Real-time Path Planning and Navigation for Multi-Agent and Heterogeneous Crowd Simulation

Transcription

1 Real-time Path Planning and Navigation for Multi-Agent and Heterogeneous Crowd Simulation Ming C. Lin Department of Computer Science University of North Carolina at Chapel Hill Joint work with Avneesh Sud, Russell Gayle, Jur Van den Berg, Sean Curtis, Stephen Guy, Erik Andersen, and Dinesh Manocha Problem Definition Navigating to goal - important behavior in multiple agents (robots or virtual agents) simulation Navigation requires path planning Compute collision-free paths Satisfy constraints on the path

2 Applications Training and Mission Rehearsal Disaster Response Urban Warfare Multi-robot planning Human-Robot Interaction Demining Scenario Evaluation Evacuation Planning New Territory Exploration Challenges Path planning for multiple (thousands of) independent agents simultaneously Each agent is a dynamic obstacle Exact path planning for each agent in dynamic environments difficult

3 Goal Real-time path planning for heterogeneous crowds Non uniform distribution Independent goals Indoor Environment: Tradeshow Goal Real-time path planning for heterogeneous crowds Non uniform distribution Independent goals Large urban environments

4 Goal Real-time path planning for heterogeneous crowds in dynamic environments Moving obstacles Evolving navigable regions Weapons effects Safety zones Real-time Path Planning for Virtual Agents in Dynamic Environments [Sud et al.; IEEE VR 2007]

5 Multi-Agent Navigation Graph Unified data structure for path planning of multiple agents Computed using 1 st and 2 nd order Voronoi diagrams Multi-Agent Navigation Graph Unified data structure for path planning of multiple agents Computed using 1 st and 2 nd order Voronoi diagrams Advantage: Provides pairwise proximity information for all agents simultaneously Compute collision free paths of all agents from single MaNG

6 1 st Order Voronoi Diagram (VD 1 ) Agents Static Obstacle 1 st Order Voronoi Diagram (VD 1 ) Agents Static Obstacle

7 2 nd Order Voronoi Diagram (VD 2 ) VD 1 and VD 2 VD 1 VD 2

8 Voronoi Graphs VG 1 U VG 2 2 nd nearest nbr graph 2 nd order Voronoi graph 1 st order Voronoi graph

9 MaNG Subset of the 2 nd nearest neighbor graph Static Obstacle Multi-Agent Navigation Graph Unified data structure for path planning of multiple agents Computed using 1 st and 2 nd order Voronoi diagrams Advantage: Reduce omputation of many 1 st order Voronoi graphs to computation of a single MaNG

10 MaNG: Planner For each agent: 1. Connect agent (source) to VG 2 edges Agent MaNG: Planner For each agent: 1. Connect agent (source) to VG 2 edges 2. Connect destination to VG 1 edges

11 MaNG: Planner For each agent: 1. Connect agent (source) to VG 2 edges 2. Connect destination to VG 1 edges 3. Assign edge weights MaNG: Planner For each agent: 1. Connect agent (source) to VG 2 edges 2. Connect destination to VG 1 edges 3. Assign edge weights 4. Graph search

12 MaNG: Planner For each time step: Compute MaNG once Compute paths for all agents from same MaNG MaNG: Planner 2 nd order Voronoi diagram gives proximity to closest obstacle [Sud et al.06] Compute force fields at each step Repulsive forces from closest obstacle

13 MaNG Computation Computing exact Voronoi diagram difficult Non-linear boundaries High complexity MaNG Computation Computing exact Voronoi diagram difficult Compute Discrete Voronoi Diagram (DVD) Interactive computation using GPU [Sud et al. 06] Culling techniques for fast 2D computation (paper)

14 MaNG Computation Computing exact Voronoi diagram difficult Compute Discrete Voronoi Diagram (DVD) Compute closest site at finite set of points Undersampling Fixed grid resolution on GPU

15 Undersampling Disconnected Voronoi regions Complex graph Solution: Local tests to reduce graph complexity without changing connectivity (paper) Demos Fruit stealing Crowds in urban environment

16 Demos Fruit stealing Dynamic goal update Swarming behavior observed Crowds in urban environment Demo: Stealing Fruit 100-Agent simulation at 9 fps

17 Demos Fruit stealing Crowds in small urban environment Dynamic obstacles Demos: Crowd 100-Agent simulation at 10 fps

18 Main Approaches Adaptive Elastic Roadmaps (AERO): Connectivity graph structure that adapts to environment updates Pedestrian Levels of Detail (PLOD): Hierarchical data structure to accelerate large-scale crowd simulations Preliminary Results Interactive global path planning and local collision avoidance among virtual agents Capture independent behavior Individual goals, states

19 Preliminary Results Interactive global path planning and local collision avoidance among virtual agents Capture independent and collective behavior Individual goals, states Lane formation, oscillations Preliminary Results: Crowd Simulation

20 Adaptive Elastic ROadmaps Global connectivity graph for simultaneous path planning Continuously adapts to dynamic environment Deforms using local force models and global constraints Coherent agent motion Adaptive Elastic ROadmaps

21 Pedestrian Levels of Detail Hierarchical data structure to accelerate large-scale simulation of heterogeneous crowds Agents adaptively clustered based on pedestrian state = dynamic state, spatial proximity, behavior Efficient selective updates Empirically observed in real pedestrian flows Pedestrian Levels of Detail

22 Overview Adaptive Elastic Roadmap Environment (Static Obstacles, Dynamic Obstacles, and Agents) Scripted Behaviors PLOD Tree Event Queue Local Dynamics Collision Detection Demo: Maze agents navigating a maze 8 entry and exit points Closeup demonstrating lane formation

23 Demo: Maze Demo: Tradeshow Tradeshow attendees navigating an indoor environment of an exhibit hall 511 Booths agents visit multiple booths, stop at certain booths

24 Demo: Tradeshow Demo: City Environment Multiple city blocks, 924 buildings 2000 pedestrians 50 moving vehicles

25 Demo: City Environment Advantages Generality No assumption on motion Efficiency Selective hierarchical updates Computation using GPUs Global path planning with independent and collective effects

26 Summary Interactive global path planning and collision avoidance among thousands of virtual agents Application to heterogeneous crowd simulation Questions?

27 April 18, 2007 Reciprocal Velocity Obstacles for Mutli-Agent Navigation Independent Navigation Continuous cycle of sensing and acting (small time step Δt) Each cycle: each agent observes other agents (position, velocity) And select a new velocity for itself for the next cycle Problem: It does not know what the other agents are going to do How to act? (i.e. what velocity to select) Global planning vs. Local navigation Basic Idea Use position information of other agent, as well as velocity Assume other agents are moving obstacles (that maintain their current velocity for a while) Feurtey 00 Lamarche, Donikian 04 Reynolds 99 Velocity Obstacles [Fiorini, Shiller, 98] Case Study 3 - Part II - Ming Lin

28 April 18, 2007 Velocity Obstacle γ(p, v) = {p + tv t > 0} VO A B(v B ) = {v A γ(p A, v A v B ) B A } 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 Case Study 3 - Part II - Ming Lin

29 April 18, 2007 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 (RVO) Reciprocal Velocity Obstacle RVO A B(v B, v A ) = {v A 2v A v A VO A B(v B )} Case Study 3 - Part II - Ming Lin

30 April 18, 2007 Using RVO In each cycle, select velocity outside reciprocal velocity obstacle of any other agent Guaranteed to give safe navigation Guaranteed to prevent oscillations We use RVO as core operator of our navigation system Multi-Agent Navigation System 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 Each time step: for each agent: Compute preferred velocity Select new velocity (RVO) Update position of agent according to new velocity Case Study 3 - Part II - Ming Lin

31 April 18, 2007 Global Path Planning Global Path Planning Preprocessing Take only static obstacles into account Visibility graph (or other roadmap) Case Study 3 - Part II - Ming Lin

32 April 18, 2007 Select Preferred Velocity During simulation For each agent: Compute shortest path using roadmap Use direction along path as preferred velocity No local minima Select New Velocity Case Study 3 - Part II - Ming Lin

33 April 18, 2007 Select New Velocity Outside the union of the reciprocal velocity obstacles, closest to preferred velocity 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 Case Study 3 - Part II - Ming Lin

34 April 18, 2007 Adding Realism Orientation and Kinodynamics Inferring Orientation Orientation in direction of motion Side-steps? Backsteps? Kinodynamic constraints Maximum velocity Maximum acceleration More complicated based on orientation Case Study 3 - Part II - Ming Lin

35 April 18, 2007 Selecting Neighbors Neighbor region More region (based on orientation) Results - Stadium scenario 250 agents entering a stadium four narrow entrances forming the word I3D2008 on the field 97 fps (without visualization) on an 8-core Intel Xeon 2.66 GHz Case Study 3 - Part II - Ming Lin

36 April 18, 2007 Results - Stadium scenario Results - Office scenario 1000 agents evacuating an office building two narrow exits densely crowded scenario 46 fps (without visualization) on an 8-core Intel Xeon 2.66 GHz Case Study 3 - Part II - Ming Lin

37 April 18, 2007 Results - Office scenario Results - Crosswalk scenario 100 agents in each corner of the crossroads move to other side of street opposite flow of agents: automatic lane formation 57 fps (without visualization) on an 8-core Intel Xeon 2.66 GHz Case Study 3 - Part II - Ming Lin

38 April 18, 2007 Results - Crosswalk scenario System Demonstrations Real-time Capture Case Study 3 - Part II - Ming Lin

39 April 18, 2007 Extension to 3D 500 agents on a sphere moving to the other side Composite Agents Case Study 3 - Part II - Ming Lin

40 April 18, 2007 Results - Scalability Performance (16 cores, Sitterson scene) Performance (5000 agents, Sitterson scene) Running time (sec/frame) Number of Agents Frame rate (frame/sec) Number of Cores Summary Powerful and simple (easy to implement) local collision avoidance technique for multi-agent navigation Allows for easy integration with global planning, kinodynamic constraints, visibility constraints, etc. Scalable with number of agents and number of processors used Application to Crowd Simulation & Games Case Study 3 - Part II - Ming Lin

41 April 18, 2007 Research Sponsors Army Research Office Defense Advanced Research Projects Agency Department of Energy (Fellowship) Intel Corporation National Science Foundation RDECOM Case Study 3 - Part II - Ming Lin