RRT Algorithm Programming and Simulation for Robot Path Planning to Obtain Shortest Path

The RRT (Rapidly-exploring Random Tree) algorithm is a probabilistically complete algorithm commonly used in robot path planning, particularly suitable for high-dimensional space searches in complex environments. Its core principle involves exploring the environment by randomly sampling and expanding a tree structure, gradually constructing feasible paths from start to goal positions.

When implementing the RRT algorithm for robot path planning in MATLAB, the first step requires environment initialization including obstacle configuration, start point, and goal point definitions. The algorithm begins from the start point, generates target points through random sampling, then finds the nearest node in the existing tree structure and extends a new node toward the target point. During expansion, collision detection must be performed to ensure the new node doesn't collide with obstacles - this typically involves using line intersection checks or distance calculations between nodes and obstacle boundaries.

To optimize the path, improved algorithms like RRT* can be introduced, which employ rewiring strategies to gradually optimize path cost, ultimately obtaining shorter or smoother paths. The rewiring process involves comparing new connection costs with existing ones and updating parent nodes when better paths are found. During simulation, MATLAB's visualization tools can intuitively demonstrate tree growth and final path generation through plotting functions like plot(), line(), and scatter().

Through multiple iterations, the RRT algorithm can effectively avoid obstacles and find feasible paths. By leveraging MATLAB's numerical computation and graphical plotting capabilities, performance metrics such as path length and algorithm convergence speed can be further analyzed to validate planning effectiveness. Key MATLAB functions for implementation include rand() for random sampling, pdist2() for distance calculations, and plot() for visualization.