Abstract
Least action principles provide an insightful starting point from which problems involving constraints and task-level objectives can be addressed. In this paper, the principle of least action is first treated with regard to holonomic constraints in multibody systems. A variant of this, the principle of least curvature or straightest path, is then investigated in the context of geodesic paths on constrained motion manifolds. Subsequently, task space descriptions are addressed and the operational space approach is interpreted in terms of least action. Task-level control is then applied to the problem of cost minimization. Finally, task-level optimization is formulated with respect to extremizing an objective criterion, where the criterion is interpreted as the action of the system. Examples are presented which illustrate these approaches.
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References
Anderson, F.C., Pandy, M.G.: Static and dynamic optimization solutions for gait are practically equivalent. J. Biomech. 34(2), 153–161 (2001)
Bajodah, A.H., Hodges, D.H., Chen, Y.: Inverse dynamics of servo-constraints based on the generalized inverse. Nonlinear Dyn. 39(1–2), 179–196 (2005)
Baumgarte, J.: Stabilization of constraints and integrals of motion in dynamical systems. Comput. Methods Appl. Mech. Eng. 1, 1–16 (1972)
Biess, A., Nagurka, M., Flash, T.: Simulating discrete and rhythmic multi-joint human arm movements by optimization of nonlinear performance indices. Biol. Cybern. 95(1), 31–53 (2006)
Blajer, W., Kolodziejczyk, K.: A geometric approach to solving problems of control constraints: theory and a DAE framework. Multibody Syst. Dyn. 11(4), 343–364 (2004)
Bloch, A.M.: Nonholonomic Mechanics and Control. Springer, Berlin (2003)
Bryson, A.E.: Dynamic Optimization. Addison-Wesley, Reading (1999)
Crowninshield, R.D., Brand, R.A.: A physiologically based criterion of muscle force prediction in locomotion. J. Biomech. 14, 793–801 (1981)
De Sapio, V., Khatib, O.: Operational space control of multibody systems with explicit holonomic constraints. In Proceedings of the 2005 IEEE International Conference on Robotics and Automation, Barcelona, pp. 2961–2967 (2005)
De Sapio, V., Warren, J., Khatib, O., Delp, S.: Simulating the task-level control of human motion: a methodology and framework for implementation. Vis. Comput. 21(5), 289–302 (2005)
De Sapio, V., Khatib, O., Delp, S.: Task-level approaches for the control of constrained multibody systems. Multibody Syst. Dyn. 16(1), 73–102 (2006)
De Sapio, V., Warren, J., Khatib, O.: Predicting reaching postures using a kinematically constrained shoulder model. In: Lenarčič, J., Roth, B. (eds.) Advances in Robot Kinematics, pp. 209–218. Springer, Berlin (2006)
Gauss, K.F.: Über ein neues allgemeines Grundgesetz der Mechanik (On a new fundamental law of mechanics). J. Reine Angew. Math. 4, 232–235 (1829)
Goldstein, H., Poole, C., Safko, J.: Classical Mechanics, 3rd edn. Addison-Wesley, Reading (2002)
Hertz, H.: The Principles of Mechanics Presented in a New Form. Dover, New York (2004)
Holzbaur, K.R.S., Murray, W.M., Delp, S.L.: A model of the upper extremity for simulating musculoskeletal surgery and analyzing neuromuscular control. Ann. Biomed. Eng. 33(6), 829–840 (2005)
Khatib, O.: A unified approach to motion and force control of robot manipulators: the operational space formulation. Int. J. Robot. Res. 3(1), 43–53 (1987)
Khatib, O.: Inertial properties in robotic manipulation: an object level framework. Int. J. Robot. Res. 14(1), 19–36 (1995)
Lanczos, C.: The Variational Principles of Mechanics, 4th edn. Dover, New York (1986)
Marsden, J.E., Ratiu, T.S.: Introduction to Mechanics and Symmetry. Springer, Berlin (1999)
Optimization Toolbox 3—User’s Guide. The Mathworks (2007)
Papastavridis, J.G.: Analytical Mechanics: A Comprehensive Treatise on the Dynamics of Constrained Systems for Engineers, Physicists, and Mathematicians. Oxford University Press, Oxford (2002)
Roberts, S.M., Shipman, J.S.: Two-Point Boundary Value Problems: Shooting Methods. American Elsevier, Oxford (1972)
Soechting, J.F., Buneo, C.A., Herrmann, U., Flanders, M.: Moving effortlessly in three dimensions: does donders law apply to arm movement? J. Neurosci. 15(9), 6271–6280 (1995)
Stengel, R.F.: Optimal Control and Estimation. Dover, New York (1994)
Uno, Y., Kawato, M., Suzuki, R.: Formation and control of optimal trajectory in human multijoint arm movement. Biol. Cybern. 61, 89–101 (1989)
Vujanovic, B.D., Atanackovic, T.M.: An Introduction to Modern Variational Techniques in Mechanics and Engineering. Birkhäuser, Basel (2004)
Zajac, F.E.: Muscle and tendon: properties, models, scaling, and application to biomechanics and motor control. In: Bourne, J.R. (ed.) Critical Reviews in Biomedical Engineering, pp. 359–411. CRC Press, Boca Raton (1989)
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De Sapio, V., Khatib, O. & Delp, S. Least action principles and their application to constrained and task-level problems in robotics and biomechanics. Multibody Syst Dyn 19, 303–322 (2008). https://doi.org/10.1007/s11044-007-9097-8
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DOI: https://doi.org/10.1007/s11044-007-9097-8