Using the Corridor Map Method for Path Planning for a Large Number of Characters Roland Geraerts, Arno Kamphuis, Ioannis Karamouzas, Mark Overmars MIG’08

Do We Need a New Path Planning Algorithm? RoboticsVirtual environments Nr. Entitiesa few robotsmany characters Nr. DOFsmany DOFsa few DOFs CPU timemuch time availablelittle time available Type pathnice pathnatural path AlgorithmsA*, roadmap-based, waypoint-based, …

Goals Fast and flexible path planner Real-time planning for thousands of characters Dealing with local hazards Natural paths Smooth Short Keeps some distance to obstacles Avoids other characters …

Outline Corridor Map Method Path variation Obstacle avoidance Crowd simulation Coherent groups Conclusions & future work

The Corridor Map Method Construction phase (off-line) Create a system of collision-free corridors for the static obstacles Extract the Generalized Voronoi Diagram If a path exists, then it can be found All cycles are included Corridors have maximum clearance Sampled GVDCorridor Map: GVD + clearance info

The Corridor Map Method Construction phase (off-line) McKenna MOUT environmentFootprint and Corridor Map: 0.05s

The Corridor Map Method Construction phase (off-line) City environmentFootprint and Corridor Map: 0.64s

The Corridor Map Method Query phase (on-line) Extract corridor for given start and goal  provides global route The characters follows an attraction point  provides local route Runs along backbone path toward goal Used to define a force function, applied to the character Path is obtained by integration over time while updating the velocity, position, and attraction point of the character Yields a smooth (C1-continuous) path Other behavior: locally adjust path by adding forces Query pointsCorridor and backbone path Path

The Corridor Map Method Query phase (on-line) McKenna MOUT environmentCorridor and path: 0.2ms (average)

The Corridor Map Method Query phase (on-line) City environmentCorridor and path: 1.2ms (average)

Path Variation Alternative paths for a character Provides a less predictable opponent (in a game) May enhance the realism of the gaming experience Approach Add a random force (bias) to the character Control the direction of the bias by e.g. Perlin Noise 100 random pathsLane formationShorter path

Obstacle Avoidance Helbing and Molnar’s social force model; forces: Acceleration toward the desired velocity of motion Repulsive forces from other characters and borders to keep some clearance Attractive forces among characters We need efficient nearest neighbor computations 2D grid storing the characters

Crowd Simulation Goal oriented behavior Each character has its own long term goal A start and goal fixes a corridor When a character has reached its goal, a new goal will be chosen Wandering behavior Each character makes local decisions Each character follows its attraction point When the attraction point reaches a vertex in the corridor map, one of the outgoing edges is selected

Crowd Simulation Goal oriented behavior Forces: standard force, biasing force, collision avoidance force

Crowd Simulation Goal oriented behavior Forces: standard force, biasing force, collision avoidance force

Coherent Groups In a coherent group, characters stay close to each other Group coherence is obtained by limiting The width of the corridor The extent along the corridor where the characters can move Large width and areaSmall width, large areaSmall width and area

Coherent Groups

Conclusions The Corridor Map Method is fast ~10,000 characters can be simulated in real-time The Corridor Map Method is flexible Path variation Collision avoidance Crowds Coherent groups The Corridor Map Method produces natural paths Smooth Short Keeps some distance to obstacles …