A biomechanical inactivation principle
This paper develops the mathematical side of a theory of inactivations in human biomechanics. This theory has been validated by practical experiments, including zero-gravity experiments. The theory mostly relies on Pontryagin’s maximum principle on the one side and on transversality theory on the other side. It turns out that the periods of silence in the activation of muscles that are observed in practice during the motions of the arm can appear only if “something like the energy expenditure” is minimized. Conversely, minimization of a criterion taking into account the “energy expenditure” guaranties the presence of these periods of silence, for sufficiently short movements.
Unable to display preview. Download preview PDF.
- 2.C. G. Atkeson and J. M. Hollerbach, “Kinematic Features of Unrestrained Vertical Arm Movements,” J. Neurosci. 5(9), 2318–2330 (1985).Google Scholar
- 4.N. Bernstein, The Co-ordination and Regulation of Movements (Pergamon Press, Oxford, 1967).Google Scholar
- 11.T. Flash and N. Hogan, “The Coordination of Arm Movements: An Experimentally Confirmed Mathematical Model,” J. Neurosci. 5(7), 1688–1703 (1985).Google Scholar
- 16.M. Hallett and C. D. Marsden, “Ballistic Flexion Movements of the Human Thumb,” J. Physiol. 294, 33–50 (1979).Google Scholar
- 20.R. Kalman, “When Is a Linear Control System Optimal?,” Trans. ASME, Ser. D: J. Basic Eng. 86, 51–60 (1964).Google Scholar
- 23.A. Y. Ng and S. Russell, “Algorithms for Inverse Reinforcement Learning,” in Proc. 17th Int. Conf. on Machine Learning (Morgan Kaufmann Publ., San Francisco, CA, 2000), pp. 663–670.Google Scholar
- 24.J. Nishii and T. Murakami, “Energetic Optimality of Arm Trajectory,” in Proc. Int. Conf. on Biomechanics of Man (Charles Univ., Prague, 2002), pp. 30–33.Google Scholar
- 25.K. C. Nishikawa, S. T. Murray, and M. Flanders, “Do Arm Postures Vary with the Speed of Reaching?,” J. Neurophysiol. 81(5), 2582–2586 (1999).Google Scholar
- 26.C. Papaxanthis, T. Pozzo, and M. Schieppati, “Trajectories of Arm Pointing Movements on the Sagittal Plane Vary with both Direction and Speed,” Exp. Brain Res. 148(4), 498–503 (2003).Google Scholar
- 28.L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mishchenko, The Mathematical Theory of Optimal Processes (Fizmatgiz, Moscow, 1961; Pergamon Press, Oxford, 1964).Google Scholar
- 30.J. F. Soechting and F. Lacquaniti, “Invariant Characteristics of a Pointing Movement in Man,” J. Neurosci. 1(7), 710–720 (1981).Google Scholar
- 31.E. Todorov, “Optimal Control Theory,” in Bayesian Brain: Probabilistic Approaches to Neural Coding, Ed. by K. Doya et al. (MIT Press, Cambridge, MA, 2007), Ch. 12, pp. 269–298.Google Scholar