PRM: Probabilistic Roadmap Method in 3D and with 7-DOF robot arm

PRM is a sampling-based robot motion-planning technique developed in the 1990s that is still in use today. We start with PRM on a two-link robot with two rotational joints. The PRM has two phases, the learning and the query phase: In the learning phase, you (a) Generate random points in the configuration space and calculate if they are in the free configuration space (green points) or in collision with obstacles (red points). (b) Attempt to connect points in the free configuration space to their nearest neighbors less than radius distance apart using the local planner. These two steps generate the roadmap. In practice, you repeat these learning steps for as long as you have time and memory to store the results. In the query phase, the local planner attempts to connect the initial configuration to the nearest point in the roadmap and the goal configuration to the nearest point in the roadmap. Then a graph search is used to find the shortest path in the roadmap. In this demonstration, I use A* search to find the shortest path. All code is available as online Mathematica demonstrations. https://demonstrations.wolfram.com/Pr... https://demonstrations.wolfram.com/Pr... https://demonstrations.wolfram.com/Pr... https://demonstrations.wolfram.com/Di... https://demonstrations.wolfram.com/Pr... https://demonstrations.wolfram.com/Ch... This is part a of Lecture 23, Intro to Robotics Part a: Probabilistic Roadmap Methods:    • PRM: Probabilistic Roadmap Method in 3D an...   Part b: distance norms    • How close are 2 configurations of a robot?...   Full Playlist "Intro to Robotics":    • Intro2Robotics Lecture 1a: course overview...