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Reciprocal Velocity Obstacles for Real-Time Multi-Agent Navigation

Jur van den BergMing Lin

Dinesh Manocha

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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

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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?

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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]

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Velocity Obstacle

(p, v) = {p + tv | t > 0}

• VOAB(vB) = {vA | (pA, vA – vB) B –A }

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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

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Oscillations

• Example: two agents with opposite directions

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Oscillations

• Example: two agents with opposite directions

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Oscillations

• Example: two agents with opposite directions

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Oscillations

• Example: two agents with opposite directions

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Oscillations

• Example: two agents with opposite directions

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Oscillations

• Example: two agents with opposite directions

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Oscillations

• Example: two agents with opposite directions

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Oscillations

• Example: two agents with opposite directions

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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

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Reciprocal Velocity Obstacle

• RVOAB(vB, vA) = {v’A | 2v’A – vA VOA

B(vB)}

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Oscillations?

• Example: two agents with opposite directions

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Oscillations?

• Example: two agents with opposite directions

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Oscillations?

• Example: two agents with opposite directions

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Oscillations?

• Example: two agents with opposite directions

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Oscillations?

• Example: two agents with opposite directions

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Oscillations?

• Example: two agents with opposite directions

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No Oscillations

• Example: two agents with opposite directions

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No Oscillations and Safe

• Example: two agents with opposite directions

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Generalized RVOs

• Different distribution of effort in avoiding each other than 50%-50%

• Parameter ; 0: no effort; 1: all effort• RVOA

B(vB, vA, ) = {v’A | (1/)v’A + (1 – 1/)vA VOAB(vB)}

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Generalized RVOs

• 0% - 100%

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Generalized RVOs

• 25% - 75%

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Generalized RVOs

• 75% - 25%

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Generalized RVOs

• 100% - 0%

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Multi-Agent Navigation

• N agents A1, …, AN with positions p1, …, pN, velocities v1, …, vN, preferred speeds vpref

1, …, vprefN and goals g1, …, gN

• Time stept• Each time step: for each agent:

♦ Compute preferred velocity (global path planning)♦ Select new velocity♦ Update position of agent according to new velocity

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Select New Velocity

• Outside the union of the reciprocal velocity obstacles, closest to preferred velocity

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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

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Kinodynamic Constraints

• Maximum velocity

• Maximum acceleration

• More complicated…

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Neighbor Region

• More efficient• Circular

neighbor region

• Visibility neighbor region…

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Experiments

• Circle: move to antipodal position on circle

12 agents

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Experiments

• Circle: move to antipodal position on circle

250 agents

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Results

• Office experiment

Performance (16 cores, Sitterson scene)

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More Demos

• Office evacuation (Jason Sewall)• Crosswalk (Sachin Patil)• Subway station (Sean Curtis)• Stadium evacuation (Sachin

Patil)

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Public Library

• http://gamma.cs.unc.edu/RVO/Library

• Easy to use

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Extension to 3D

500 agents on a sphere moving to the other side

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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)

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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)

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Experiments

• (High-speed) moving obstacle: car