Optimal Control for a Pitcher’s Motion Modeled as Constrained Mechanical System

̈baum, Sina Ober-Blo; Timmermann, Julia

doi:10.1115/detc2009-87081

Cited by 7 publications

(4 citation statements)

References 17 publications

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“…The DMOC has already been applied successfully to some interesting applications, e.g. compass gait biped [17], double pendulum on a cart [18], pitcher's arm [19], and low thrust transfer and the optimal control of formation flying satellites [20], [21].…”

Section: Introductionmentioning

confidence: 99%

Optimal trajectory planning for robotic manipulators using Discrete Mechanics and Optimal Control

Shareef

Trächtler

2014

2014 IEEE Conference on Control Applications (CCA)

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In this paper, the problem of trajectory optimization for robotic manipulators is solved by a newly developed methodology called Discrete Mechanics and Optimal Control (DMOC). This new methodology is based on the direct discretizaion of the Lagrange-d'Alembert principle. The constraints for the objective function to be optimized are the forced discrete Euler-Lagrange equations. In this paper, DMOC is applied to a Delta robot to optimize the desired cost function for a predefined geometrical path. The challenges to use DMOC for a Parallel Kinematic Machine (PKM) are also discussed because it is the first time, to the best of author's knowledge, that DMOC is used for a PKM. The optimal results obtained from DMOC are compared with the optimal solutions obtained by other state-of-the-art techniques which show the effectiveness of this new methodology.

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Section: Introductionmentioning

confidence: 99%

Optimal trajectory planning for robotic manipulators using Discrete Mechanics and Optimal Control

Shareef

Trächtler

2014

2014 IEEE Conference on Control Applications (CCA)

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“…This methodology was introduced by Junge et al 35 Preservation of momentum maps, conservation of modified energy, and the ease in implementation are the important characteristics of DMOC that are discussed by Ober-Blöbaum. compass gait biped, 41 double pendulum on a cart, 43 pitcher's arm, 44 image analysis, 42 and low-thrust transfer and the optimal control of formation flying satellites. compass gait biped, 41 double pendulum on a cart, 43 pitcher's arm, 44 image analysis, 42 and low-thrust transfer and the optimal control of formation flying satellites.…”

Section: Introductionmentioning

confidence: 99%

“…40 DMOC has already been applied successfully to some interesting applications, e.g. compass gait biped, 41 double pendulum on a cart, 43 pitcher's arm, 44 image analysis, 42 and low-thrust transfer and the optimal control of formation flying satellites. 45,46 The variational structure of mechanical system is directly discretized in this method.…”

Section: Introductionmentioning

confidence: 99%

Simultaneous path planning and trajectory optimization for robotic manipulators using discrete mechanics and optimal control

Shareef

Trächtler

2014

Robotica

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In robotics, path planning and trajectory optimization are usually performed separately to optimize the path from the given starting point to the ending point in the presence of obstacles. In this paper, path planning and trajectory optimization for robotic manipulators are solved simultaneously by a newly developed methodology called Discrete Mechanics and Optimal Control (DMOC). In DMOC, the Lagrange-d'Alembert equation is discretized directly unlike the conventional variational optimization method in which first the Euler-Lagrange equations are derived and then discretization takes place. In this newly developed method, the constraints for optimization of a desired objective function are the forced discrete Euler-Lagrange equations. In this paper, DMOC is used for simultaneous path planning and trajectory optimization for robotic manipulators in the presence of known static obstacles. Two numerical examples, applied on a DELTA parallel robot, are discussed to show the applicability of this new methodology. The optimal results obtained from DMOC are compared with the other state-of-the-art techniques. The difficulties and problems associated in using the DMOC for Parallel Kinematic Machine (PKM) are also discussed in this paper.

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“…A first application of DMOC was the calculation of low thrust transfers and the optimal control of formation flying satellites in , , and Junge et al (2006). In Ober-Blöbaum and Timmermann (2009), this method has been used to determine the optimal motion of a pitcher's arm to maximize the velocity of his pitch. This application of DMOC to a multibody system uses a recently developed extension of DMOC to constrained mechanical systems, called DMOCC (Discrete Mechanics and Optimal Control for Constrained Systems), see Leyendecker et al (2007) or Leyendecker et al (2009).…”

Section: Introductionmentioning

confidence: 99%

Discrete Mechanics and Optimal Control and its Application to a Double Pendulum on a Cart

Timmermann

Khatab

Ober‐Blöbaum

et al. 2011

IFAC Proceedings Volumes

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Optimal Control for a Pitcher’s Motion Modeled as Constrained Mechanical System

Abstract: In this contribution, a recently developed optimal control method for constrained mechanical systems is

Cited by 7 publications

References 17 publications

Optimal trajectory planning for robotic manipulators using Discrete Mechanics and Optimal Control

Optimal trajectory planning for robotic manipulators using Discrete Mechanics and Optimal Control

Simultaneous path planning and trajectory optimization for robotic manipulators using discrete mechanics and optimal control

Discrete Mechanics and Optimal Control and its Application to a Double Pendulum on a Cart

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