A map is useless if you don't know how to move through it. Path planning is the algorithmic bridge between 'Where am I?' and 'Where do I want to be?'.
1A* (A-Star) Search
A* is the industry standard for pathfinding in 2D and 3D grid environments (like a warehouse floor). It combines two scores: g(n) (the actual cost from the start to the current cell) and h(n) (the Heuristic estimate of the cost from the cell to the goal). By always exploring the node with the lowest combined score, A* finds the mathematically Optimal path with minimal effort. It is the core algorithm behind everything from video game NPCs to vacuum robot navigation.
2Rapidly-exploring Random Trees (RRT)
When a robot has many 'Degrees of Freedom' (like a 7-joint industrial arm), a grid search becomes impossible—the number of combinations is too high. RRT solves this by using Random Sampling. It picks a random point in space and tries to 'Grow' its existing path tree toward that point. This approach is 'Probabilistically Complete': if you let it run long enough, it will find a path. RRT excels at finding valid paths through complex 'Keyhole' obstacles that would baffle other algorithms.
3The Planning Hierarchy
Navigation is split into two layers. The Global Planner (A*/RRT) runs once at the start (or whenever the destination changes) to find a high-level route. The Local Planner (also called a 'Path Follower') runs constantly (at 50Hz+). Its job is to keep the robot on the global path while performing Reactive Obstacle Avoidance. If a person walks in front of the robot, the local planner stops or swerves, then returns to the global path once the coast is clear.
