Temporal finite element formulation of optimal control in mechanisms

Eriksson, Anders; Nordmark, Arne

doi:10.1016/j.cma.2010.02.003

Cited by 14 publications

(17 citation statements)

References 36 publications

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“…The kinetic and potential energies for the system considered give the set of equilibrium equations in (1) through a weak or a collocation formulation [20]. The resulting expressions for the basic equations are normally complex, but with high degrees of regularity.…”

Section: Basic Formulationmentioning

confidence: 99%

“…The present formulation considers linear or non-linear kinematic restrictions on the coordinates, and kinetic restrictions on the control variables [20]. Most restrictions are valid for every instance of the interval under consideration, but are implemented at each time node, or at a limited set of time instances within each time element.…”

Section: Basic Formulationmentioning

confidence: 99%

“…In this work, the discretization of both q(t) and a(t) divides the full interval into N t equal time elements, cf. [20]. Displacement coordinates and control variables are in the examples represented by locally linear Lagrange interpolation [20], which means that…”

Section: Basic Formulationmentioning

confidence: 99%

“…Several cost functions are possible as criteria for an optimal movement [18,20]. In the present experiments, a cost function was defined from integrals of squared control quantities:…”

Section: Basic Formulationmentioning

confidence: 99%

“…This paper studies the optimization of a target movement, based on the previous work [19,20]. It is thereby a 'least effort' optimization of a movement of a mechanical system, and related to work in [21,22].…”

Section: Introductionmentioning

confidence: 99%

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Optimization in simulations of human movement planning

Eriksson¹,

Svanberg²

2011

Numerical Meth Engineering

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SUMMARYThis paper discusses optimization algorithms in movement simulations for models of humans, humanoid robots or other mechanisms. Targeted movements between two configurations define a dynamically redundant system, for which there is freedom in the choice of control force time variations. A previously developed formulation for the treatment of targeted dynamics for mechanisms was used as a basis. The paper describes the development of an algorithm related to the method of moving asymptotes for the necessary optimization. The algorithm is specifically adapted to problems which are large and non-linear but sparse, and which include very high numbers of design variables as well as constraints. In particular, non-linear equality constraints from dynamic equilibrium equations are important. The optimization algorithm was developed to include these, but also in order to allow successively increasing penalty factors for constraint violations. The resulting setting was shown to be able to handle the systems established, robustly giving convergence to at least a local minimum also for very distant start iterates. The existence of very closely situated local optima, representing very similar movements, was discovered for the problem formulation, calling for an ad hoc method for finding the best of these local optima.

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Section: Basic Formulationmentioning

confidence: 99%

Section: Basic Formulationmentioning

confidence: 99%

Section: Basic Formulationmentioning

confidence: 99%

“…Several cost functions are possible as criteria for an optimal movement [18,20]. In the present experiments, a cost function was defined from integrals of squared control quantities:…”

Section: Basic Formulationmentioning

confidence: 99%