# Probabilistic Roadmap Method for Robot Arm

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This Demonstration uses the Probabilistic Roadmap Method (PRM) to plan a motion path for a two-link robot that avoids collisions with a blue sphere and an orange sphere. First, click "add 100 vertices" to randomly sample configurations and calculate if they collide with obstacles (red points) or are safe (green points). Next, select "radius" value to try to connect safe vertices less than radius distance apart into a roadmap. If a path from the initial to goal configuration is found, it can be traversed with the "progress" slider. Although the PRM does not need to calculate the configuration space obstacles, you can make them visible with a checkbox.

Contributed by: Aaron T. Becker and Yitong Lu (January 2020)
Open content licensed under CC BY-NC-SA

## Details

The goal of robot motion planning is to find a continuous path from an initial configuration to a goal configuration that is collision free. A configuration is a complete specification of every point of the robot. This Demonstration uses a two-link robot with two rotational joints that can each rotate from 0 to 2. The resulting configuration space can be represented as a toroid, and so wraps from 2 to 0 on the edges of the plot shown. Obstacles in the robot's workspace map to obstacle regions in the configuration space, but computing these regions is computationally expensive.

Changing the obstacle positions requires rebuilding the roadmap. Longer radius values require more computation but result in a denser roadmap and shorter paths.

PRM was developed in 1996 by Lydia Kavraki et al. [1]. PRMs generate a roadmap that can be reused for subsequent motion-planning queries. PRM was designed for high-dimension configuration spaces (dimensions of 5 or more), but this Demonstration uses two dimensions for ease of visualization.

[1] L. E. Kavraki, P. Svestka, J-C. Latombe and Mark H. Overmars. "Probabilistic Roadmaps for Path Planning in High-Dimensional Configuration Spaces." IEEE Transactions on Robotics and Automation, 12(4), 1996 pp. 566–580. doi:10.1109/70.508439.

## Permanent Citation

Aaron T. Becker and Yitong Lu

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