How to use RRT (Rapidly-exploring Random Tree) in automated assembly lines

Using RRT (Rapidly-exploring Random Tree) in automated assembly lines involves planning the paths for robotic arms or other automation equipment to optimize their movement through the workspace.

Process:

1. Define the Workspace:
   • Represent the assembly line environment, including obstacles and the workspace for the robot.
2. Initialize RRT:
   • Start with an initial tree node representing the robot’s starting position.
3. Sample Random Points:
   • Generate random points in the workspace to explore possible paths.
4. Find Nearest Node:
   • For each sampled point, find the nearest node in the existing tree.
5. Extend the Tree:
   • Create a new node by extending from the nearest node toward the sampled point. Ensure this extension is collision-free.
6. Check for Goal:
   • Check if the newly added node is close enough to the goal position. If so, attempt to find a path to the goal.
7. Repeat:
   • Continue sampling, extending, and checking until a path to the goal is found or a stopping criterion is met.
8. Path Extraction:
   • Once the goal is reached, backtrack through the tree to extract the path from the start to the goal.

Example with Python Code:

We’ll use a 2D workspace for simplicity, and matplotlib for visualization.

import numpy as np
import matplotlib.pyplot as plt
from matplotlib.patches import Rectangle

# Parameters
workspace_size = (20, 20)
num_nodes = 1000
step_size = 1.0
goal_radius = 1.5

# Obstacles (example: one rectangle)
obstacles = [Rectangle((5, 5), 5, 5, color='red', alpha=0.5)]

def is_collision_free(start, end, obstacles):
    """Check if the path from start to end collides with any obstacles."""
    for obs in obstacles:
        if obs.contains_point(start) or obs.contains_point(end):
            return False
        # Simple collision check: line-segment with rectangle (not fully accurate)
        if (start[0] < obs.get_x() + obs.get_width() and
            end[0] > obs.get_x() and
            start[1] < obs.get_y() + obs.get_height() and
            end[1] > obs.get_y()):
            return False
    return True

def rrt(start, goal, num_nodes, step_size, obstacles):
    """RRT algorithm to find a path from start to goal."""
    nodes = [start]
    parent = {}
    found = False
    
    for _ in range(num_nodes):
        rand_point = np.random.rand(2) * workspace_size
        nearest_node = min(nodes, key=lambda n: np.linalg.norm(np.array(n) - np.array(rand_point)))
        direction = np.array(rand_point) - np.array(nearest_node)
        norm = np.linalg.norm(direction)
        direction = direction / norm
        new_node = np.array(nearest_node) + direction * min(step_size, norm)
        
        if is_collision_free(nearest_node, new_node, obstacles):
            nodes.append(tuple(new_node))
            parent[tuple(new_node)] = nearest_node
            
            if np.linalg.norm(new_node - np.array(goal)) < goal_radius:
                found = True
                goal_node = tuple(new_node)
                break
    
    if not found:
        return None
    
    path = [goal_node]
    while path[-1] in parent:
        path.append(parent[path[-1]])
    
    return path[::-1]

# Visualization
start = (0, 0)
goal = (18, 18)
path = rrt(start, goal, num_nodes, step_size, obstacles)

# Plotting
fig, ax = plt.subplots()
ax.set_xlim(0, workspace_size[0])
ax.set_ylim(0, workspace_size[1])
ax.set_aspect('equal')
for obs in obstacles:
    ax.add_patch(obs)
ax.plot(*start, 'go', label='Start')
ax.plot(*goal, 'ro', label='Goal')
if path:
    path = np.array(path)
    ax.plot(path[:, 0], path[:, 1], 'b-', label='Path')
ax.legend()
plt.show()

Explanation of the Code:

1. Parameters:
   • workspace_size: Size of the 2D workspace.
   • num_nodes: Number of nodes to sample.
   • step_size: Maximum distance to extend the tree.
   • goal_radius: Radius around the goal within which the path is considered successful.
2. Obstacles:
   • Simple rectangular obstacles are defined and checked for collisions.
3. RRT Function:
   • Samples random points and extends the tree, checking for collisions and proximity to the goal.
4. Visualization:
   • Uses matplotlib to visualize the workspace, obstacles, start, goal, and path.

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