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Sado, Danuta; Gajos, Krzysztof

doi:10.1023/a:1025825224440

Cited by 13 publications

(2 citation statements)

References 9 publications

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“…The dynamic behavior after feedback was observed, and the results were verified by maximum Lyapunov exponents showing that chaotic behavior arose from extremely low proportional and differential gain. Sado and Gajos [6] studied a three-degrees-of-freedom suspension double pendulum mechanism, simulating the excited vibration generated by the flexible element between the fixed ends. The damping coefficient was used as the bifurcation parameter to analyze the chaos.…”

Section: Introductionmentioning

confidence: 99%

Identification and Machine Learning Prediction of Nonlinear Behavior in a Robotic Arm System

Wang

Zhu

2021

Symmetry

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In this study, the subject of investigation was the dynamic double pendulum crank mechanism used in a robotic arm. The arm is driven by a DC motor though the crank system and connected to a fixed side with a mount that includes a single spring and damping. Robotic arms are now widely used in industry, and the requirements for accuracy are stringent. There are many factors that can cause the induction of nonlinear or asymmetric behavior and even excite chaotic motion. In this study, bifurcation diagrams were used to analyze the dynamic response, including stable symmetric orbits and periodic and chaotic motions of the system under different damping and stiffness parameters. Behavior under different parameters was analyzed and verified by phase portraits, the maximum Lyapunov exponent, and Poincaré mapping. Firstly, to distinguish instability in the system, phase portraits and Poincaré maps were used for the identification of individual images, and the maximum Lyapunov exponents were used for prediction. GoogLeNet and ResNet-50 were used for image identification, and the results were compared using a convolutional neural network (CNN). This widens the convolutional layer and expands pooling to reduce network training time and thickening of the image; this deepens the network and strengthens performance. Secondly, the maximum Lyapunov exponent was used as the key index for the indication of chaos. Gaussian process regression (GPR) and the back propagation neural network (BPNN) were used with different amounts of data to quickly predict the maximum Lyapunov exponent under different parameters. The main finding of this study was that chaotic behavior occurs in the robotic arm system and can be more efficiently identified by ResNet-50 than by GoogLeNet; this was especially true for Poincaré map diagnosis. The results of GPR and BPNN model training on the three types of data show that GPR had a smaller error value, and the GPR-21 × 21 model was similar to the BPNN-51 × 51 model in terms of error and determination coefficient, showing that GPR prediction was better than that of BPNN. The results of this study allow the formation of a highly accurate prediction and identification model system for nonlinear and chaotic motion in robotic arms.

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Section: Introductionmentioning

confidence: 99%

Identification and Machine Learning Prediction of Nonlinear Behavior in a Robotic Arm System

Wang

Zhu

2021

Symmetry

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“…An auto parametric non-ideal system with pendulum was studied by [1], and an auto parametric system with two pendulums harmonically excited was studied by [2]. The first detailed study on non-ideal vibrating systems was done by [3].…”

Section: Introductionmentioning

confidence: 99%

On nonlinear dynamics and control of a robotic arm with chaos

Félix

Silva

Balthazar

et al. 2014

MATEC Web of Conferences

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Abstract. In this paper a robotic arm is modelled by a double pendulum excited in its base by a DC motor of limited power via crank mechanism and elastic connector. In the mathematical model, a chaotic motion was identified, for a wide range of parameters. Controlling of the chaotic behaviour of the system, were implemented using, two control techniques, the nonlinear saturation control (NSC) and the optimal linear feedback control (OLFC). The actuator and sensor of the device are allowed in the pivot and joints of the double pendulum. The nonlinear saturation control (NSC) is based in the order second differential equations and its action in the pivot/joint of the robotic arm is through of quadratic nonlinearities feedback signals. The optimal linear feedback control (OLFC) involves the application of two control signals, a nonlinear feedforward control to maintain the controlled system to a desired periodic orbit, and control a feedback control to bring the trajectory of the system to the desired orbit. Simulation results, including of uncertainties show the feasibility of the both methods, for chaos control of the considered system.

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