From f88c77c21788d32a01e83d2e33c0e156157d92e3 Mon Sep 17 00:00:00 2001 From: Erwin Lejeune Date: Mon, 9 Feb 2026 15:37:33 +0400 Subject: [PATCH 01/10] add Elastic Bands path planner component A* seed path optimised with Elastic Bands (Quinlan & Khatib, 1993): bubble chain with contraction/repulsive forces, SDF-based obstacle distance, and overlap maintenance. --- .../elastic_bands_path_planner.py | 489 ++++++++++++++++++ 1 file changed, 489 insertions(+) create mode 100644 src/components/plan/elastic_bands/elastic_bands_path_planner.py diff --git a/src/components/plan/elastic_bands/elastic_bands_path_planner.py b/src/components/plan/elastic_bands/elastic_bands_path_planner.py new file mode 100644 index 00000000..c54c43af --- /dev/null +++ b/src/components/plan/elastic_bands/elastic_bands_path_planner.py @@ -0,0 +1,489 @@ +""" +elastic_bands_path_planner.py + +Elastic Bands path planner. + +Uses A* to find an initial path on an occupancy grid, then smooths it +with the Elastic Bands algorithm (Quinlan & Khatib, 1993). + +Each waypoint is wrapped in a "bubble" whose radius equals the distance +to the nearest obstacle (from a signed-distance field). Internal +contraction forces pull the band taut while external repulsive forces +push it away from obstacles. An overlap constraint maintains connectivity +by inserting / deleting bubbles as needed. + +Reference: + Elastic Bands: Connecting Path Planning and Control + http://www8.cs.umu.se/research/ifor/dl/Control/elastic%20bands.pdf + +Author: Wang Zheng (@Aglargil), adapted to project architecture +""" + +import numpy as np +import heapq +import json +import matplotlib.pyplot as plt +import matplotlib.animation as anm +import sys +from pathlib import Path +from matplotlib.colors import ListedColormap +from matplotlib.patches import Circle +from scipy.ndimage import distance_transform_edt + +abs_dir_path = str(Path(__file__).absolute().parent) +relative_path = "/../../../components/" +relative_simulations = "/../../../simulations/" + +sys.path.append(abs_dir_path + relative_path + "visualization") +sys.path.append(abs_dir_path + relative_path + "state") +sys.path.append(abs_dir_path + relative_path + "obstacle") +sys.path.append(abs_dir_path + relative_path + "mapping/grid") + +from min_max import MinMax # noqa: E402 + + +# --------------------------------------------------------------------------- +# Bubble +# --------------------------------------------------------------------------- + +class _Bubble: + """A single bubble in the elastic band.""" + + MAX_RADIUS = 100.0 + MIN_RADIUS = 0.5 + + def __init__(self, position, radius): + self.pos = np.array(position, dtype=float) + self.radius = float(np.clip(radius, self.MIN_RADIUS, self.MAX_RADIUS)) + + +# --------------------------------------------------------------------------- +# Core Elastic Bands optimiser (grid-index space) +# --------------------------------------------------------------------------- + +class _ElasticBandsOptimiser: + """ + Operates entirely in **grid-index** space. + + Parameters + ---------- + initial_path : list[tuple[int,int]] + Waypoints as (col, row) grid indices. + sdf : np.ndarray + Signed-distance field (in grid cells) — same shape as the grid. + ``sdf[row, col]`` gives the distance to the nearest obstacle. + rho0 : float + Maximum distance for applying repulsive force. + kc, kr : float + Contraction / repulsive force gains. + lambda_ : float + Overlap constraint factor. + step_size : float + Finite-difference step for SDF gradient. + max_iter : int + Maximum optimisation iterations. + """ + + def __init__(self, initial_path, sdf, *, + rho0=20.0, kc=0.05, kr=-0.1, lambda_=0.7, + step_size=3.0, max_iter=60): + self.sdf = sdf + self.rows, self.cols = sdf.shape + self.rho0 = rho0 + self.kc = kc + self.kr = kr + self.lambda_ = lambda_ + self.step_size = step_size + self.max_iter = max_iter + + # Build initial bubble chain + self.bubbles = [ + _Bubble(p, self._rho(p)) for p in initial_path + ] + self._maintain_overlap() + + # Snapshot history for animation (list of bubble-chain snapshots) + self.history: list[list[_Bubble]] = [self._snapshot()] + + # -- SDF helpers ------------------------------------------------------- + + def _rho(self, pos): + """Distance to nearest obstacle at *pos* (col, row).""" + c, r = int(round(pos[0])), int(round(pos[1])) + c = np.clip(c, 0, self.cols - 1) + r = np.clip(r, 0, self.rows - 1) + return float(self.sdf[r, c]) + + # -- Forces ------------------------------------------------------------ + + def _contraction_force(self, i): + if i == 0 or i == len(self.bubbles) - 1: + return np.zeros(2) + prev = self.bubbles[i - 1].pos + nxt = self.bubbles[i + 1].pos + cur = self.bubbles[i].pos + d_prev = prev - cur + d_next = nxt - cur + n_prev = np.linalg.norm(d_prev) + 1e-9 + n_next = np.linalg.norm(d_next) + 1e-9 + return self.kc * (d_prev / n_prev + d_next / n_next) + + def _repulsive_force(self, i): + b = self.bubbles[i].pos + rho = self.bubbles[i].radius + if rho >= self.rho0: + return np.zeros(2) + h = self.step_size + dx = np.array([h, 0.0]) + dy = np.array([0.0, h]) + grad_x = (self._rho(b - dx) - self._rho(b + dx)) / (2 * h) + grad_y = (self._rho(b - dy) - self._rho(b + dy)) / (2 * h) + grad = np.array([grad_x, grad_y]) + return self.kr * (self.rho0 - rho) * grad + + # -- Update step ------------------------------------------------------- + + def _update_bubbles(self): + new = [] + for i, bub in enumerate(self.bubbles): + if i == 0 or i == len(self.bubbles) - 1: + new.append(bub) + continue + f_total = self._contraction_force(i) + self._repulsive_force(i) + v = self.bubbles[i - 1].pos - self.bubbles[i + 1].pos + v_norm2 = np.dot(v, v) + 1e-9 + # Remove tangential component (project onto normal) + f_star = f_total - (np.dot(f_total, v) / v_norm2) * v + alpha = bub.radius # adaptive step + new_pos = bub.pos + alpha * f_star + new_pos[0] = np.clip(new_pos[0], 0, self.cols - 1) + new_pos[1] = np.clip(new_pos[1], 0, self.rows - 1) + new.append(_Bubble(new_pos, self._rho(new_pos))) + self.bubbles = new + + # -- Overlap maintenance ----------------------------------------------- + + def _maintain_overlap(self): + # Insert + i = 0 + while i < len(self.bubbles) - 1: + bi, bj = self.bubbles[i], self.bubbles[i + 1] + dist = np.linalg.norm(bi.pos - bj.pos) + if dist > self.lambda_ * (bi.radius + bj.radius): + mid = (bi.pos + bj.pos) / 2 + self.bubbles.insert(i + 1, _Bubble(mid, self._rho(mid))) + i += 2 + else: + i += 1 + # Delete redundant + i = 1 + while i < len(self.bubbles) - 1: + prev, nxt = self.bubbles[i - 1], self.bubbles[i + 1] + if np.linalg.norm(prev.pos - nxt.pos) <= self.lambda_ * (prev.radius + nxt.radius): + del self.bubbles[i] + else: + i += 1 + + # -- Snapshot ---------------------------------------------------------- + + def _snapshot(self): + return [_Bubble(b.pos.copy(), b.radius) for b in self.bubbles] + + # -- Run --------------------------------------------------------------- + + def optimise(self): + """Run the full optimisation loop, recording history.""" + for _ in range(self.max_iter): + self._update_bubbles() + self._maintain_overlap() + self.history.append(self._snapshot()) + + +# --------------------------------------------------------------------------- +# Public planner (follows project API) +# --------------------------------------------------------------------------- + +class ElasticBandsPathPlanner: + """ + Elastic Bands path planner operating on a 2-D occupancy grid. + + 1. Loads the grid and computes a signed-distance field. + 2. Runs A* to obtain an initial path. + 3. Optimises the path with the Elastic Bands algorithm. + 4. Optionally saves a search/optimisation GIF. + + Constructor parameters match the project convention used by + ``AStarPathPlanner``, ``DijkstraPathPlanner``, etc. + """ + + def __init__(self, start, goal, map_file, *, + x_lim=None, y_lim=None, + path_filename=None, gif_name=None, + max_iter=60): + self.start = start + self.goal = goal + self.explored_nodes = [] + + # Load grid + self.grid = self._load_grid(map_file) + x_min, x_max = x_lim.min_value(), x_lim.max_value() + y_min, y_max = y_lim.min_value(), y_lim.max_value() + self.resolution = (x_max - x_min) / self.grid.shape[1] + self.x_range = np.arange(x_min, x_max, self.resolution) + self.y_range = np.arange(y_min, y_max, self.resolution) + self.rows, self.cols = self.grid.shape + + # SDF: distance (in cells) to nearest obstacle for every free cell + obstacle_mask = (self.grid >= 0.99) + self.sdf = distance_transform_edt(~obstacle_mask) + + # A* initial path + self.path = [] + self._astar_path = self._astar_search() + if not self._astar_path: + print("Elastic Bands: A* found no initial path.") + return + + # Elastic bands optimisation + self._optimiser = _ElasticBandsOptimiser( + self._astar_path, self.sdf, max_iter=max_iter, + ) + self._optimiser.optimise() + + # Final smoothed path (grid indices) + self.path = [(int(round(b.pos[0])), int(round(b.pos[1]))) + for b in self._optimiser.bubbles] + + # Save sparse path + if path_filename: + sparse = self._make_sparse_path(self.path) + self._save_path(sparse, path_filename) + + # Visualise + self.visualize_search(gif_name) + + # -- Grid I/O ---------------------------------------------------------- + + @staticmethod + def _load_grid(file_path): + ext = Path(file_path).suffix + if ext == '.npy': + return np.load(file_path) + if ext == '.png': + g = plt.imread(file_path) + if g.ndim == 3: + g = np.mean(g, axis=2) + return (g > 0.5).astype(float) + if ext == '.json': + with open(file_path, 'r') as f: + return np.array(json.load(f)) + raise ValueError(f"Unsupported grid format: {ext}") + + # -- A* seed path ------------------------------------------------------ + + def _astar_search(self): + """Run A* on the grid, return path as list of (col, row) tuples.""" + sx = int((self.start[0] - self.x_range[0]) / self.resolution) + sy = int((self.start[1] - self.y_range[0]) / self.resolution) + gx = int((self.goal[0] - self.x_range[0]) / self.resolution) + gy = int((self.goal[1] - self.y_range[0]) / self.resolution) + start_idx = (sx, sy) + goal_idx = (gx, gy) + + print(f"Elastic Bands — A* seed Start(grid): {start_idx}, " + f"Goal(grid): {goal_idx}") + + open_list = [] + heapq.heappush(open_list, (0, start_idx)) + came_from = {} + cost = {start_idx: 0} + + while open_list: + _, current = heapq.heappop(open_list) + self.explored_nodes.append(current) + if current == goal_idx: + return self._reconstruct(came_from, start_idx, goal_idx) + for dx, dy in [(-1, 0), (1, 0), (0, -1), (0, 1), + (1, 1), (-1, -1), (1, -1), (-1, 1)]: + nb = (current[0] + dx, current[1] + dy) + if not (0 <= nb[0] < self.cols and 0 <= nb[1] < self.rows): + continue + if self.grid[nb[1], nb[0]] >= 0.99: + continue + step = 1.414 if (dx != 0 and dy != 0) else 1.0 + nc = cost[current] + step + if nb not in cost or nc < cost[nb]: + cost[nb] = nc + h = ((nb[0] - gx) ** 2 + (nb[1] - gy) ** 2) ** 0.5 + heapq.heappush(open_list, (nc + h, nb)) + came_from[nb] = current + return [] + + @staticmethod + def _reconstruct(came_from, start, goal): + path, cur = [], goal + while cur != start: + path.append(cur) + cur = came_from[cur] + path.append(start) + return path[::-1] + + # -- Path utilities ---------------------------------------------------- + + def _grid_to_world(self, node): + return (self.x_range[0] + node[0] * self.resolution, + self.y_range[0] + node[1] * self.resolution) + + def _make_sparse_path(self, path, num_points=20): + if len(path) <= num_points: + return [self._grid_to_world(p) for p in path] + indices = np.linspace(0, len(path) - 1, num_points, dtype=int) + return [self._grid_to_world(path[i]) for i in indices] + + def _save_path(self, path, filename): + Path(filename).parent.mkdir(parents=True, exist_ok=True) + with open(filename, 'w') as f: + json.dump([list(p) for p in path], f) + + # -- Visualisation ----------------------------------------------------- + + def visualize_search(self, gif_name=None): + """Render a GIF showing A* search → initial path → EB optimisation.""" + if gif_name is None: + return + if not self._astar_path: + return + + history = self._optimiser.history + explored = self.explored_nodes + + # Sub-sample phases + max_search = 80 + step_s = max(1, len(explored) // max_search) + search_frames = list(range(0, len(explored), step_s)) + if search_frames[-1] != len(explored) - 1: + search_frames.append(len(explored) - 1) + + max_opt = 60 + step_o = max(1, len(history) // max_opt) + opt_indices = list(range(0, len(history), step_o)) + if opt_indices[-1] != len(history) - 1: + opt_indices.append(len(history) - 1) + + path_draw_frames = 20 + hold_frames = 15 + + total = (len(search_frames) + path_draw_frames + hold_frames + + len(opt_indices) + hold_frames) + offsets = np.cumsum([0, len(search_frames), path_draw_frames, + hold_frames, len(opt_indices), hold_frames]) + + def _phase(i): + for p in range(5): + if i < offsets[p + 1]: + return p, i - int(offsets[p]) + return 4, hold_frames - 1 + + # Colour map + cmap = ListedColormap([ + [1.0, 1.0, 1.0], # 0 free + [0.4, 0.8, 1.0], # 1 explored + [0.0, 0.8, 0.0], # 2 A* path + [0.78, 0.78, 0.78], # 3 old path (greyed) + [0.5, 0.5, 0.5], # 4 clearance + [0.0, 0.0, 0.0], # 5 obstacle + ]) + + base_grid = self.grid.copy() + + def _disc(d): + out = np.zeros_like(d, dtype=int) + out[d == 0] = 0 + out[np.isclose(d, 0.25)] = 1 + out[np.isclose(d, 0.5)] = 2 + out[np.isclose(d, 0.6)] = 3 + out[np.isclose(d, 0.75)] = 4 + out[d >= 0.99] = 5 + return out + + def _paint(disp, cells, val): + for gx, gy in cells: + if 0 <= gx < disp.shape[1] and 0 <= gy < disp.shape[0]: + if disp[gy, gx] < 0.99: + disp[gy, gx] = val + + titles = [ + lambda l: f"A* Initial Search ({search_frames[min(l, len(search_frames)-1)]+1}/{len(explored)})", + lambda _: "Initial Path Found (A*)", + lambda _: "Initial Path Found (A*)", + lambda l: f"Elastic Bands Optimisation ({min(l+1, len(opt_indices))}/{len(opt_indices)})", + lambda _: "Elastic Bands — Optimised Path", + ] + + def update(i, ax): + phase, local = _phase(i) + disp = base_grid.copy() + + if phase == 0: + idx = search_frames[min(local, len(search_frames) - 1)] + _paint(disp, explored[:idx + 1], 0.25) + elif phase == 1: + _paint(disp, explored, 0.25) + frac = min(local + 1, path_draw_frames) + n = max(1, int(len(self._astar_path) * frac / path_draw_frames)) + _paint(disp, self._astar_path[:n], 0.5) + elif phase == 2: + _paint(disp, explored, 0.25) + _paint(disp, self._astar_path, 0.5) + elif phase == 3: + # Grey out the A* path, show EB iteration + _paint(disp, explored, 0.25) + _paint(disp, self._astar_path, 0.6) + snap = history[opt_indices[min(local, len(opt_indices) - 1)]] + eb_cells = [(int(round(b.pos[0])), int(round(b.pos[1]))) + for b in snap] + _paint(disp, eb_cells, 0.5) + else: + _paint(disp, explored, 0.25) + _paint(disp, self._astar_path, 0.6) + _paint(disp, self.path, 0.5) + + ax.clear() + ax.imshow(_disc(disp), + extent=[self.x_range[0], self.x_range[-1], + self.y_range[0], self.y_range[-1]], + origin='lower', cmap=cmap, vmin=0, vmax=5, alpha=0.85) + ax.plot(self.start[0], self.start[1], 'go', markersize=8, label="Start") + ax.plot(self.goal[0], self.goal[1], 'ro', markersize=8, label="Goal") + + # Draw bubbles during optimisation phase + if phase >= 3: + snap = (history[opt_indices[min(local, len(opt_indices) - 1)]] + if phase == 3 else self._optimiser.bubbles) + for bub in snap: + wx = self.x_range[0] + bub.pos[0] * self.resolution + wy = self.y_range[0] + bub.pos[1] * self.resolution + r_world = bub.radius * self.resolution + circ = Circle((wx, wy), r_world, fill=False, + color='green', alpha=0.25, linewidth=0.5) + ax.add_patch(circ) + + ax.set_title(titles[phase](local), fontsize=14) + ax.legend(loc='upper left') + + fig = plt.figure(figsize=(10, 8)) + ax = fig.add_subplot(111) + ax.set_aspect("equal") + ax.set_xlabel("X [m]", fontsize=15) + ax.set_ylabel("Y [m]", fontsize=15) + + print(f"Elastic Bands search animation: {total} frames") + anime = anm.FuncAnimation(fig, update, fargs=(ax,), + frames=total, interval=30, repeat=False) + try: + anime.save(gif_name, writer="pillow", fps=20) + print(f"Search GIF saved to {gif_name}") + except Exception as e: + print(f"Error saving search GIF: {e}") + plt.clf() + plt.close() From cc7d54b03e03a09e7f7da8a8b8b8e96bd2e0071d Mon Sep 17 00:00:00 2001 From: Erwin Lejeune Date: Mon, 9 Feb 2026 15:37:42 +0400 Subject: [PATCH 02/10] add Elastic Bands path planning simulation --- .../elastic_bands_path_planning.py | 112 ++++++++++++++++++ 1 file changed, 112 insertions(+) create mode 100644 src/simulations/path_planning/elastic_bands_path_planning/elastic_bands_path_planning.py diff --git a/src/simulations/path_planning/elastic_bands_path_planning/elastic_bands_path_planning.py b/src/simulations/path_planning/elastic_bands_path_planning/elastic_bands_path_planning.py new file mode 100644 index 00000000..8cf6463e --- /dev/null +++ b/src/simulations/path_planning/elastic_bands_path_planning/elastic_bands_path_planning.py @@ -0,0 +1,112 @@ +""" +elastic_bands_path_planning.py + +Simulation that demonstrates Elastic Bands path smoothing. + +Two GIFs are produced: + 1. **elastic_bands_search.gif** – grid animation: A* initial search, + initial path, then iterative elastic-bands optimisation with bubbles. + 2. **elastic_bands_navigate.gif** – car-following navigation on the + smoothed path using PurePursuit. +""" + +import numpy as np +import sys +import json +from pathlib import Path + +abs_dir_path = str(Path(__file__).absolute().parent) +relative_path = "/../../../components/" +relative_simulations = "/../../../simulations/" + +sys.path.append(abs_dir_path + relative_path + "visualization") +sys.path.append(abs_dir_path + relative_path + "state") +sys.path.append(abs_dir_path + relative_path + "vehicle") +sys.path.append(abs_dir_path + relative_path + "obstacle") +sys.path.append(abs_dir_path + relative_path + "mapping/grid") +sys.path.append(abs_dir_path + relative_path + "course/cubic_spline_course") +sys.path.append(abs_dir_path + relative_path + "control/pure_pursuit") +sys.path.append(abs_dir_path + relative_path + "plan/elastic_bands") + +from global_xy_visualizer import GlobalXYVisualizer +from min_max import MinMax +from time_parameters import TimeParameters +from vehicle_specification import VehicleSpecification +from state import State +from four_wheels_vehicle import FourWheelsVehicle +from obstacle import Obstacle +from obstacle_list import ObstacleList +from cubic_spline_course import CubicSplineCourse +from pure_pursuit_controller import PurePursuitController +from binary_occupancy_grid import BinaryOccupancyGrid +from elastic_bands_path_planner import ElasticBandsPathPlanner + + +# flag to show plot figure +# when executed as unit test, this flag is set as false +show_plot = True + + +def main(): + """Main process function""" + + # set simulation parameters + x_lim, y_lim = MinMax(-5, 55), MinMax(-20, 25) + sim_dir = (abs_dir_path + relative_simulations + + "path_planning/elastic_bands_path_planning/") + map_path = sim_dir + "map.json" + path_filename = sim_dir + "path.json" + search_gif_path = sim_dir + "elastic_bands_search.gif" + navigate_gif_path = sim_dir + "elastic_bands_navigate.gif" + + # ---- grid + static obstacles ---- + occ_grid = BinaryOccupancyGrid(x_lim, y_lim, resolution=0.5, + clearance=1.5, map_path=map_path) + + obst_list = ObstacleList() + obst_list.add_obstacle(Obstacle(State(x_m=10.0, y_m=15.0), + length_m=10, width_m=8)) + obst_list.add_obstacle(Obstacle(State(x_m=40.0, y_m=0.0), + length_m=2, width_m=10)) + occ_grid.add_object(obst_list) + occ_grid.save_map() + + # ---- Elastic Bands plan ---- + planner = ElasticBandsPathPlanner( + (0, 0), (50, -10), map_path, + x_lim=x_lim, y_lim=y_lim, + path_filename=path_filename, + gif_name=search_gif_path if show_plot else None, + ) + + if not planner.path: + print("Elastic Bands: no path found – aborting.") + return + + # ---- navigation GIF (car following) ---- + with open(path_filename, 'r') as f: + sparse_path = json.load(f) + + sparse_x = [p[0] for p in sparse_path] + sparse_y = [p[1] for p in sparse_path] + + course = CubicSplineCourse(sparse_x, sparse_y, 20) + + vis = GlobalXYVisualizer(x_lim, y_lim, TimeParameters(span_sec=25), + show_zoom=False, gif_name=navigate_gif_path) + vis.add_object(obst_list) + vis.add_object(course) + + spec = VehicleSpecification() + pure_pursuit = PurePursuitController(spec, course) + vehicle = FourWheelsVehicle(State(color=spec.color), spec, + controller=pure_pursuit, show_zoom=False) + vis.add_object(vehicle) + + if not show_plot: + vis.not_show_plot() + vis.draw() + + +if __name__ == "__main__": + main() From 4ca6d599d8b7495cdff542dd986c1f8c0eb7cd29 Mon Sep 17 00:00:00 2001 From: Erwin Lejeune Date: Mon, 9 Feb 2026 15:39:31 +0400 Subject: [PATCH 03/10] add Elastic Bands simulation assets (GIFs, map, path) --- .../elastic_bands_navigate.gif | Bin 0 -> 1117768 bytes .../elastic_bands_search.gif | Bin 0 -> 2613642 bytes .../elastic_bands_path_planning/map.json | 1 + .../elastic_bands_path_planning/path.json | 1 + 4 files changed, 2 insertions(+) create mode 100644 src/simulations/path_planning/elastic_bands_path_planning/elastic_bands_navigate.gif create mode 100644 src/simulations/path_planning/elastic_bands_path_planning/elastic_bands_search.gif create mode 100644 src/simulations/path_planning/elastic_bands_path_planning/map.json create mode 100644 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