Least action principles and their application to constrained and task-level problems in robotics and biomechanics
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.
KeywordsLeast action Constraints Task-level control Musculoskeletal system Optimization
Unable to display preview. Download preview PDF.
- 7.Bryson, A.E.: Dynamic Optimization. Addison-Wesley, Reading (1999) Google Scholar
- 9.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) Google Scholar
- 13.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) Google Scholar
- 14.Goldstein, H., Poole, C., Safko, J.: Classical Mechanics, 3rd edn. Addison-Wesley, Reading (2002) Google Scholar
- 15.Hertz, H.: The Principles of Mechanics Presented in a New Form. Dover, New York (2004) Google Scholar
- 17.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) Google Scholar
- 19.Lanczos, C.: The Variational Principles of Mechanics, 4th edn. Dover, New York (1986) Google Scholar
- 21.Optimization Toolbox 3—User’s Guide. The Mathworks (2007) Google Scholar
- 24.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) Google Scholar
- 28.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) Google Scholar