Abstract
This paper presents an efficient optimal control and recursive dynamics-based computer animation system for simulating and controlling themotion of articulated figures. A quasi-Newton nonlinear programmingtechnique (super-linear convergence) is implemented to solve minimumtorque-based human motion-planning problems. The explicit analyticalgradients needed in the dynamics are derived using a matrix exponentialformulation and Lie algebra. Cubic spline functions are used to make thesearch space for an optimal solution finite. Based on our formulations,our method is well conditioned and robust, in addition to beingcomputationally efficient. To better illustrate the efficiency of ourmethod, we present results of natural looking and physically correcthuman motions for a variety of human motion tasks involving open andclosed loop kinematic chains.
Similar content being viewed by others
References
Ahrikencheikh, C. and Seireg, A., Optimized-Motion Planning: Theory and Implementation, Wiley-Interscience, New York, 1994.
Alexander, R., 'A minimum energy cost hypothesis for human arm trajectories', Biological Cybernetics 76, 1997, 97-105.
Angeles, J. and Ma, O., 'Dynamic simulation of n-axis serial robotic manipulators using a natural orthogonal complement', The International Journal of Robotics Research 7(5), 1988, 32-47.
Ayoub, M.M. and Lin, C.J., 'Biomechanics of manual material handling through simulation: Computational aspects', Computers Ind. Engineering 29(1), 1995, 427-431.
Badler, N.I., Phillips, C.B. and Webber, B.L., Simulating Humans: Computer Graphics Animation and Control, Oxford University Press, New York, 1993.
Bordlie, K.W., The State of the Art in Numerical Analysis, Chapter III, Academic Press, New York, 1977.
Brandl, H., Johanni, R. and Otter, M., 'A very efficient algorithm for the simulation of robots and similar multibody systems without inversion of the mass matrix', in Proceedings of IFAC/IFIP/IMACS International Symposium on the Theory of Robots, Vienna, Austria, 1986.
Brandl, H., Johanni, R. and Otter, M., 'An algorithm for the simulation of multibody systems with kinematic loops', in Proceedings of the IFToMM Seventh World Congress on the Theory of Machines and Mechanisms, Sevilla, Spain, 1987.
Churchill, S.E. and Oser, H., Fundamentals of Space Life Sciences, Vol. 2, Krieger, Malabar, FL, 1997.
Cohen, M.F., 'Interactive spacetime control for animation', in Computer Graphics (SIGGRAPH '92 Proceedings), Vol. 26, 1992, 293-302.
Dennis, J.E. and Schnabel, R.B., Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Prentice Hall, Englewood Cliffs, NJ, 1983.
Engeln-Mullges, G. and Uhlig, F. Numerical Algorithms with C, Springer-Verlag, Berlin, 1996.
Featherstone, R., Robot Dynamics Algorithms, Kluwer Academic Publishers, Boston, 1987.
Greenwood, D.T., Principles of Dynamics, Prentice Hall, Englewood Cliffs, NJ, 1988.
Gregory, J. and Lin, C., Constrained Optimization in the Calculus of Variations and Optimal Control Theory, Van Nostrand Reinhold, New York, 1992.
Lathrop, R.H., 'Constrained (closed-loop) robot simulation by local constaint propagation', in Proceedings of the 1986 IEEE International Conference on Robotics and Automation, San Francisco, CA, April, IEEE, New York, 1986, 689-694.
Lilly, K.W., Efficient Dynamic Simulation of Robotic Mechanisms, Kluwer Academic Publishers, Dordrecht, 1993.
Lo, J., Metaxas, D. and Badler, N.I., 'Controlling a dynamic system with open and closed loops: Application to ladder climbing', in ASME Design Automation Conference Proceedings, Sacramento, CA, September, ASME, New York, 1997.
Oh, S.Y. and Orin, D.E., 'Dynamic computer simulation of multiple closed-chain robotic mechanisms', in Proceedings of the 1986 IEEE International Conference on Robotics and Automation, San Francisco, CA, April, IEEE, New York, 1986, 15-20.
Plücker, J., Neue Geometrie des Raumes gegründet auf die Betrachtung der geraden Linie als Raumelement, B.G. Teubner, Leipzig, 1868.
Popovic, Z. and Witkin, A., 'Physically based motion transformation', in Computer Graphics (SIGGRAPH '99 Proceedings), Vol. 33, 1999, 11-20.
Press, W. and Teukolsky, S. Numerical Recipes in C, Cambridge University Press, Cambridge, 1992.
Rockafellar, R.T., 'The multiplier method of hestenes and powell applied to convex programming', Journal of Optimization Theory and Applications 12(6), 1973, 555-562.
Rose, C., Guenter, B., Bodenheimer, B. and Cohen, M.F., 'Efficient generation of motion transitions using spacetime constraints', in SIGGRAPH 96 Conference Proceedings, Annual Conference Series, 1996, 147-154.
Schaffner, G., Newman, D.J. and Robinson, S.K., 'Inverse dynamic simulation and computer animation of extra vehicular activity', in AIAA 35th Aerospace Sciences Meeting, Reno, NV, American Institute of Aeronautics and Astronautics, Washington, DC, 1997.
Skrinar, A., Burdett, R.G. and Simon, S.R., 'Comparison of mechanical work and metabolic energy consumption during normal gait', Journal of Orthopedic Research 1(1), 1983, 63-72.
Vanderplaats, G.N., Numerical Optimization Techniques for Engineering Design: With Applications, McGraw-Hill, New York, 1984.
Walker, M.W. and Orin, D.E., 'Efficient dynamic computer simulation of robotic mechanisms', Journal of Dynamic Systems, Measurement and Control 104, 1982, 205-211.
Winter, D.A., Biomechanics and Motor Control of Human Movement, second edition, John Wiley & Sons, New York, 1990.
Witkin, A. and Kass, M., 'Spacetime constraints', ACM Computer Graphics 22(4), 1988.
Yamaguchi, G.T., Performing Whole-Body Simulations of Gait with 3-D, Springer-Verlag, 1990.
Zefran, M. and Kumar, V., 'Optimal control of systems with unilateral constraints', in International Conference on Robotics and Automation, Nagoya, Japan, 1995.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Lo, J., Huang, G. & Metaxas, D. Human Motion Planning Based on Recursive Dynamics and Optimal Control Techniques. Multibody System Dynamics 8, 433–458 (2002). https://doi.org/10.1023/A:1021111421247
Issue Date:
DOI: https://doi.org/10.1023/A:1021111421247