT*.")
+    rr.script_add_args(parser)
+    parser.add_argument("--max-step-size", type=float, default=0.1)
+    parser.add_argument("--iterations", type=int, help="How many iterations it should do")
+    args = parser.parse_args()
+    rr.script_setup(args, "")
+
+    max_step_size = args.max_step_size
+    neighborhood_size = max_step_size * 1.5
+
+    start_point = np.array([0.2, 0.5])
+    end_point = np.array([1.8, 0.5])
+
+    rr.set_time_sequence("step", 0)
+    rr.log(
+        "description",
+        rr.TextDocument(
+            """
+Visualizes the path finding algorithm RRT* in a simple environment.
+
+The algorithm finds a [path](recording://map/path) between two points by randomly expanding a [tree](recording://map/tree/edges) from the [start point](recording://map/start).
+After it has added a [random edge](recording://map/new/new_edge) to the tree it looks at [nearby nodes](recording://map/new/close_nodes) to check if it's faster to reach them through this [new edge](recording://map/new/new_edge) instead, and if so it changes the parent of these nodes.
+This ensures that the algorithm will converge to the optimal path given enough time.
+
+A more detailed explanation can be found in the original paper
+Karaman, S. Frazzoli, S. 2011. "Sampling-based algorithms for optimal motion planning".
+or in [this medium article](https://theclassytim.medium.com/robotic-path-planning-rrt-and-rrt-212319121378)
+            """.strip(),
+            media_type=rr.MediaType.MARKDOWN,
+        ),
+    )
+    rr.log(
+        "map/start",
+        rr.Points2D([start_point], radii=0.02, colors=[[255, 255, 255, 255]]),
+    )
+    rr.log(
+        "map/destination",
+        rr.Points2D([end_point], radii=0.02, colors=[[255, 255, 0, 255]]),
+    )
+
+    mp = Map()
+    mp.log_obstacles("map/obstacles")
+
+    __path = rrt(mp, start_point, end_point, max_step_size, neighborhood_size, args.iterations)
+
+    rr.script_teardown(args)
+
+
+if __name__ == "__main__":
+    main()

examples/python/rrt-star/requirements.txt

@@ -0,0 +1,2 @@
+numpy
+rerun-sdk