Optimal rigid body motions, part 2: Minimum time solutions

Chowdhry, Rajiv S.; Cliff, Eugene M.

doi:10.1007/bf00940626

Cited by 5 publications

(4 citation statements)

References 6 publications

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“…,(7),(9), and(11), as well as the reactions of non-123 holonomic constraints and the driving force and torque 124 (12)-(15) are obtained in accordance with the con-125 straints (1) and (2). Taking this into account and the 126 Coulomb friction laws, necessary dynamic conditions 127 for the realization of motion in accordance with the con-128 straints (1) and (2) are that the magnitudes of interaction129…”

mentioning

confidence: 58%

“…Here, it should be pointed out that the brachis-208 tochrone problem and the minimum time optimal con-209 trol problems (see e.g., [10][11][12][13]) are very similar. The 210 difference between these two types of optimal control 211 problems is that in the minimum time optimal con-212 trol problems the request for the conservation of total 213 mechanical energy of the controlled mechanical system 214 is not imposed on control forces.…”

Section: Optimal Control Problem Formulationmentioning

confidence: 94%

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The brachistochronic motion of a wheeled vehicle

et al. 2016

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The paper considers the brachistochronic motion of a wheeled vehicle on a horizontal plane surface. The objective is to transfer the vehicle from the specified initial position with given initial kinetic energy to the specified terminal position in minimum time with conserved total mechanical energy of the vehicle. The problem is solved by applying Pontryagin's maximum principle and singular optimal control theory. The projection of the reaction force of the horizontal plane applied on the front vehicle wheels onto the axis of the front vehicle axle is taken for a control variable. The cases of unbounded and bounded value of this projection are considered. The shooting method is used to solve the two-point boundary value problem arising from Pontryagin's maximum principle and singular optimal control theory.

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mentioning

confidence: 58%

Section: Optimal Control Problem Formulationmentioning

confidence: 94%

The brachistochronic motion of a wheeled vehicle

et al. 2016

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“…The motions of the mechanical systems from one to another specified configuration for a minimum time, where the mentioned condition for the power of control forces does not hold (see e.g. Chowdhry and Cliff, 1991;Seywald and Kumar, 1993;van Willigenburg and Loop, 1991), are referred to as the optimum time motions or minimum time motions. Therefore, in view of the power of control forces these two types of motion should be distinguished, although they both have the same goal of optimization -minimization of the time of motion.…”

Section: Description Of the System And Brachistochrone Problem Formulmentioning

confidence: 99%

On the brachistochronic motion of mechanical systems with unilateral constraints

Šalinić

Obradović

Mitrović

2012

Mechanics Research Communications

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“…Note that motions of mechanical systems from one to another specified configuration for a minimum time, where the power of control forces does not equal zero (see e.g., [25,26]) are referred to as the optimum time motions or minimum time motions. Also, more details about the choice of control forces for realization of the brachistochronic motion of mechanical systems can be found in [27].…”

Section: The Brachistochronic Rolling Of the Disk Under The Sufficienmentioning

confidence: 99%

The brachistochronic motion of a vertical disk rolling on a horizontal plane without slip

Obradović

Šalinić²,

Radulović

2017

Theor appl mech (Belgr)

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This paper deals with the brachistochronic motion of a thin uniform disk rolling on a horizontal plane without slip. The problem is formulated and solved within the frame of the optimal control theory. The brachistochronic motion of the disk is controlled by three torques. The possibility of the realization of the brachistochronic motion found in presence of Coulomb dry friction forces is inspected. Also, the influence of values of the coefficient of dry friction on the structure of the extremal trajectory is analyzed. Two illustrative numerical examples are provided.

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Optimal rigid body motions, part 2: Minimum time solutions

Cited by 5 publications

References 6 publications

The brachistochronic motion of a wheeled vehicle

The brachistochronic motion of a wheeled vehicle

On the brachistochronic motion of mechanical systems with unilateral constraints

The brachistochronic motion of a vertical disk rolling on a horizontal plane without slip

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