Optimal gait and form for animal locomotion

ABSTRACT

We present a fully automatic method for generating gaits and morphologies for legged animal locomotion. Given a specific animal's shape we can determine an efficient gait with which it can move. Similarly, we can also adapt the animal's morphology to be optimal for a specific locomotion task. We show that determining such gaits is possible without the need to specify a good initial motion, and without manually restricting the allowed gaits of each animal. Our approach is based on a hybrid optimization method which combines an efficient derivative-aware spacetime constraints optimization with a derivative-free approach able to find non-local solutions in high-dimensional discontinuous spaces. We demonstrate the effectiveness of this approach by synthesizing dynamic locomotions of bipeds, a quadruped, and an imaginary five-legged creature.

REFERENCES

• 1: Alexander, M. 1996. Optima for Animals. Princeton University Press.
• 2: Joel Auslander , Alex Fukunaga , Hadi Partovi , Jon Christensen , Lloyd Hsu , Peter Reiss , Andrew Shuman , Joe Marks , J. Thomas Ngo, Further experience with controller-based automatic motion synthesis for articulated figures, ACM Transactions on Graphics (TOG), v.14 n.4, p.311-336, Oct. 1995 [doi>10.1145/225294.225295]
• 3: Anthony C. Fang , Nancy S. Pollard, Efficient synthesis of physically valid human motion, ACM Transactions on Graphics (TOG), v.22 n.3, July 2003
• 4: Philip E. Gill , Walter Murray , Michael A. Saunders, SNOPT: An SQP Algorithm for Large-Scale Constrained Optimization, SIAM Review, v.47 n.1, p.99-131, 2005 [doi>10.1137/S0036144504446096]
• 5: Radek Grzeszczuk , Demetri Terzopoulos , Geoffrey Hinton, NeuroAnimator: fast neural network emulation and control of physics-based models, Proceedings of the 25th annual conference on Computer graphics and interactive techniques, p.9-20, July 1998 [doi>10.1145/280814.280816]
• 6: Brian Guenter, Efficient symbolic differentiation for graphics applications, ACM Transactions on Graphics (TOG), v.26 n.3, July 2007
• 7: Häkkinen, K., and Keskinen, K. L. 2006. Muscle cross-sectional area and voluntary force production characteristics in elite strength- and endurance-trained athletes and sprinters. European Journal of Applied Physiology (Apr), 215--220.
• 8: Hansen, N., and Kern, S. 2004. Evaluating the CMA evolution strategy on multimodal test functions. In Parallel Problem Solving from Nature PPSN VIII, Springer, X. Yao et al., Eds., vol. 3242 of LNCS, 282--291.
• 9: Hansen, N., Hansen, N., Ostermeier, A., and Ostermeier, A. 1996. Adapting arbitrary normal mutation distributions in evolution strategies: the covariance matrix adaptation. Morgan Kaufmann, 312--317.
• 10: Chris Hecker , Bernd Raabe , Ryan W. Enslow , John DeWeese , Jordan Maynard , Kees van Prooijen, Real-time motion retargeting to highly varied user-created morphologies, ACM Transactions on Graphics (TOG), v.27 n.3, August 2008
• 11: Jessica K. Hodgins , Nancy S. Pollard, Adapting simulated behaviors for new characters, Proceedings of the 24th annual conference on Computer graphics and interactive techniques, p.153-162, August 1997 [doi>10.1145/258734.258822]
• 12: Hutchinson, J. R., and Gatesy, S. M. 2006. Dinosaur locomotion: Beyond the bones. Nature 440, 7082 (Mar), 292--294.
• 13: Koh, B.-I., Reinbolt, J. A., George, A. D., Haftka, R. T., and Fregly, B. J. 2008. Limitations of parallel global optimization for large-scale human movement problems. Medical Engineering and Physics.
• 14: Kry, P. G., Reveret, L., Faure, F., and Cani, M.-P. 2009. Modal locomotion: Animating virtual characters with natural vibrations. Computer Graphics Forum.
• 15: Zicheng Liu , Steven J. Gortler , Michael F. Cohen, Hierarchical spacetime control, Proceedings of the 21st annual conference on Computer graphics and interactive techniques, p.35-42, July 1994 [doi>10.1145/192161.192169]
• 16: C. Karen Liu , Aaron Hertzmann , Zoran Popović, Learning physics-based motion style with nonlinear inverse optimization, ACM Transactions on Graphics (TOG), v.24 n.3, July 2005
• 17: C. Karen Liu , Aaron Hertzmann , Zoran Popović, Composition of complex optimal multi-character motions, Proceedings of the 2006 ACM SIGGRAPH/Eurographics symposium on Computer animation, September 02-04, 2006, Vienna, Austria
• 18: Paul, A., and Bongard, J. C. 2001. The road less travelled: Morphology in the optimization of biped robot locomotion. In In Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS2001, IEEE Press, 226--232.
• 19: Zoran Popović , Andrew Witkin, Physically based motion transformation, Proceedings of the 26th annual conference on Computer graphics and interactive techniques, p.11-20, July 1999 [doi>10.1145/311535.311536]
• 20: Marc H. Raibert , Jessica K. Hodgins, Animation of dynamic legged locomotion, Proceedings of the 18th annual conference on Computer graphics and interactive techniques, p.349-358, July 1991
• 21: Rose, C., Guenter, B., Bodenheimer, B., and Cohen, M. F. 1996. Efficient generation of motion transitions using spacetime constraints. 147--154.
• 22: Alla Safonova , Jessica K. Hodgins , Nancy S. Pollard, Synthesizing physically realistic human motion in low-dimensional, behavior-specific spaces, ACM Transactions on Graphics (TOG), v.23 n.3, August 2004
• 23: Karl Sims, Evolving virtual creatures, Proceedings of the 21st annual conference on Computer graphics and interactive techniques, p.15-22, July 1994 [doi>10.1145/192161.192167]
• 24: Srinivasan, M., and Ruina, A. 2006. Computer optimization of a minimal biped model discovers walking and running. Nature 439, 7072 (Jan), 72--75.
• 25: Thompson, D. W. 1992. On Growth and Form: The Complete Revised Edition. Dover.
• 26: Michiel van de Panne, Parameterized Gait Synthesis, IEEE Computer Graphics and Applications, v.16 n.2, p.40-49, March 1996 [doi>10.1109/38.486679]
• 27: Weibel, E. R., Tayor, C. R., and Bolis, L. 1998. Principles of Animal Design. Cambridge University Press.
• 28: Andrew Witkin , Michael Kass, Spacetime constraints, Proceedings of the 15th annual conference on Computer graphics and interactive techniques, p.159-168, June 1988

INDEX TERMS

Primary Classification:
  I. Computing Methodologies
  I.3 COMPUTER GRAPHICS
      I.3.7 Three-Dimensional Graphics and Realism
          Subjects: Animation

Keywords:
animation, character dynamics, gait, spacetime optimization