1. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Reciprocal Velocity Obstacles for Real-Time Multi-Agent Navigation Jur van den Berg Ming Lin Dinesh Manocha

2. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Multi-Agent Navigation N agents share an environment Move from start to goal without mutual collisions (and collisions with obstacles) Decoupled ♦ Simultaneous independent navigation for each agent ♦ Global path planning and local collision avoidance decoupled ♦ Real-time

3. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Problem Description Independent Navigation Continuous cycle of sensing and acting Global path planning vs. local navigation Each cycle: each agent observes other agents (position, velocity) But does not know what they are going to do How to act?

4. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Previous Approaches Potential Field (particle model) Assume other agents are static obstacles Assume other agents are moving obstacles (that maintain their current velocity for a while) ♦ Velocity Obstacles [Fiorini, Shiller, 98]

5. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Velocity Obstacle  (p, v) = {p + tv | t > 0} VO A B (v B ) = {v A |  (p A, v A – v B )  B  –A   }

6. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Using Velocity Obstacles In each cycle, select velocity outside velocity obstacle of any moving obstacle For multi-agent navigation? Agents are not passively moving, but react on each other Result: oscillations

7. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Oscillations Example: two agents with opposite directions

8. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Oscillations Example: two agents with opposite directions

9. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Oscillations Example: two agents with opposite directions

10. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Oscillations Example: two agents with opposite directions

11. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Oscillations Example: two agents with opposite directions

12. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Oscillations Example: two agents with opposite directions

13. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Oscillations Example: two agents with opposite directions

14. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Oscillations Example: two agents with opposite directions

15. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL New Approach Prevent oscillations No communication among agents or global coordination Simple idea: instead of choosing a new velocity outside the velocity obstacle, take the average of a velocity outside the velocity obstacle and the current velocity Formalized into Reciprocal Velocity Obstacle

16. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Reciprocal Velocity Obstacle RVO A B (v B, v A ) = {v’ A | 2v’ A – v A  VO A B (v B )}

17. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Oscillations? Example: two agents with opposite directions

18. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Oscillations? Example: two agents with opposite directions

19. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Oscillations? Example: two agents with opposite directions

20. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Oscillations? Example: two agents with opposite directions

21. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Oscillations? Example: two agents with opposite directions

22. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Oscillations? Example: two agents with opposite directions

23. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL No Oscillations Example: two agents with opposite directions

24. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL No Oscillations and Safe Example: two agents with opposite directions

25. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Generalized RVOs Different distribution of effort in avoiding each other than 50%-50% Parameter  ;   0: no effort;   1: all effort RVO A B (v B, v A,  ) = {v’ A | (1/  )v’ A + (1 – 1/  )v A  VO A B (v B )}

26. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Generalized RVOs 0% - 100%

27. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Generalized RVOs 25% - 75%

28. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Generalized RVOs 75% - 25%

29. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Generalized RVOs 100% - 0%

30. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Multi-Agent Navigation N agents A 1, …, A N with positions p 1, …, p N, velocities v 1, …, v N, preferred speeds v pref 1, …, v pref N and goals g 1, …, g N Time step  t Each time step: for each agent: ♦ Compute preferred velocity (global path planning) ♦ Select new velocity ♦ Update position of agent according to new velocity

31. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Select New Velocity Outside the union of the reciprocal velocity obstacles, closest to preferred velocity

32. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Select New Velocity Environment may become crowded: no valid velocity Solution: select velocity inside RVO but penalize ♦ Expected time to collision ♦ Distance to preferred velocity Select velocity with minimal penalty

33. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Kinodynamic Constraints Maximum velocity Maximum acceleration More complicated…

34. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Neighbor Region More efficient Circular neighbor region Visibility neighbor region…

35. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Experiments Circle: move to antipodal position on circle 12 agents

36. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Experiments Circle: move to antipodal position on circle 250 agents

37. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Results Office experiment

38. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL More Demos Office evacuation (Jason Sewall)Office evacuation Crosswalk (Sachin Patil)Crosswalk Subway station (Sean Curtis)Subway station Stadium evacuation (Sachin Patil)Stadium evacuation

39. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Public Library http://gamma.cs.unc.edu/RVO/Library Easy to use

40. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Extension to 3D 500 agents on a sphere moving to the other side

41. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Conclusion and Future Work Conclusion ♦ Powerful and simple (easy to implement) local collision avoidance technique for multi-agent navigation ♦ Scalable with number of agents and number of processors used Future work ♦ Model human behavior - Human dynamics ♦ Implementation on mobile robots (sensing etc.) ♦ Application to flocks and schools (3D)

42. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Further Reading Van den Berg et al. n-body Reciprocal Collision Avoidance (ISRR 2009) Pettre et al. Experiment-based Modeling, Simulation and Validation of Interactions between Virtual Walkers (SCA 2009)

43. The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Experiments (High-speed) moving obstacle: car