Real-time Continuous Collision Detection and Penetration Depth Computation

Transcription

1 Real-time Continuous Collision Detection and Penetration Depth Computation Young J. Kim Ewha Womans University

2 Non-penetration Constraint No overlap between geometric objects interior( A) B A B A B A B Crucial for mimicking the physical presence 2

3 Earlier Research Focused on checking for whether there is any overlap between A and B, fixed in space Tons of papers published in the area of collision detection Well-studied and matured technology Not clear how to resolve such overlap 3

4 Recent Research Trends Avoid inter-penetration Continuous collision detection (CCD) Allow inter-penetration but backtrack Penetration depth (PD) A B A 4

5 Autonomous Ice Serving Robot (with Zhixing Xue at FZI) 5

6 Outline Recent research results CCD (rigid, polygon-soups, articulated) PD (translational) Applications Real-time rigid body dynamics Robotic grasping CAD disassembly 6

7 CONTINUOUS COLLISION DETECTION (CCD) 7

8 Discrete Collision Detection Collision Missing 8

9 Continuous Collision Detection Motion trajectory f(t) is known in advance Time of Contact f() t 9

10 Applications of Continuous CD Rigid body dynamics Find the time of contact (ToC) to apply forces 10

11 Applications of Continuous CD Motion planning Check whether a path is collision-free 11

12 Previous Work on CCD Algebraic solution -[Canny86], [Redon00], [Kim03], [Choi06] Swept volume -[Abdel-Malek02],[Hubbard93], [Redon04a,b] Bisection -[Redon02], [Schwarzer02] Kinetic data structures -[Kim98], [Kirkpatrick00], [Agarwal01] Minkowski sum -[Bergen04] Conservative advancement [Mirtich96], [Mirtich00],[Coumans 2006],[Zhang06], [Tang09] 12

13 Conservative Advancement (CA) Assume objects are convex Find the 1 st time of contact (ToC) of a moving object 13

14 Conservative Advancement (CA) t i 1. Find a step size to conservatively advance the object before collision occurs 2. Repeat until inter-distance < ε ToC = t 1 + t 2 + t 3 + t

15 Calculating t in CA p v n d d, n: closest distance, direction vector v: velocity t t d v ( t) max( n( t) v ( dt t) n( t) ) dt

16 Calculating t in CA Distance t 0 t d v( t) n( t) dt t 0 t d max( v( t) n( t) ) dt d Motion Bound 16

17 Extension to Non-convex [Zhang et. al PG 06] Use of convex decomposition Build a hierarchy of decomposed convex pieces and perform CA hierarchically 17

18 Bunny vs. Bunny 70K triangles/bunny 110 FPS # of iterations

19 Torusknot vs. Torusknot 2.8K 1067 FPS # of iterations K 400 FPS # of iterations K 186 FPS # of iterations

20 Extension to Polygon-Soups [Tang et. al IEEE ICRA 09] Construct the bounding volume hierarchy of polygons Motion bound calculation Bounding volume Triangles t d 20

21 Extension to Polygon-Soups [Tang et. al IEEE ICRA 09] We use swept sphere volumes [Larsen et. al IEEE ICRA 1999] 21

22 Motion Bound Calculation Motion bound of SSV (e.g. PSS) ω n c r 1 ω : rotational velocity n : closest direction r : radius of PSS 22

23 C 2 A:Controlling the CA Iterations timing(ms) Normalized distance timing distance Iteration step 1. Compute approximate distance in the beginning 2. Compute exact distance toward the end 23

24 Gears Hammer Clubs Results - Timings 4X 4X 28X C2A C 2 A Without CC2A 2 A (ms) (ms) 24

25 Comparisons against [Zhang 06] Dynamic Bunnies C2AC 2 A FAST Zhang 06 Bunnies Toruskots (ms) [Zhang 06] can handle only manifold surfaces 25

26 Extension to Articulated Models [Zhang et. al SIGGRAPH 07] Treat each link as a rigid body Apply CA to each link independently Taking the minimum of CA results 26

27 Motion Bound Calculation t d i 1 j j 1 0 k 1 j 1 υ1 n n ω1 L 1 υ j n ω 1 ωk L j j 2 k 2 0 v i : velocity of link i 1 L 2 2 L 3 1 ω 2 2 ω 3 i-1 ω i : rotational velocity of link i w.r.t. link i-1 0 ω 1 0 L 1 i-1 L i : difference vector btwn the links 27

28 Problems in Straightforward CA Problems O(n 2 ) checking between individual links 28

29 Spatial Culling Cull the link pairs that are far apart Use bounding volume-based collision-culling 29

30 Spatial Culling using Dynamic AABB Goal Compute an axis-aligned bounding box (AABB) that bounds the motion of a moving link 30

31 Bounding Volume Culling Interval Arithmetic Taylor Models 31

32 Locomotion Benchmark CCD performance 1.22 msec Mannequin 15 links, 20K tri Obstacles 101K tri Locomotion SW Footstep TM 32

33 Exercise Benchmark Mannequin 15 links, 20K triangles Self-CCD performance 0.38 msec 33

34 Motion Planning Benchmark 1 Excavator 52 links, 19K tri Obstacles 0.4M tri CCD performance 100~700 msec 34

35 Motion Planning Benchmark 2 Tower crane 14 links, 1288 tri CCD performance 5.66~15.1 msec 35

36 Articulated Body Dynamics Benchmark Four trains 10 links, 23K tri (each) CCD performance 535 msec 36

37 Software Implementations Source codes are available (2-manifold) (polygon-soups) (articulated) 37

38 PENETRATION DEPTH (PD) COMPUTATION 38

39 Pointwise Penetration Depth [Tang et. al SIGGRAPH 09] Defined as deepest interpenetrating points 39

40 Pointwise Penetration Depth 1. Find intersection surfaces and 2. Penetration depth = Penetration Depth

41 Pointwise Penetration Depth Demo (40K Bunny vs 40K Bunny) 41

42 Benchmark: Pointwise PD Model complexity 50K tri Avg. Performance 3.88ms/pair 42

43 Benchmark: Pointwise PD Model complexity 3.5K tri Avg. performance 0.95ms/pair 43

44 Penetration Depth [Dobkin 93] Minimum translational distance to separate overlapping objects A B Penetration Depth 44

45 Applications of Penetration Depth Dynamics simulation Penalty-based Impulse-based A Impulse Point of Impact B Penetration Depth 45

46 Previous Work on PD Convex polytopes -[Cameron and Culley86], [Dobkin93], [Agarwal00], [Bergen01], [Kim04] Non-convex polyhedra -[Kim02],[Redon and Lin06], [Lien08a,b], [Hachenberger09] Distance fields -[Fisher and Lin01], [Hoff02], [Sud06] Pointwise PD -[Tang09] Generalized PD [Ong and Gilbert96], [Ong96], [Zhang07] Volumetric PD - [Wellner and Zachmann09] 46

47 Minkowski Sum P Q { p q p P, q Q} P Q { p q p P, q Q} Q P P Q 47

48 Proximity VS Minkowski Sum Penetration Depth Closest Distance P Q 48

49 Combinatorial Explosion Complexity of Minkowski Sum O(m 3 n 3 ) with m and n triangles 49

50 PD Estimation [Je et. al Tech Report 2010] Penetration Depth o Boundary of Minkowski Sums 50

51 Out-Projection = CCD Out-Projection q f q 0 o Boundary of Minkowski Sums 51

52 In-Projection = LCP (Linear Complementarity Problem) Je et. al Tech Report 2010 q 2 In-Projection o Boundary of Minkowski Sums 52

53 PolyDepth: Iterative Optimization Out-Projection q f q 1 q 2 q 0 In-Projection Penetration Depth o Boundary of Minkowski Sums 53

54 PolyDepth Performance Spoon: 1.3K triangles Cup: 8.4K triangles Time: 1~7 msec 54

55 PolyDepth Performance Bunny: 40K triangles Dragon: 174K triangles Time: 2~15 msec 55

56 Comparison against Exact Solution Accuracy Performance 56

57 APPLICATIONS 57

58 Real-time Physics Simulation using PD 214K triangles in total 802K triangles in total 58

59 Robotic Grasping using CCD With Zhixing FZI 59

60 CAD Disassembly using CCD With Liangjun Stanford/UNC 60

61 Summary CCD PD Concept Collision avoidance Collision correction Usages 1. Constraint-based dynamics 2. Exact motion planning 3. Grasping 1. Penalty-, impulsebased dynamics 2. Retraction-based motion planning Complexities O(mn) O(m 3 n 3 ) 61

62 Future Work Continuous collision detection N-body Non-linear motion PD Articulated body Deformable N-body 62

63 Collision Culling of a Millon Bodies on GPUs [Liu et al. SIGGRAPH ASIA 2010] Real-time Dynamics Simulation of 16,000 Rigid Bodies 63

64 Acknowledgements Min Tang, Xinyu Zhang, Minkyoung Lee, Youngeun Lee (Ewha) Stephane Redon (INRIA) Dinesh Manocha (UNC) Liangjun Zhang (Stanford) Zhixing Xue (FZI) KEIT/MKE (IT core research) KRF (Young investigator award) 64

65 Main References X. Zhang, M. Lee, Y. Kim, Interactive Continuous Collision Detection for Non-convex Polyhedra, Pacific Graphics X. Zhang, S. Redon, M. Lee, Y. Kim, Continuous Collision Detection for Articulated Models using Taylor Models and Temporal Culling, SIGGRAPH M. Tang, Y. Kim, D. Manocha, C 2 A: Controlled Conservative Advancement for Interactive Continuous Collision Detection, IEEE ICRA

66 Main References M. Tang, M. Lee, Y. Kim, Interactive Hausdorff Distance Computation for General Polygonal Models, SIGGRAPH C. Je, M. Tang, Y. Lee, M. Lee, Y. Kim, PolyDepth: Real-time Penetration Depth Computation using Iterative Contact-space Projection, Ewha Technical Report M. Tang, Y. Kim, D. Manocha, Efficient Local Planning using Connection Collision Query, Ewha Technical Report

67 Thank you for listening!