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Multimodal Rendering of Walking Over Virtual Grounds

Abstract

The addition of multimodal feedback during navigation in a virtual environment is fundamental when aiming at fully immersive and realistic simulations. Several visual, acoustic, haptic or vibrotactile perceptual cues can be generated when walking over a ground surface. Such sensory feedback can provide crucial and varied information regarding either the ground material itself, the properties of the ground surface such as slope or elasticity, the surrounding environment, the specificities of the foot-floor interaction such as gait phase or forces, or even users’ emotions. This chapter addresses the multimodal rendering of walking over virtual ground surfaces, incorporating haptic, acoustic and graphic rendering to enable truly multimodal walking experiences.

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Notes

  1. 1.

    http://www.soundobject.org/SDT/

  2. 2.

    http://niw.soundobject.org

References

  1. Adjémian F, Evesque P (2002) Different regimes of stick-slip in granular matter: from quasi- periodicity to randomness. In: EGS XXVII general assembly

    Google Scholar 

  2. Alava MJ, Nukala PKVV, Zapperi S (2006) Statistical models of fracture. Adv Phys 55(3):349–476

    Google Scholar 

  3. Avanzini F, Rocchesso D (2001) Modeling collision sounds: non-linear contact force. In: Proceedings of COST-G6 conference on digital audio effects, pp 61–66

    Google Scholar 

  4. Avanzini F, Serafin S, Rocchesso D (2005) Interactive simulation of rigid body interaction with friction-induced sound generation. IEEE Trans Speech Audio Process 13(5):1073–1081

    Article  Google Scholar 

  5. Baldassarri A, Dalton F, Petri A, Zapperi S, Pontuale G, Pietronero L (2006) Brownian forces in sheared granular matter. Phys Rev Lett 96(11):118002

    Google Scholar 

  6. Barrass S, Adcock M (2002) Interactive granular synthesis of haptic contact sounds. In: Proceedings of AES. 22nd international conference on virtual, synthetic and entertainment audio

    Google Scholar 

  7. Blesser B (2001) An interdisciplinary synthesis of reverberation viewpoints. J Audio Eng Soc 49(10):867–903

    Google Scholar 

  8. Bresciani J-P, Ernst MO, Drewing K, Bouyer G, Maury V, Kheddar A (2005) Feeling what you hear: auditory signals can modulate tactile tap perception. Exp Brain Res 162:172–180

    Google Scholar 

  9. Burdea GC, Akay M (1996) Force and touch feedback for virtual reality. Wiley, New York

    Google Scholar 

  10. Christensen RR, Hollerbach JM, Xu Y, Meek SG (2000) Inertial-force feedback for the treadport locomotion interface. Presence: Teleoper Virtual Environ 9(1):1–14

    Google Scholar 

  11. Chueng P (2002) Designing sound canvas: the role of expectation and discrimination. In: Proceedings of ACM CHI extended abstracts on human factors in computing systems. pp 848–849

    Google Scholar 

  12. Cirio G, Marchal M, Hillaire S, Lécuyer A (2011) Six degrees-of-freedom haptic interaction with fluids. IEEE Trans Visual Comput Graph 17(11):1714–1727

    Google Scholar 

  13. Cirio G, Marchal M, Lécuyer A, Cooperstock J (2012) Vibrotactile rendering of splashing fluids. IEEE Trans Haptics 99:1

    Google Scholar 

  14. Cook PR (2002) Modeling Bill’s gait: analysis and parametric synthesis of walking sounds. In: Proceedings of audio engineering society 22nd conference on virtual, synthetic and entertainment audio, Espoo, Finland

    Google Scholar 

  15. Cook PR (2002) Real sound synthesis for interactive applications. AK Peters, Natick

    Google Scholar 

  16. Courtney A, Chow HM (2000) A study of tile design for tactile guide pathways. Int J Ind Ergon 25(6):693–698

    Article  Google Scholar 

  17. Cress DH (1978) Terrain considerations and data base development for the design and testing of devices to detect intruder-induced ground motion. Technical report M-78-1, U.S. Army Engineer Waterways Experiment Station, Vicksburg, Mississippi

    Google Scholar 

  18. Crossan A, Williamson J, Murray-Smith R (2004) Haptic granular synthesis: targeting, visualisation and texturing. In: Proceedings of international symposium on non-visual & multimodal visualization, pp 527–532

    Google Scholar 

  19. Dalton F, Farrelly F, Petri A, Pietronero L, Pitolli L, Pontuale G (2005) Shear stress fluctuations in the granular liquid and solid phases. Phys Rev Lett 95(13):138001

    Google Scholar 

  20. Darken RP, Cockayne WR, Carmein D (1997) The omni-directional treadmill: a locomotion device for virtual worlds. In: Proceedings of the 10th annual ACM symposium on user interface software and technology. pp 213–221

    Google Scholar 

  21. Delle Monache S, Polotti P, Rocchesso D (2010) A toolkit for explorations in sonic interaction design. In: Proceedings of the ACM 5th audio mostly conference. pp 1–7

    Google Scholar 

  22. Dickstein R, Plax M (2012) Metronome rate and walking foot contact time in young adults. Percept Mot Skills 114(1):21–28

    Article  Google Scholar 

  23. Dixon SJ, Collop AC, Batt ME (2000) Surface effects on ground reaction forces and lower extremity kinematics in running. Med Sci Sports Exerc 32(11):1919–1926

    Google Scholar 

  24. Dixon SJ, Cooke A (2004) Shoe-surface interaction in tennis. In: Hung GK, Pallis JM (eds) Biomedical engineering principles in sports. Kluwer Academic/Plenum Publishers, New York, p 125

    Google Scholar 

  25. Ekimov A, Sabatier J (2006) Vibration and sound signatures of human footsteps in buildings. J Acoust Soc Am 120:762

    Google Scholar 

  26. Ekimov A, Sabatier J (2008) A review of human signatures in urban environments using acoustic and seismic methods. In: Proceedings of IEEE technologies for homeland security

    Google Scholar 

  27. Farnell AJ (2007) Marching onwards—procedural synthetic footsteps for video games and animation. In: Pd convention

    Google Scholar 

  28. Farrington SM (1998) Invariant acoustic cues for determining source characteristics of footstep sounds. Master’s thesis, State University of New York

    Google Scholar 

  29. Ferris DP, Louie M, Farley CT (1998) Running in the real world: adjusting leg stiffness for different surfaces. Proc R Soc B: Biol Sci 265(1400):989

    Google Scholar 

  30. Fontana F, Bresin R (2003) Physics-based sound synthesis and control: crushing, walking and running by crumpling sounds. In: Proceedings of colloquium on musical informatics, Florence, Italy, pp 109–114

    Google Scholar 

  31. Fontana F, Morreale F, Regia-Corte T, Lécuyer A, Marchal M (2011) Auditory recognition of floor surfaces by temporal and spectral cues of walking. In: Proceedings of international conference on auditory display

    Google Scholar 

  32. Freeman J, Lessiter J (2001) Hear there & everywhere: the effects of multi-channel audio on presence. In: Proceedings of ICAD 2001, pp 231–234

    Google Scholar 

  33. Fukumoto M, Sugimura T (2001) Active click: tactile feedback for touch panels. In: Proceedings of ACM CHI extended abstracts. pp 121–122

    Google Scholar 

  34. Funkhouser T, Tsingos N, Jot JM (2003) Survey of methods for modeling sound propagation in interactive virtual environment systems. Presence

    Google Scholar 

  35. Galbraith F, Barton M (1970) Ground loading from footsteps. J Acoust Soc Am 48:1288–1292

    Google Scholar 

  36. Gaver WW (1993) What in the world do we hear? An ecological approach to auditory event perception. Ecol Psychol 5(1):1–29

    Article  MathSciNet  Google Scholar 

  37. Gibson JJ (1977) The theory of affordances. In: Erlbaum L (eds) Perceiving, Acting, and Knowing. Erlbaum, Hillsdale

    Google Scholar 

  38. Giordano BL, McAdams S, Rocchesso D (2010) Integration of acoustical information in the perception of impacted sound sources: the role of information accuracy and exploitability. J Exp Psychol: Hum Percept Perform 36(2):462–476

    Article  Google Scholar 

  39. Giordano BL, McAdams S, Visell Y, Cooperstock J, Yao H-Y, Hayward V (2008) Non-visual identification of walking grounds. J Acous Soc Am 123(5):3412

    Google Scholar 

  40. Hachisu T, Cirio G, Marchal M, Lécuyer A, Kajimoto H (2011) Pseudo-haptic feedback augmented with visual and tactile vibrations. In: Proceedings of international symposium on VR innovations, pp 331–332

    Google Scholar 

  41. Hardin EC, van den Bogert AJ, Hamill J (2004) Kinematic adaptations during running: effects of footwear, surface, and duration. Med Sci Sports Exerc 36(5):838

    Google Scholar 

  42. Hayward V (2007) Physically-based haptic synthesis. In: Lin M, Otaduy M (eds) Haptic rendering: foundations, algorithms and applications. AK Peters, Natick

    Google Scholar 

  43. Hayward V, Astley OR, Cruz-Hernandez M, Grant D, Robles-De-La-Torre G (2004) Haptic interfaces and devices. Sens Rev 24(1):16–29

    Google Scholar 

  44. Hayward V, Maclean K (2007) Do it yourself haptics, part I. IEEE Robot Autom 14:88–104

    Google Scholar 

  45. Herrmann HJ, Roux S (1990) Statistical models for the fracture of disordered media. North Holland, Amsterdam

    Google Scholar 

  46. Hollerbach J (2008) Locomotion interfaces and rendering. In: Lin M, Otaduy M (eds) Haptic rendering: foundations, algorithms and applications. AK Peters, Natick

    Google Scholar 

  47. Hötting K, Röder B (2004) Hearing cheats touch, but less in congenitally blind than in sighted individuals. Psychol Sci 15:60–64

    Google Scholar 

  48. Iwata H (1999) Walking about virtual environments on an infinite floor. In: Proceedings of IEEE international conference on virtual reality, pp 286–293

    Google Scholar 

  49. Iwata H (2008) Haptic interface. In: Sears A, Jacko JA (eds) The human-computer interaction handbook, 2nd edn. Lawrence Erlbaum Assoc, New York

    Google Scholar 

  50. Kennedy PM, Inglis JT (2002) Distribution and behaviour of glabrous cutaneous receptors in the human foot sole. J Physiol 583(3):731–742

    Google Scholar 

  51. Kinsella-Shaw JM, Shaw B, Turvey MT (1992) Perceiving “walk-on-able” slopes. Ecol Psychol 4(4):223–239

    Article  Google Scholar 

  52. Klatzky RL, Pai DK, Krotkov EP (2000) Perception of material from contact sounds. Presence: Teleoper Virtual Environ 9(4):399–410

    Article  Google Scholar 

  53. Kobayashi Y, Osaka R, Hara T, Fujimoto H (2008) How accurately people can discriminate the differences of floor materials with various elasticities. IEEE Trans Neural Syst Rehabil Eng 16(1):99–105

    Article  Google Scholar 

  54. Kobayashi Y, Takashima T, Hayashi M, Fujimoto H (2005) Gait analysis of people walking on tactile ground surface indicators. IEEE Trans Neural Syst Rehabil Eng 13(1):53–59

    Article  Google Scholar 

  55. Kuchenbecker KJ, Fiene J, Niemeyer G (2006) Improving contact realism through event-based haptic feedback. IEEE Trans Visual Comput Graph 12(2):219–230

    Article  Google Scholar 

  56. LaViola JJ, Feliz DA, Keefe DF, Zeleznik RC (2001) Hands-free multi-scale navigation in virtual environments. In: Proceedings of the ACM symposium on interactive 3D graphics. pp 9–15

    Google Scholar 

  57. Law AW, Ip J, Peck B, Visell Y, Kry PG, Cooperstock JR (2009) Multimodal floor for immersive environments. In: ACM SIGGRAPH emerging technologies

    Google Scholar 

  58. Lécuyer A (2009) Simulating haptic feedback using vision: a survey of research and applications of pseudo-haptic feedback. Presence: Teleoper Virtual Environ 18(1):39–53

    Google Scholar 

  59. Lécuyer A, Burkhardt J-M, Etienne L (2004) Feeling bumps and holes without a haptic interface: the perception of pseudo-haptic textures. In: Proceedings of SIGCHI conference on human factors in computing systems, pp 239–246

    Google Scholar 

  60. Lécuyer A, Burkhardt J-M, Henaff J-M, Donikian S (2006) Camera motions improve sensation of walking in virtual environments. In: Proceedings of IEEE international conference on virtual reality, pp 11–18

    Google Scholar 

  61. Li X, Logan RJ, Pastore RE (1991) Perception of acoustic source characteristics: walking sounds. J Acoust Soc Am 90(6):3036–3049

    Article  Google Scholar 

  62. MacLean KE (2008) Foundations of transparency in tactile information design. IEEE Trans Haptics 1(2):84–95

    Article  MathSciNet  Google Scholar 

  63. MacLellan MJ, Patla AE (2006) Adaptations of walking pattern on a compliant surface to regulate dynamic stability. Exp Brain Res 173(3):521–530

    Google Scholar 

  64. Mahvash M, Hayward V (2001) Haptic rendering of cutting: a fracture mechanics approach. Haptics-e 2(3):1–12

    Google Scholar 

  65. Marchal M, Lécuyer A, Cirio G, Bonnet L, Emily M (2010) Walking up and down in immersive virtual worlds: novel interactive techniques based on visual feedback. In: Proceedings of IEEE symposium on 3D user interface, pp 19–26

    Google Scholar 

  66. Marigold DS, Patla AE (2005) Adapting locomotion to different surface compliances: neuromuscular responses and changes in movement dynamics. J Neurophysiol 94(3):1733

    Google Scholar 

  67. Michon JA (ed) (1993) Generic intelligent driver support. CRC Press, Boca Raton

    Google Scholar 

  68. Morioka M, Whitehouse DJ, Griffin MJ (2008) Vibrotactile thresholds at the fingertip, volar forearm, large toe, and heel. Somatosens Mot Res 25(2):101–112

    Google Scholar 

  69. Moritz CT, Farley CT (2004) Passive dynamics change leg mechanics for an unexpected surface during human hopping. J Appl Physiol 97(4):1313

    Google Scholar 

  70. Moritz CT, Greene SM, Farley CT (2004) Neuromuscular changes for hopping on a range of damped surfaces. J Appl Physiol 96(5):1996

    Google Scholar 

  71. Nashel A, Razzaque S (2003) Tactile virtual buttons for mobile devices. In: Proceedings of ACM CHI. pp 854–855

    Google Scholar 

  72. Nasuno S, Kudrolli A, Bak A, Gollub JP (1998) Time-resolved studies of stick-slip friction in sheared granular layers. Phys Rev E 58(2):2161–2171

    Google Scholar 

  73. Nasuno S, Kudrolli A, Gollub JP (1997) Friction in granular layers: hysteresis and precursors. Phys Rev Lett 79(5):949–952

    Google Scholar 

  74. Nordahl R (2006) Increasing the motion of users in photorealistic virtual environments by utilizing auditory rendering of the environment and ego-motion. In: Proceedings of presence, pp 57–62

    Google Scholar 

  75. Norman D (2007) The design of future things. Basic Books, New York

    Google Scholar 

  76. Papetti S, Civolani M, Fontana F (2011) Rhythmnshoes: a wearable foot tapping interface with audio-tactile feedback. In: Proceedings of international conference of new interfaces for musical expression

    Google Scholar 

  77. Papetti S, Fontana F, Civolani M, Berrezag A, Hayward V (2010) Audio-tactile display of ground properties using interactive shoes. In: Haptic and audio interaction design, pp 117–128

    Google Scholar 

  78. Pastore RE, Flint JD, Gaston JR, Solomon MJ (2008) Auditory event perception: the source-perception loop for posture in human gait. Percept Psychophys 70(1):13–29

    Article  Google Scholar 

  79. Perreault S, Gosselin CM (2008) Cable-driven parallel mechanisms: application to a locomotion interface. J Mech Des 130:102301

    Google Scholar 

  80. Poupyrev I, Maruyama S, Rekimoto J (2002) Ambient touch: designing tactile interfaces for handheld devices. In: Proceedings of ACM UIST. pp 51–60

    Google Scholar 

  81. Razzaque S, Kohn Z, Whitton MC (2001) Redirected walking. In: Proceedings of Eurographics, pp 289–294

    Google Scholar 

  82. Rosburg T (2008) Tactile ground surface indicators in public places. In: Grunwald M (ed) Human haptic perception: basics and applications. Birkhäuser, Basel, pp 491–499

    Google Scholar 

  83. Rossignol S, Dubuc R, Gossard JP (2006) Dynamic sensorimotor interactions in locomotion. Physiol Rev 86(1):89

    Google Scholar 

  84. Rovan J, Hayward V (2000) Typology of tactile sounds and their synthesis in gesture-driven computer music performance. In: Wanderley M, Battier M (eds) Trends in gestural control of music. Editions IRCAM, Paris

    Google Scholar 

  85. Rovers AF, van Essen H (2006) Guidelines for haptic interpersonal communication applications. Virtual Real 9:177–191

    Article  Google Scholar 

  86. Sanders RD, Scorgie MA (2002) The effect of sound delivery methods on a user’s sense of presence in a virtual environment

    Google Scholar 

  87. Schafer RM (1977) The tuning of the world. Random House, New York

    Google Scholar 

  88. Serafin S, Fontana F, Turchet L, Papetti S (2012) Auditory rendering and display of interactive floor cues. In: Fontana F, Visell Y (eds) Walking with the senses, Chap 7. Logos Verlag, Berlin, pp 123–152

    Google Scholar 

  89. Serafin S, Turchet L, Nordahl R, Dimitrov S, Berrezag A, Hayward V (2010) Identification of virtual grounds using virtual reality haptic shoes and sound synthesis. In: Proceedings of Eurohaptics, p 61

    Google Scholar 

  90. Slater M, Usoh M, Steed A (1995) Taking steps: the influence of a walking technique on presence in virtual reality. ACM Trans Comput-Hum Inter 2(3):201–219

    Google Scholar 

  91. Srinivasan MA, Basdogan C (1997) Haptics in virtual environments: taxonomy, research status, and challenges. Comput Graph 21(4):393–404

    Article  Google Scholar 

  92. Stiles VH, James IT, Dixon SJ, Guisasola IN (2009) Natural turf surfaces: the case for continued research. Sports Med 39(1):65

    Google Scholar 

  93. Styns F, van Noorden L, Moelants D, Leman M (2007) Walking on music. Hum Movem Sci 26(5):769–785

    Article  Google Scholar 

  94. Swapp D, Williams J, Steed A (2010) The implementation of a novel walking interface within an immersive display. In: Proceedings of IEEE Symposium on 3D user interfaces, pp 71–74

    Google Scholar 

  95. Tax A, van Wezel B, Dietz V (1995) Bipedal reflex coordination to tactile stimulation of the sural nerve during human running. J Neurophysiol 73(5):1947–1964

    Google Scholar 

  96. Templeman JN, Denbrook PS, Sibert LE (1999) Virtual locomotion: walking in place through virtual environments. Presence: Teleoper Virtual Environ 8(6):598–617

    Google Scholar 

  97. Terziman L, Lécuyer A, Hillaire S, Wiener JM (2009) Can camera motions improve the perception of traveled distance in virtual environments? In: Proceedings of IEEE international conference on virtual reality, pp 131–134

    Google Scholar 

  98. Terziman L, Marchal M, Multon F, Arnaldi B, Lécuyer A (2012) The king-kong effects: improving sensation of walking in VR with visual and tactile vibrations at each step. In: Proceedings of IEEE symposium on 3D user interfaces, pp 19–26

    Google Scholar 

  99. Tramberend H, Hasenbrink F, Eckel G, Lechner U, Goebel M (1997) CyberStage—an advanced virtual environment. ERCIM News 31:22–23

    Google Scholar 

  100. Trulsson M (2001) Mechanoreceptive afferents in the human sural nerve. Exp Brain Res 137(1):111–116

    Article  Google Scholar 

  101. Turchet L, Marchal M, Lécuyer A, Serafin S, Nordahl R (2010) Influence of visual feedback for perceiving walking over bumps and holes in desktop VR. In: Proceedings of 17th ACM symposium on virtual reality software and technology, pp 139–142

    Google Scholar 

  102. Turchet L, Serafin S, Nordahl R (2010) Physically based sound synthesis and control of footsteps sounds. In: Proceedings of conference on digital audio effects

    Google Scholar 

  103. van den Doel K, Kry PG, Pai DK (2001) FoleyAutomatic: physically-based sound effects for interactive simulation and animation. In: Proceedings of the 28th annual conference on computer graphics and interactive techniques pp 537–544

    Google Scholar 

  104. van Ulzen NR, Lamoth CJC, Daffertshofer A, Semin GR, Beek PJ (2008) Characteristics of instructed and uninstructed interpersonal coordination while walking side-by-side. Neurosci Lett 432(2):88–93

    Google Scholar 

  105. Velazquez R (2008) On-shoe tactile display. In: Proceedings of the IEEE international workshop on haptic audio visual environment and their applications

    Google Scholar 

  106. Visell Y, Cooperstock J (2010) Design of a vibrotactile display via a rigid surface. In: Proceedings of IEEE haptics symposium, pp 133–140

    Google Scholar 

  107. Visell Y, Cooperstock J, Giordano BL, Franinovic K, Law A, McAdams S, Jathal K, Fontana F (2008) A vibrotactile device for display of virtual ground materials in walking. In: Proceedings of Eurohaptics 2008, pp 420–426

    Google Scholar 

  108. Visell Y, Fontana F, Giordano BL, Nordahl R, Serafin S, Bresin R (2009) Sound design and perception in walking interactions. Int J Hum-Comput Studies 67:947–959

    Google Scholar 

  109. Visell Y, Giordano BL, Millet G, Cooperstock JR (2011) Vibration influences haptic perception of surface compliance during walking. PLoS one 6(3):e17697

    Google Scholar 

  110. Visell Y, Law A, Cooperstock JR (2009) Touch is everywhere: floor surfaces as ambient haptic interfaces. IEEE Trans Haptics 2:148–159

    Google Scholar 

  111. Visell Y, Law A, Smith S, Rajalingham R, Cooperstock JR (2010) Contact sensing and interaction techniques for a distributed multimodal floor display. In: Proceedings of IEEE Symposium on 3D user interfaces. pp 75–78

    Google Scholar 

  112. Visell Y, Law A, Ip J, Smith S, Cooperstock JR (2010) Interaction capture in immersive virtual environments via an intelligent floor surface. In: Proceedings of IEEE international conference on virtual reality, pp 313–314

    Google Scholar 

  113. Watters BG (1965) Impact noise characteristics of female hard-heeled foot traffic. J Acoust Soc Am 37:619–630

    Article  Google Scholar 

  114. Weinstein S (1968) Intensive and extensive aspects of tactile sensitivity as a function of body part, sex, and laterality. In: Kenshalo DR (ed) The skin senses. Thomas, Springfield

    Google Scholar 

  115. Wells C, Ward LM, Chua R, Inglis JT (2003) Regional variation and changes with ageing in vibrotactile sensitivity in the human footsole. J Gerontol A Biol Sci Med Sci 58(8):B680–B686

    Article  Google Scholar 

  116. Zehr EP, Stein RB, Komiyama T (1998) Function of sural nerve reflexes during human walking. J Physiol 507:305–314

    Article  Google Scholar 

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Marchal, M. et al. (2013). Multimodal Rendering of Walking Over Virtual Grounds. In: Steinicke, F., Visell, Y., Campos, J., Lécuyer, A. (eds) Human Walking in Virtual Environments. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-8432-6_12

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