Roland GeraertsICRA 2010

Planning Short Paths with Clearance using Explicit Corridors

Requirements

Fast and flexible 2D path planner• Real-time planning for thousands of characters• Dealing with local hazards• Global path

Natural paths• Smooth• Short• Keeps some distance to

obstacles• Avoids other characters• …

Titan Quest: Immortal throne

Path planning system

Build a data structure• Explicit Corridor Map: Medial Axis + annotated event points

Perform query• Compute corridor• Compute Indicative Route• Compute path

Explicit Corridor Map Corridor Indicative Route Path

Data structure: Explicit Corridor Map

Basis: Medial Axis Plus: annotated event points on the edges

• Placed at curve change on the edges• Occurs at crossing between site normal and edge• Annotation: its two closest points on the sites

Equals: planar subdivision• Memory footprint: linear in the number of vertices• There is no need for storing pixels

Perspective view (Z-buffer)

Top view (Frame buffer)

GPU computation

Query phase

Perform query (on-line)• Find the retraction of the start and goal• Connect the start and goal to the Explicit Corridor Map• Compute the shortest backbone path (using A*)

Explicit Corridor Map Explicit Corridorwith backbone path

Query

Explicit Corridors: Obtaining clearance

Minimum clearance in Explicit Corridors• Move each closest point cp toward its center point c• The displacement equals the desired clearance clmin

• Insert event point(s) if clmin > distance(c, cp)

c cp

Explicit Corridor Shrunk corridors Shrinking a corridor

Explicit Corridors: Shortest paths

Computing the shortest path• Construct a triangulation

– At most 2n+2 triangles– If the start/goal is not included, add a triangle

• Compute the shortest path– Funnel algorithm [Guibas et al. 1987]

Explicit Corridor Triangulation Shortest path

li ri

li+1 ri+1

sg

Explicit Corridors: Shortest paths

Computing the shortest minimum clearance path• Shrink the corridor

– Construction time: linear in the number of event points

• Compute the shortest path– Adjust Funnel algorithm to deal with circular arcs– Construction time: linear in the number of event points

Explicit Corridor Triangulation Shortest path

Query phase

Compute a smooth path: Indicative Route Method• Compute the shortest minimum-clearance path• Define the attraction force

– Pulls the character toward the goal

• Define the boundary force– Keeps the character inside the corridor

• Define other forces– Leads to other behaviors

• Time-integrate the forces– Yields a smooth (C1-continous) path

Query phase

Query phase• Using other forces

Smooth path Short path Obstacle avoidance

Coherent groups Path variation Camera path

Crowd simulation

Stealth-based path planning

Explicit Corridor Map: Experiments

Performance• Setup

– NVIDIA GeForce 8800 GTX graphics card– Intel Core2 Quad CPU 2.4 GHz, 1 CPU used

• Experiments– City: 500x500 meter, 4000x4000 pixels, 548 convex polygons

Explicit Corridor Map: Experiments

Performance• Setup

– NVIDIA GeForce 8800 GTX graphics card– Intel Core2 Quad CPU 2.4 GHz, 1 CPU used

• Experiments– City: 500x500 meter, 4000x4000 pixels, 548 convex polygons

time: 0.3s

Query phase: Experiments

Performance• Setup

– Intel Core2 Quad CPU 2.4 GHz, 1 CPU

• Experiments– City: 500x500 meter, 1.000 random queries

• Results (average query time)

Query phase: Experiments

Performance• Setup

– Intel Core2 Quad CPU 2.4 GHz, 1 CPU

• Experiments– City: 500x500 meter, 1 query

• Results (query time)– 2.8 ms

ECM (0.3s) Explicit corridor Shrunk corridor Triangulation Shortest path Smooth path

Conclusions

Advantages• Flexible path planner generates natural paths• Computation of smooth, short minimum clearance paths• The algorithms run in linear time and are fast in practice• The algorithms are simple

Open problems• Handle large dynamic changes efficiently• Handle 2.5D/3D environments

Questions

Contact• Roland Geraerts (roland@cs.uu.nl)• Home page: www.cs.uu.nl/~roland• Conference: www.motioningames.org