### Informed RRT* Algorithm for Path Planning and Robotics Navigation The **Informed RRT*** algorithm is an advanced variant of the Rapidly-exploring Random Tree (RRT*) method, specifically designed to improve efficiency in finding optimal paths within complex environments. Unlike traditional RRT*, which explores all possible areas randomly until convergence on a near-optimal solution occurs, Informed RRT* restricts sampling efforts only inside regions that could potentially contain better solutions than those already found. This approach significantly reduces unnecessary exploration while ensuring asymptotic optimality—the guarantee that as more samples are added over time, the quality of the generated path will converge towards global optimum[^3]. For implementation purposes, consider initializing nodes representing start and goal positions followed by iterative insertion operations where new points get connected back into existing structures via edges adhering to collision-free constraints. During this process, whenever a lower-cost route between two waypoints emerges during tree expansion phases, subsequent searches focus exclusively around ellipsoidal volumes enclosing both endpoints along with intermediate vertices forming part of current best-known trajectories[^1]. ```python import numpy as np from scipy.spatial import cKDTree class Node: def __init__(self, point, cost=np.inf, parent=None): self.point = point self.cost = cost self.parent = parent def informed_rrt_star(start_point, end_point, obstacles, max_iter=5000): # Initialize trees... pass # Implementation details omitted here. ```