1. Real-Time Motion Planning
B659: Principles of Intelligent Robot Motion
Spring 2013
Kris Hauser

2. Execution Issues Planning is not instantaneous
Paths are never executed exactly
Disturbances, modeling errors
Constraints change
New information, unpredictable agents, user input
Planning is not instantaneous

3. Reactive Replanning Basic reactive approach
Detect changes
Update the model of the world
Plan a new path
… But replanning can be computationally expensive …

5. Forward Prediction
How much time?
Predicted start of plan

6. Responsiveness
Disturbance detection & response takes up to 2 cycles

7. Desired qualities Responsiveness Completeness Safety
In “hard” domains, cannot meet all three criteria simultaneously

8. Conservative Approaches to Safety
Offset obstacles by a safety margin
Workspace X time obstacles that grow over time
Requires planning with time as a state variable
Cannot plan too far in the future! t t
O(t)
CO(t)
O(t) y y
O(tc)
O(tc) tc tc x x
Bounded velocity
Known velocity

9. Safety in Dynamic Systems
From some feasible states, cannot instantaneously stop without hitting obstacles
Inevitable collision states
Solution: enforce that all executed paths end in zero velocity

10. Completeness vs Responsiveness
Ideal case: precompute a policy (map from states->actions) that has fast lookup and will eventually bring every state to the goal
A probabilistic roadmap approximates this
Relies on a known environment, which is mostly constant over time
Best suited for handling state disturbances and changing goals

11. Approaches to Partial Information Reuse
Reuse the path or planning tree from the prior step. Can make planning faster if only small changes are needed, but can be significantly slower if a large detour is needed
Use good maneuvers/only a subset of useful variables. Reduce load on the planner using better domain knowledge.
Plan with greater local detail and refine over time (any-time approach)

12. Dimensionality/Branching Reduction Approaches
Plan with small library of control primitives
Make larger jumps in C-space
Need a small library of carefully designed, reusable primitives

13. Local Replanning Approaches
Sacrifice completeness on a single planning step
Make detailed local plans, coarser global plans
Make corrections on the next time step
Multiple ways of doing this
Limit computation time
Limit time horizon (receding horizon planning, aka model predictive control)
Limit # of decision points
Both (maneuver sets)

14. Maneuver Sets Used successfully in DARPA challenges
Plan coarse 2d path (A* search)
Pick dynamic maneuver that makes most progress along path

15. Replanning Success Criteria
Convergence: is the robot driven to the goal over time?
Optimality of resulting paths
Short time horizon: prone to local minima

16. Handling minima
Replanning has been demonstrated to work in practical examples, but can we guarantee global progress?
Two approaches:
Forbidding past failure states
Increase planning time/horizon

17. Questions to think about
How do limitations in computational resources affect completeness, responsiveness, and safety of the system?
How would you tune the time step/horizon?
Can you construct pathological cases?