01
Planning Problem
A motion planner searches for a feasible path from an initial configuration to a goal while satisfying constraints such as collision avoidance, joint limits, velocity limits, acceleration limits, and dynamic feasibility.
find q(t) such that q(0)=q_start, q(T)=q_goal
02
Planning Methods
- Graph search uses discrete state representations and algorithms such as Dijkstra's algorithm or A*.
- Sampling-based planning explores continuous configuration spaces with methods such as PRM and RRT.
- Optimization-based planning minimizes cost functions subject to constraints.
- Reactive methods generate local behavior from current observations.
03
Planning and Control
Planning chooses feasible future behavior; control makes the physical robot follow that behavior. Real robots require both because open-loop execution is sensitive to uncertainty and disturbances.