Implementing A* and RRT Motion Planning for Robotics

Two primary motion planning techniques for robotics are A* and RRT (Rapidly-exploring Random Tree). A* excels when the environment can be represented as a graph or grid, while RRT is more useful in continuous or high-dimensional configuration spaces.

A* planning involves combining the cost already traveled with an estimate of the remaining cost. The formula f(n) = g(n) + h(n) is used, where g(n) is the cost from the start, h(n) estimates the cost to the goal, and f(n) ranks candidate nodes. For instance, consider a grid:

S . . # . . . . . . # . . . . . . . . # . . # # # . # . . . . . . . G

The planner explores promising cells while avoiding blocked cells. The Python skeleton for A* planning is provided in the source.

On the other hand, RRT operates differently. Instead of systematically exploring grid cells, it samples random points and gradually grows a tree. The typical loop involves sampling a random configuration, finding the nearest existing node, steering toward the sample, checking for collision, and adding the new node if valid. This process is repeated until the goal is reached. The RRT skeleton is also provided in the source.

Comparing the two methods, A* is deterministic and works well in grid/graph representation, especially for mobile robot maps. It's suitable for exact grid path planning. However, RRT is sampling-based and more suitable for continuous or high-dimensional spaces, making it ideal for complex robotic manipulators. While A* yields an exact grid path, RRT does not guarantee this.

To improve RRT, one can use goal-biased sampling, better steering techniques, path smoothing, collision-aware sampling, and robot-specific considerations such as joint space planning for robotic arms and production checklist validation for safety and feasibility of planned solutions.