Geometric and Discrete Path Planning for Interactive Virtual Worlds

Transcription

1 Introduction Topics Geometric and Discrete Path Planning for Interactive Virtual Worlds Marcelo Kallmann University of California Merced Overview of the classical Computational Geometry and AI algorithms related to path planning Overview of recent advances in planning methods for interactive virtual environments Mubbasir Kapadia Rutgers University Course Topics 1) Discrete and Geometric Planning (Marcelo,30min) A*, Shortest Paths, Visibility Graphs, Dijkstra, Shortest Path Maps, Navigation Meshes Course Topics 2) Advanced Planning Techniques (Mubbasir,20min) Extending classical A* to real-time constraints and dynamic scenarios, navigation with constraints, using GPU to speed up computations Examples: the shortest path map (left) and local clearance triangulation (right)

2 Course Topics 3) Planning for Character Animation (Mubbasir and Marcelo, 30min) Character navigation problems, full-body and behavior planning, interactive narrative, etc. Course: Modules - Introduction (3 min) - Discrete and Geometric Planning (Marcelo) (30min) - Advanced Planning Techniques (Mubbasir) (20min) - Planning for Animation (Mubbasir and Marcelo) (30min) - Questions and Discussion (7min) (We will take quick questions after each part as well) Additional Information We will cover a lot of material in little time Most topics will be covered as an overview Additional Material SIGGRAPH course notes Webpages of the authors: Recent book published by the authors: Geometric and Discrete Path Planning for Interactive Virtual Worlds Morgan & Claypool, 2016

3 1 Geometric Path Planning 2 Module I Discrete and Geometric Planning Introduction to Discrete Search Marcelo Kallmann mkallmann@ucmerced.edu Discrete Search 3 Ex: 4-Connected Grid Discretization 4 Main classical algorithms Dijkstra Search expansion outwards from source A* Reduces the number of nodes expanded with the use of a heuristic function Both can be applied to generic graphs Positive edge weights only 4- or 8-connected grids are also graphs

4 Equivalent to a Graph 5 Equivalent to a Graph 6 Example in Grid Discretization 7 Example in Grid Discretization 8 Example in a grid

5 Example in Grid Discretization Q: Example in Grid Discretization Example in Grid Discretization 11 Example in Grid Discretization

6 Example in Grid Discretization 13 Example in Grid Discretization Example in Grid Discretization 15 Example in Grid Discretization

7 Example in Grid Discretization 17 Example in Grid Discretization Example in Grid Discretization 19 Example in Grid Discretization

8 Example in Grid Discretization 21 Example in Grid Discretization wave front propagation wave front propagation Algorithm: Dijkstra Initialization 23 Algorithm: Dijkstra Iteration 1: all neighbors go to Q 24

9 Algorithm: Dijkstra Iteration 2: decrease key called for v 25 Algorithm: Dijkstra Iteration 3: target node t goes to Q 26 Algorithm: Dijkstra Iteration 4: decrease key called for t 27 Algorithm: Dijkstra Iteration 5 28

10 Example 29 Algorithm: A* Includes Heuristic 30 Cost becomes cost-to-come + cost-to-go Typical cost-to-go heuristic: dist(node,goal) Example 31 Analysis Priority Queue 32 Dijkstra A* Self-balancing binary tree or a binary min-heap Insertion, removal and decrease: O(log(k)) Simplifications possible Decrease operation not as simple to implement Good option: to insert again instead of a decrease Overall time O ( (n+m) log n ) (n = number of vertices, m = number of edges) Equivalent to O ( m log n ) Note: m may be O(n 2 )

11 Geometric Path Planning Euclidean Shortest Paths (ESPs) 33 Euclidean Shortest Paths Shortest paths in the Euclidean plane Paths are globally shortest in the plane And not in a given graph representing the plane Cannot be efficiently reduced to a simple graph search Most popular method Search the Visibility Graph unfortunately it has O(n 2 ) edges (n = # obs vertices) 34 But it can be computed in O(n log n) Using the continuous Dijkstra approach Optimal algorithm difficult to implement in practice More about that later 35 Visibility Graph Edges connect all pairs of visible vertices 36 Visibility Graph

12 Visibility Graph 37 Visibility Graph 38 It can be preprocessed Query points added later at run-time Visibility Graph 39 Visibility Graph 40 Full visibility graph Optimizations are possible Optimizations are possible Ex: discard edges connecting concave corners p p q q

13 Visibility Graph Final graph for path search Ready for a discrete path search algorithm p 41 Visibility Graph Preprocessing for a specific clearance value Lozano-Pérez and Wesley 1979 Chew 1985 First dilates the environment, then computes visibility graph of tangents Pre-computation: O(n 2 log n), size: O(n 2 ), query: O(n 2 log n) 42 Shortest path in the Visibility Graph is the ESP q Clearance-independent preprocessing possible Wein, van den Berg and Halperin, the visibility Voronoi complex and its applications, 2007 Preprocessing: O ( n 2 log n ) Query time: O ( n log n + m ) = O ( n 2 ) Probably the best practical method for global optimality Pre-processing for a source point: 43 The Shortest Path Tree Contains shortest paths from all vertices to source point Can be computed from the visibility graph with an exhaustive Dijkstra Expansion 44 Shortest Path Tree

14 The Shortest Path Tree: Example 45 The Shortest Path Tree: Example 46 The Shortest Path Tree The SPT is rooted at some source point Given a destination point, how to use the SPT? First compute visible vertices V to query point Identify vertex v V that is in the shortest path to source point Simple given that vertices store their geodesic distances to the SPT source (cost g) Shortest path is branch passing by v Continuous Dijkstra

15 Continuous Dijkstra 49 Continuous Dijkstra 50 Addresses the whole plane Wavefront propagation Principle is the same as discrete SPT But is continuous, will generate a Shortest Path Map (SPM) partition of the plane in O(n) cells Represents all shortest paths from the source to any point in the continuous plane Once the SPM is computed, ESPs to the source point can be efficiently computed Every point in the wavefront border has equal distance to the source point p p It is based on the simulation of a continuous wavefront propagation from the source point [Mitchell 1991; Mitchell 1993], [Hershberger and Suri 1997] Continuous Dijkstra 51 Continuous Dijkstra 52 Wavefront propagation Wavefront propagation Vertices hit by the wavefront will be visible to their wave generators Every time a vertex is reached, a new wave generator will cover the unseen region from the previous generator

16 Continuous Dijkstra 53 Continuous Dijkstra 54 Wavefront propagation Wavefront propagation New vertices are processed as they are reached New vertices are processed as they are reached Continuous Dijkstra 55 Continuous Dijkstra 56 Wavefront propagation All points in the wavefront border remain with equal geodesic distance to the source point Front will eventually collide with itself forming hyperbolic frontiers Front collisions

17 Continuous Dijkstra 57 Continuous Dijkstra 58 Result: Shortest Path Map Path extraction from SPM Captures all possible shortest paths to the source point First find region containing goal point, then trace back generator vertices q p Continuous Dijkstra: Example 59 Continuous Dijkstra: Example 60

18 Continuous Dijkstra: Example 61 Continuous Dijkstra: Example 62 p q Camporesi and Kallmann, Computing Shortest Path Maps with GPU Shaders, MIG Camporesi and Kallmann, Computing Shortest Path Maps with GPU Shaders, MIG Continuous Dijkstra: Extensions 63 Additional Geometric Representations useful for Path Planning (work in preparation)

19 Navigation Meshes Navigation Meshes Navigation meshes are a representation of the free environment For virtual worlds, being fast is most important Computing ESPs is usually not addressed What properties should we expect? 66 Summary of Expected Properties Linear number of cells Critical for path search to run in optimal times Quality of paths Locally shortest paths should be provided Arbitrary clearance Same structure should handle any clearance value Representation robustness Intersections, overlaps, etc. should be handled Dynamic updates Efficient updates when environment changes 67 Approaches Many approaches are possible Coarser cell decompositions possible (less nodes to search) Ex.: NEOGEN [Oliva and Pelechano 2013] Complete solutions for path planning have been developed Ex.: Recast & Detour toolkit, freely available However meshes need to be preprocessed for each given desired clearance 68

20 Approaches Structures most suitable for handling arbitrary clearance efficiently: Medial Axis CDTs 69 Medial Axis Medial Axis as a navigation mesh Good amount of work available For ex.: extensions for multi layered environments and for handling dynamic updates available Geraerts, Planning Short Paths with Clearance using Explicit Corridors, 2010 van Toll et al., Navigation Meshes for Realistic Multi-Layered Environments, 2011 van Toll et al., A Navigation Mesh for Dynamic Environments, Medial axis represents paths of maximum clearance CDT decomposes the free space in O(n) triangles Triangulations 71 Triangulations 72 Triangulations as navigation meshes Triangle meshes are relatively simple to build Are composed of only straight edges Paths can be easily computed However handling clearance is not straightforward Can easily generate locally shortest paths For instance corridors will be already triangulated and ready for the Funnel algorithm (recent benchmark work shows that triangulations are faster) However, clearance not directly represented Clearance checks per edge not enough Even if additional free edges are inserted to improve capturing clearance in corridors [Lamarche and Donikian, Crowd of Virtual Humans: a New Approach for Real Time Navigation in Complex and Structured Environments, 2004] Clearance checks per triangle not enough Previous attempts do not always work [Demyen and Buro, Efficient triangulation-based pathfinding, 2006]

21 Triangulations Local Clearance Triangulations (LCTs) Proposes a refinement strategy for CDTs allowing clearance information to be stored in the triangulation 73 Local Clearance Triangulations Clearance Defined per triangle traversal Traversal from ab to bc: 74 Details in TOG 2014 Kallmann, Dynamic and Robust Local Clearance Triangulations, 2014 Traversal clearance: s is the constraint behind ac and closest to b Local Clearance Triangulations 75 Local Clearance Triangulations 76 However clearance metric not enough But it can work if there are no disturbances Clearance in the red arrow direction not well captured By refining the triangulation disturbances can be eliminated and correct paths are obtained Triangle being traversed Traversal disturbance

22 Local Clearance Triangulations 77 Local Clearance Triangulations 78 Refinements solve disturbances Refinements solve disturbances Disturbances appear when a traversal does not correctly captures the local clearance of all possible exit directions Now all disturbances have been eliminated with refinements Correct result: no valid path exists Traversal disturbance New traversal now correctly captures narrow passage Local Clearance Triangulations 79 Example LCT 80 Example of refinements Total number of vertices remain O(n)

23 Example LCT 81 Example LCT 82 Test environment for The Sims 4: each small square represents a static character, later dynamically removed when it is time to walk [used with permission] Example 83 New Results on LCTs 84 Dynamic Operations with management of refinements Robust operations addressing self-intersections at run-time Efficiently representation of environments at different scales, Dynamic and Robust Local Clearance Triangulations, TOG 2014

24 Dynamic Updates: Example 85 Robustness: Example 86 Robust watertight dynamic updates at run-time Dynamic updates while maintaining the mesh ready for arbitrary clearance path queries Robustness with floating point representation is achieved with one exact point location test for correctness detection and perturbation of invalid coordinates Summary Euclidean Shortest Paths are difficult to be computed efficiently Visibility Graph popular but is a O(n 2 ) structure Continuous Dijkstra methods promising Navigation Meshes Focus on efficient path planning Medial axis gives paths of maximum clearance Triangulations can be used to efficiently compute paths with arbitrary clearance Questions?

25 Challenges Real-?me Planning in Dynamic Environments Advanced Planning Techniques Mubbasir Kapadia Planning with Constraints Scaling to large worlds and many agents Proposed Solu?ons Real-?me Planning in Dynamic Environments From Classical A* to Any?me Dynamic Search Planning with Constraints Scaling to large worlds and many agents Proposed Solu?ons Real-?me Planning in Dynamic Environments From Classical A* to Any?me Dynamic Search Planning with Constraints Constraint- Aware Naviga?on in Dynamic Environments Scaling to large worlds and many agents

26 Proposed Solu?ons Real-?me Planning in Dynamic Environments From Classical A* to Any?me Dynamic Search Planning with Constraints Constraint- Aware Naviga?on in Dynamic Environments Scaling to large worlds and many agents Any?me Dynamic Search on the GPU A* Search Algorithm Computes op*mal g- values of relevant states Dijkstra s Search Expansion Expands state in the order of f = g values A* Search Expansion Expands state in the order of f = g+h values Courtesy Likhachev 2010

27 A* Search Expansion Expands state in the order of f = g+h values Weighted A* Search Expansion Expands states in the order of f = g + ε.h values For large problems, this results in A* quickly running out of memory ε > 1 bias towards states that are closer to goal Courtesy Likhachev 2010 Courtesy Likhachev 2010 Any?me Repairing A* (ARA*) Efficient series of weighted A* searches with decreasing ε Any?me Repairing A* (ARA*) ARA*: Any?me A* with Provable Bounds on Sub- Op?mality Maxim Likhachev, Geoff Gordon and Sebas?an Thrun Advances in Neural Informa*on Processing Systems, 2003

28 Any?me Repairing A* (ARA*) Any?me Repairing A* (ARA*) Consistent State: Inconsistent State: Any?me Repairing A* (ARA*) Any?me D* Combined proper*es of any*me and dynamic planning Set ε to large value While goal is not reached ComputePathWithReuse() Publish ε-suboptimal path Follow path until map is updated Update corresponding edge costs Set start to current state of agent If significant changes were observed Increase ε or replan from scratch Else Decrease ε Any?me search in dynamic graphs Maxim Likhachev, Dave Ferguson, Geoff Gordon, Anthony Stentz, and Sebas?an Thrun Journal of Ar*ficial Intelligence, 2008

29 Any?me D* Combined proper*es of any*me and dynamic planning Set ε to large value While goal is not reached ComputePathWithReuse() Publish ε-suboptimal path Follow path until map is updated Update corresponding edge costs Set start to current state of agent If significant changes were observed Increase ε or replan from scratch Else Decrease ε Any?me search in dynamic graphs Maxim Likhachev, Dave Ferguson, Geoff Gordon, Anthony Stentz, and Sebas?an Thrun Journal of Ar*ficial Intelligence, 2008 Any?me D* Combined proper*es of any*me and dynamic planning Set ε to large value While goal is not reached ComputePathWithReuse() Publish ε-suboptimal path Follow path until map is updated Update corresponding edge costs Set start to current state of agent If significant changes were observed Increase ε or replan from scratch Else Decrease ε Any?me search in dynamic graphs Maxim Likhachev, Dave Ferguson, Geoff Gordon, Anthony Stentz, and Sebas?an Thrun Journal of Ar*ficial Intelligence, 2008 Any?me D* Combined proper*es of any*me and dynamic planning Set ε to large value While goal is not reached ComputePathWithReuse() Publish ε-suboptimal path Follow path until map is updated Update corresponding edge costs Set start to current state of agent If significant changes were observed Increase ε or replan from scratch Else Decrease ε Any?me search in dynamic graphs Maxim Likhachev, Dave Ferguson, Geoff Gordon, Anthony Stentz, and Sebas?an Thrun Journal of Ar*ficial Intelligence, 2008 Any?me D*

30 Proposed Solu?ons Real-?me Planning in Dynamic Environments From Classical A* to Any?me Dynamic Search Planning with Constraints Constraint- Aware Naviga?on in Dynamic Environments Scaling to large worlds and many agents Any?me Dynamic Search on the GPU Global Naviga?on with Spa?al Constraints in Dynamic Environments Challenges Environment representa?on Constraint specifica?on Constraint Sa?sfac?on Extending AD* to compute and repair constraint- aware paths

31 Proposed Solu?ons Environment representa?on Hybrid representa?on for constraint- aware naviga?on Constraint specifica?on Constraint Sa?sfac?on Proposed Solu?ons Environment representa?on Hybrid representa?on for constraint- aware naviga?on Constraint specifica?on Cost mul?plier fields used to represent qualita?ve constraints Constraint Sa?sfac?on Proposed Solu?ons Environment representa?on Hybrid representa?on for constraint- aware naviga?on Constraint specifica?on Cost mul?plier fields used to represent qualita?ve constraints Constraint Sa?sfac?on An any?me dynamic planner that computes and repairs constraint- aware paths Annotated Environment

32 Problem Defini?on with Constraints Plan without constraint sa?sfac?on Plan with constraint sa?sficac?on Environment Triangula?on

33 Object annota?ons with addi?onal nodes added to Dense Uniform Graph Constraint Formula?on Hybrid graph

34 Constraint Formula?on Constraint Formula?on Constraint Formula?on Constraint Formula?on

35 Mul?ple Constraints Mul?ple Constraints Cost mul?plier for a transi?on: Cost mul?plier for a transi?on: Mul?ple Constraints Mul?ple Constraints Cost mul?plier for a transi?on: Cost mul?plier for a transi?on:

36 Mul?ple Constraints Planner: Cost Computa?on Modified cost of reaching state s: Cost mul?plier for a transi?on: Accommoda?ng Dynamic Constraints

37 Benefit of Hybrid Domain Proposed Solu?ons Real-?me Planning in Dynamic Environments From Classical A* to Any?me Dynamic Search Planning with Constraints Constraint- Aware Naviga?on in Dynamic Environments Scaling to large worlds and many agents Any?me Dynamic Search on the GPU Need for high fidelity naviga?on in complex, dynamic virtual environments

38 Challenges Large- scale, complex, dynamic environments Strict op?mality requirements Proposed Solu?ons Large- scale, complex, dynamic environments Massively parallel wave- front based search with efficient plan repair Strict op?mality requirements Scalability with number of agents Scalability with number of agents Proposed Solu?ons Large- scale, complex, dynamic environments Massively parallel wave- front based search with efficient plan repair Strict op?mality requirements Termina?on condi?on enforces strict op?mality with minimum number of GPU itera?ons Scalability with number of agents Proposed Solu?ons Large- scale, complex, dynamic environments Massively parallel wave- front based search with efficient plan repair Strict op?mality requirements Termina?on condi?on enforces strict op?mality with minimum number of GPU itera?ons Scalability with number of agents Handles any number of moving agents at no addi?onal computa?onal cost

39 Method Overview Method Overview Method Overview Method Overview

40 Method Overview Method Overview Method Overview Method Overview

41 Wavefront expansion. N =3 Wavefront expansion. N =11 Wavefront expansion. N =15 Wavefront expansion. N =18

42 Termina?on Condi?ons Non- uniform state space Exit when goal reached Exit when whole map converges Minimal map convergence with op?mality guarantees Sub- op?mal solu?on, N = 8 Termina?on Condi?ons Exit when goal reached Exit when whole map converges Minimal map convergence with op?mality guarantees

43 Op?mal solu?on, N = 17 Termina?on Condi?ons Exit when goal reached Exit when whole map converges Minimal map convergence with op?mality guarantees Op?mal solu?on, N = 12 (minimum number of itera?ons) Efficient Plan Repair for Dynamic Environments & Moving Agents

44 Mul?- Agent Planning Extended Termina?on Condi?on Mul?- Agent Simula?on Single map can be queried by all agents to compute path Movement along path using local collision avoidance Mul?ple Target Loca?ons A separate map required for each target Significant memory overhead Performance Analysis Agent Scalability Environment Scalability Memory Dynamic Planning

45 GPU- based Dynamic Search on Adap?ve Resolu?on Grids GPU- based Dynamic Search on Adap?ve Resolu?on Grids Francisco Garcia, Mubbasir Kapadia, and Norman I. Badler IEEE Interna*onal Conference on Robo*cs and Automa*on, June 2014

46 Outline Footstep Domain for Dynamic Crowds Planning Techniques for Character Anima6on Mubbasir Kapadia Precompu?ng Environment Seman?cs for Contact- Rich Character Anima?on Addi?onal Applica?on Domains Current steering algorithms cannot handle the space of all possible scenarios that agents encounter in dynamic virtual environments A par:cle- based agent representa:on cannot capture nuanced interac:ons that humans exhibit in confined and crowded situa:ons. Scenario Space: Characterizing Coverage, Quality, and Failure of Steering Algorithms Mubbasir Kapadia, Ma# Wang, Shawn Singh, Glenn Reinmann, Petros Faloutsos ACM SIGGRAPH Symposium on Computer Anima7on, August 2011

47 A par:cle- based agent representa:on cannot capture nuanced interac:ons that humans exhibit in confined and crowded situa:ons. A par:cle- based agent representa:on cannot capture nuanced interac:ons that humans exhibit in confined and crowded situa:ons. Footstep Naviga6on for Dynamic Crowds Footstep Naviga6on for Dynamic Crowds Shawn Singh, Mubbasir Kapadia, Glenn Reinmann, Petros Faloutsos Special Issue, Computer Anima7on and Virtual Worlds (CAVW), April 2011

48 State and Ac6on Space Footstep Ac6on Selec6on Footstep Domain Footstep Ac6on Selec6on Footstep Orienta6on

49 Cost Formula6on Cost Formula6on Cost Func6on Cost Func6on Heuris6c Func6on Heuris6c Func6on Spherical Inverted Pendulum Model SagiNal View Cost Formula6on Cost Func6on Heuris6c Func6on

50 Cost Formula6on Short Horizon Space- Time Planner Cost Func6on Heuris6c Func6on U Turn Dynamic Collision Bounds

51 Narrow Passageways Large Scale Simula6ons Coverage Comparison Need for high fidelity naviga6on in complex, dynamic virtual environments Scenario Space: Characterizing Coverage, Quality, and Failure of Steering Algorithms Mubbasir Kapadia, Ma# Wang, Shawn Singh, Glenn Reinmann, Petros Faloutsos ACM SIGGRAPH Symposium on Computer Anima7on, August 2011

52 The Quest for Complete Coverage Outline Footstep Domain for Dynamic Crowds Precompu6ng Environment Seman6cs for Contact- Rich Character Anima6on Addi?onal Applica?on Domains Scenario Space: Characterizing Coverage, Quality, and Failure of Steering Algorithms Mubbasir Kapadia, Ma# Wang, Shawn Singh, Glenn Reinmann, Petros Faloutsos ACM SIGGRAPH Symposium on Computer Anima7on, August 2011 REQUIREMENTS Scalability in environment and mo?on complexity Interac?vity Coupled character and environment authoring PRECISION: Precomputed Environment Seman6cs for Contact- Rich Character Anima6on Mubbasir Kapadia, Xu Xianghao, Maurizio NiS, Marcelo Kallmann, Stelian Coros, Robert W. Sumner, Markus Gross ACM SIGGRAPH Symposium on Interac7ve 3D Graphics and Games (I3D), 2016

53 REQUIREMENTS Scalability in environment and mo6on complexity REQUIREMENTS Interac6vity - - Interac?vity Coupled character and environment authoring REQUIREMENTS PRECISION SOLUTIONS Coupled character and environment authoring Mo6on Analysis: Iden?fy contact seman?cs Environment Analysis: Iden?fy how characters can interact with geometry Run6me Naviga6on & Mo6on Synthesis: Seamless integra?on with exis?ng approaches

54 PRECISION Framework PRECISION Framework Mo6on Analysis PRECISION Framework Environment Analysis

55 Original Geometry Triangulated Geometry Triangles Clustered into Surfaces Surface Grouping based on Normals

56 PRECISION Framework Mo6on Skill Detec6on Mo6on Signature Clustered Surfaces Annotated Mo6on Skills Mo6on Skill Detec6on

57 Contact Rota6on

58 Parallel Surfaces Arbitrary Orienta6ons

59 Collision- free mo6on Mo6on with collision PRECISION Framework Naviga6on Integra6on

60 Extended Naviga6on Mesh PRECISION Framework Run6me Naviga6on and Mo6on Synthesis

61 Outline ACCLMesh: Curvature- Based Naviga?on Mesh Genera?on Footstep Domain for Dynamic Crowds Precompu?ng Environment Seman?cs for Contact- Rich Character Anima?on Addi6onal Applica6on Domains ACCLMesh: Curvature- Based Naviga6on Mesh Genera6on Glen Berseth, Mubbasir Kapadia, Petros Faloutsos Computer Anima7on and Virtual Worlds (2016, To Appear)

62 Mul6- Domain Planning for Real- 6me Planning in Dynamic Environments An Event- Centric Planning Approach for Dynamic Real- Time Narra6ve Mul6- Domain Planning for Real- 6me Planning in Dynamic Environments Mubbasir Kapadia, Alejandro Beacco Porres, Francisco Garcia, Nuria Pelechano, Norman. I. Badler ACM SIGGRAPH/EG Symposium on Computer Anima?on, 2013 An Event- Centric Planning Approach for Dynamic Real- Time Narra6ve Alexander Shoulson, Max Gilbert, Mubbasir Kapadia, and Norman I. Badler Interna7onal Conference on Mo7on in Games, 2013 Conclusion Planning not limited to simple naviga?on problems or non- interac?ve applica?ons. Challenges Discre?zing problem representa?on Defining problem domain (state, ac?on space, costs, heuris?cs) Choosing right planning strategy

63 Module III Planning Techniques for Character Animation Marcelo Kallmann 1 When to use full-body motion planners? To achieve automatic motion synthesis for virtual characters among obstacles 3D collision detection always needed (bottleneck) Planners can be integrated on top of motion controllers Leveraging the quality for several powerful approaches developed in computer animation Ex.: Motion Control session yesterday Planning in High Dimensions Planning in High Dimensions Build graph representation of free space by sampling valid poses/configurations Example graph/roadmap built by sampling: Planning Collision-Free Reaching Motions for Interactive Object Manipulation and Grasping, Eurographics, 2003 Planning Collision-Free Reaching Motions for Interactive Object Manipulation and Grasping, Eurographics, 2003

64 Planning locomotion with motion capture data Adding Motion Capture Data Example approach Build a motion graph from motion capture data Search on the motion graph (graph unrolling) Good quality, but often slow to use directly Possible to improve speed with search precomputation and 2D path planning 6 Extensive literature available on the area Representative references in course notes Speeding up motion search By pre-computing search trees per node: 7 Precomputed Motion Maps Analyzing Locomotion Synthesis with Feature-Based Motion Graphs, IEEE TVCG 2012 Precomputed Motion Maps for Unstructured Motion Capture, SCA 2012 Feature-Based Locomotion with Inverse Branch Kinematics, best paper at MIG 2011

65 Precomputed Motion Maps Integrating manipulation planning with locomotion Analyzing Locomotion Synthesis with Feature-Based Motion Graphs, IEEE TVCG 2012 Precomputed Motion Maps for Unstructured Motion Capture, SCA 2012 Feature-Based Locomotion with Inverse Branch Kinematics, best paper at MIG 2011 Addressing Full-Body Manipulations 11 Addressing Full-Body Manipulations 12 Integration of two planners Motion capture concatenation search for locomotion Sampling-based planning for the arm Multi-Modal Data-Driven Motion Planning and Synthesis Mentar Mahmudi and Marcelo Kallmann ACM SIGGRAPH Conference on Motion in Games (MIG), 2015 Multi-Modal Data-Driven Motion Planning and Synthesis Mentar Mahmudi and Marcelo Kallmann ACM SIGGRAPH Conference on Motion in Games (MIG), 2015

66 Ex. Application: Virtual Demonstrators Determine suitable locations for delivering information, and then animate a solution 14 Addressing application-specific coordination constraints demonstrator target observer Planning Motions and Placements for Virtual Demonstrators Yazhou Huang and Marcelo Kallmann IEEE Transactions on Visualization and Computer Graphics (TVCG), 2015 Behavioral Model 15 Placement Determination 16 Model derived from human subjects 4 participants, actions to 6 objects, for 5 observers at different locations Action: pointing and delivering info about the object

67 Placement Determination 17 Additional Results 18 Planning Motions and Placements for Virtual Demonstrators Yazhou Huang and Marcelo Kallmann IEEE Transactions on Visualization and Computer Graphics (TVCG), 2015 Additional Information Acknowledgements Grad students and Collaborators Mentar Mahmudi, Yazhou Huang, Carlo Camporesi, Amaury Aubel Funding Agencies CITRIS Seed Funding ( #12, #14 ) National Science Foundation (IIS , BCS , CNS , CNS ) Additional Material SIGGRAPH course notes Webpages of the authors: Recent book published by the authors: Geometric and Discrete Path Planning for Interactive Virtual Worlds Morgan & Claypool, 2016 Thank You!