[Practical Exercise] RRT Algorithm Based on MATLAB: UAV Path Planning

# 2.1 Fundamental Principle of the RRT Algorithm

The Rapidly-exploring Random Tree (RRT) algorithm is a path planning algorithm based on random sampling. It explores the environment and searches for a path by iteratively expanding a tree-like structure. The algorithm process is as follows:

1. **Initialization:** Create a tree with the starting point as the root node.
2. **Random Sampling:** Randomly sample a point in the environment.
3. **Nearest Neighbor Search:** Find the node in the tree closest to the randomly sampled point.
4. **Step Size Calculation:** Calculate the step size from the nearest neighbor node to the randomly sampled point, which should be less than the maximum step size.
5. **Tree Expansion:** Extend the tree in the direction of the step size from the nearest neighbor node towards the randomly sampled point and create a new node.
6. **Goal Check:** Check if the new node has reached the goal area. If so, the algorithm ends and returns the path.
7. **Repeat:** Repeat steps 2-6 until the goal is reached or the maximum number of iterations is achieved.

# 2. Implementation of the RRT Algorithm in MATLAB

### 2.1 Fundamental Principle of the RRT Algorithm

**Pseudocode of the RRT Algorithm:**

1. Initialize the RRT tree starting from the start point
2. while termination condition is not met:
3.     Randomly sample a point q_rand in the configuration space
4.     Find the node q_near in the RRT tree closest to q_rand
5.     Extend the RRT tree towards q_rand to generate a new node q_new
6.     Add q_new to the RRT tree

**Algorithm Flowchart:**

graph LR
subgraph RRT Algorithm
     start(Initialize RRT tree) --> sample(Randomly sample a point in the configuration space) --> nearest(Find the closest node to the sampled point)
     nearest --> steer(Extend the RRT tree towards the sampled point) --> new(Generate a new node) --> add(Add the new node to the RRT tree)
end

### 2.2 Code Implementation of the RRT Algorithm in MATLAB

**MATLAB Code:**

% Initialize the RRT tree
tree = [0, 0];

% Termination condition
max_iter = 1000;

% Randomly sample the configuration space
q_rand = [rand(), rand()];

% Find the node closest to the sampled point
q_near = findNearestNode(tree, q_rand);

% Extend the RRT tree towards the sampled point
q_new = steer(q_near, q_rand, 0.1);

% Add the new node to the RRT tree
tree = [tree; q_new];

**Code Logic Analysis:**

***findNearestNode** function: Finds the node closest to a given point based on Euclidean distance.
***steer** function: Extends the RRT tree in a given direction with a step size of 0.1.
***add** function: Adds a new node to the RRT tree.

### 2.3 Parameter Settings and Optimization of the RRT Algorithm

**Parameter Settings:**

***Step Size:** Controls the step size during the expansion of the RRT tree.
***Termination Condition:** Can be a maximum number of iterations, path length, or other custom conditions.

**Optimization Methods:**

***Adaptive Step Size:** Dynamically adjust the step size based on the topology of the RRT tree.
***Heuristic Sampling:** Use heuristic functions to guide the random sampling process, improving search efficiency.
***Parallel Computing:** Utilize multi-core processors to parallelize the expansion of the RRT tree, increasing algorithm speed.

# 3.2 UAV Path Planning Method Based on the RRT Algorithm

#### Application Process of the RRT Algorithm in UAV Path Planning

The UAV path planning process based on the RRT algorithm mainly includes the following steps:

1. **Initialization:** Define the UAV's starting position and goal position, and set parameters for the RRT algorithm, such as step size and maximum number of iterations.
2. **Generate Random Points:** Randomly generate a point in the configuration space as the point to extend the tree.
3. **Nearest Neighbor Search:** Find the closest point to the extension point in the tree, known as the nearest neighbor point.
4. **Generate New Points:** Move a certain step size from the nearest neighbor point towards the extension point to generate a new point.
5. **Collision Detection:** Check if the new point collides with obstacles.
6. **Add New Points:** If the new point does not collide with obstacles, add it to the tree.
7. **Path Generation:** When the tree extends to the vicinity of the goal position, connect a path from the starting point to the goal point.

#### Optimization Strategies for the RRT Algorithm in UAV Path Planning

To improve the efficiency and robustness of the RRT algorithm in UAV path planning, the following optimization strategies can be adopted:

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