Introduction to Planning

1. Introduction to Planning

2. What is Planning? • Either a sequence of actions that get some model into a goal configuration • Rubik's Cube • Navigating a city via intersections • Robot manipulation objects • Also High level: Daily Routine

3. Planning Vocabulary • State • Rubik's Cube: 4.33E19 or 5.19E20 • Actions • Rubik's Cube: Face rotations (July 2010: 20 moves sufficient http://cube20.org/) • Initial State ,Goal State • Feasibility Measure (collisions) • Optimality Measure (path length, energy)

4. Parental Discretization Advised • These plans are in discrete spaces • Rubik's Cube: 6 faces, 3 rotations • Relatively easy to search through this space • Model as Graph (a discrete math object) • Do graph search (Dijkstra, A*, and friends) • Algorithms developed pre-1970s. • Covered in 6.01, 6.006, 6.034

5. What makes planning difficult?

6. Spaces in Planning • States are pulled out from some region and a solution path in this space • Draw n-dimension vectors from e.g. Rn • Measure optimality and feasibility in this space • Configuration Space describes robot actuator and assumes that state is known • Belief Space generalizes by including uncertainty as a distribution over states

7. Configuration Space • Have a robot arm with (e.g.) 7 degrees of freedom • Plan is a path in a 7 dimensional space • Represent 3D objects in the world and any other constraints as 7D objects • Not necessarily Rn • Can also plan in a space involving dynamic constraints (called Kinodynamic Planning) • 2 or 3 times as many dimensions • e.g. Pole vaulting

8. Wikimedia Commons

9. Planning Algorithms 2006 LaValle

10. Belief Space • Manipulating probability distributions. Distributions are over the state space • Mastermind • Start with uniform belief • Goal is to have peaking distributions indicating certainty of hidden code Wikimedia Commons