Multibody System Dynamics

, Volume 19, Issue 3, pp 303-322

First online:

Least action principles and their application to constrained and task-level problems in robotics and biomechanics

  • Vincent De SapioAffiliated withArtificial Intelligence Laboratory, Stanford University Email author 
  • , Oussama KhatibAffiliated withArtificial Intelligence Laboratory, Stanford University
  • , Scott DelpAffiliated withNeuromuscular Biomechanics Laboratory, Stanford University

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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.


Least action Constraints Task-level control Musculoskeletal system Optimization