Range maximization and brachistochrone problem with Coulomb friction, viscous drag and accelerating force

Cherkasov, O. Yu.; Zarodnyuk, A. V.; Bugrov, D. I.

doi:10.1063/1.4972632

Cited by 3 publications

(1 citation statement)

References 13 publications

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“…Friction identification and compensation are basic issues in motion control, so there is a large body of literature on these topics, only a small part of which is cited here. Some static friction model methods have been proposed, such as the classical Coulomb and viscous model [5][6][7]. The main idea of the model is that friction opposes motion and that its magnitude is independent of velocity and contact area.…”

Section: Introductionmentioning

confidence: 99%

A Novel Virtual Sensor for Estimating Robot Joint Total Friction Based on Total Momentum

Fan

Fang

et al. 2019

Applied Sciences

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Robot joint friction is an important and complicated issue in improving robot control performance. In this paper, a virtual sensor based on the total generalized momentum concept is proposed to estimate the total friction torque, including both the motor-side and link-side friction, of robot joints without joint torque sensors. The proposed algorithm only requires a robot joint dynamics model and not a complex friction model dependent on factors such as time and velocity. By compensating for the estimated friction torque with a robot joint controller, the trajectory tracking performance of the controller, especially the velocity tracking performance, can be improved. To verify the effectiveness of the developed algorithm, 2-DOF planar manipulator simulations and single-joint system experiments are conducted. The simulation and experimental results show that the designed virtual sensor can effectively estimate the total joint friction disturbance and that the controller trajectory tracking performance is improved after observed friction compensation. However, the position tracking performance improvement of the controller is less than that for the velocity tracking performance improvement during the experiments. In addition, the velocity step response ability and velocity tracking performance of the controller are improved more at low velocities than that at high velocities in the experiments. The proposed algorithm has engineering and theoretical significance for estimating robot joint friction and improving the performance of robot joint controllers.

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Section: Introductionmentioning

confidence: 99%

A Novel Virtual Sensor for Estimating Robot Joint Total Friction Based on Total Momentum

Fan

Fang

et al. 2019

Applied Sciences

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Brachistochrone problem and two-dimensional Goddard problem

Cherkasov

Malykh²,

Smirnova³

2022

Nonlinear Dyn

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On the brachistochrone of a fluid-filled cylinder

et al. 2019

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We discuss a fluid dynamic variant of the classical Bernoulli’s brachistochrone problem. The classical brachistochrone for a non-dissipative particle is governed by maximization of the particle’s kinetic energy, resulting in a cycloid. We consider a variant where the particle is replaced by a cylinder (bottle) filled with a viscous fluid and attempt to identify the shape of the curve connecting two points along which the bottle would move in the shortest time. We derive the system of integro-differential equations governing system dynamics for a given shape of the curve. Using these equations, we pose the brachistochrone problem by invoking an optimal control formalism and show that (in general) the curve deviates from a cycloid. This is due to the fact that increasing the rate of change of the bottle’s kinetic energy is accompanied by increased viscous dissipation. We show that the bottle motion is governed by a balance between the desire to minimize travel time and the need to reach the end point in the face of increased dissipation. The trade-off between these two physical forces plays a vital role in determining the brachistochrone of a fluid-filled cylinder. We show that in the two limits of either vanishing or high viscosity, the brachistochrone for this problem reduces to a cycloid. An intermediate viscosity range is identified where the fluid brachistochrone is non-cycloidal. Finally, we show the relevance of these results to the dynamics of a rolling liquid marble.

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Range maximization and brachistochrone problem with Coulomb friction, viscous drag and accelerating force

Cited by 3 publications

References 13 publications

A Novel Virtual Sensor for Estimating Robot Joint Total Friction Based on Total Momentum

A Novel Virtual Sensor for Estimating Robot Joint Total Friction Based on Total Momentum

Brachistochrone problem and two-dimensional Goddard problem

On the brachistochrone of a fluid-filled cylinder

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