“…Finally, θM=[θM1θM2θM3centerθM4θM5θM6]T represents the motor angular depicted in Figure 1(a). To reveal the connection between L i and θMi, the results of the same model in Tajdari et al (2020a) are extracted from Van Nguyen and Ha (2018); Szufnarowski (2013); thenwhere scriptAi,scriptBi,scriptCi∈U(trueX¯) andwhere θ h defines the angle between trueP→i and X→ in the XYZ axis, and β is the motor installation angle to the horizon. The defined formula in (2) explains that measuring the X¯ via a sensor mounted on the end-effector results in determining the corresponding operating angle value of each motor, which is useful to practically implement position controller approaches on such robots.Figure 1.The Stewart platform mechanism: (a) defined variables and vectors and (b) the top view of the...…”
Section: Equation Of Motionmentioning
confidence: 99%
“…Here, employing the Newton–Euler method, the dynamic formulation of the Stewart platform equipped with six rotary motors is concluded from Van Nguyen and Ha (2018); Szufnarowski (2013). The platform includes, as shown in Figure 1, a moving plate as the end-effector, a sedentary plate as the base, six rotary actuators as manipulators to move the end-effector, and six legs connected to their corresponded motors.…”
Aiming at a more efficient and accurate performance of parallel manipulators in the existence of complex kinematics and dynamics, a robust generalizable methodology is proposed here for an integrated 6-DOF Stewart platform with rotary time-delayed actuators torque control. The suggested method employs a time-delay linear–quadratic integral regulator with online artificial neural network gain adjustment. The unknown time-delay is estimated through a novel robust adaptive estimator. The global asymptotic stability of the estimator is proved via a Lyapunov function. The controller is developed in MATLAB software and implemented on the robot designed in ADAMS software to ensure that the real-time tracking error of a nonlinear system with an unknown time-delay is kept to a minimum. The sensitivity of the controller to the parameter choices is studied via implementing the controller in ADAMS software and is validated by investigating the performance on a naturalistic fabricated robot. The approach is assessed using simulation and experimental tests to show the feasibility, optimum, and zero-error convergence of the technique developed.
“…Finally, θM=[θM1θM2θM3centerθM4θM5θM6]T represents the motor angular depicted in Figure 1(a). To reveal the connection between L i and θMi, the results of the same model in Tajdari et al (2020a) are extracted from Van Nguyen and Ha (2018); Szufnarowski (2013); thenwhere scriptAi,scriptBi,scriptCi∈U(trueX¯) andwhere θ h defines the angle between trueP→i and X→ in the XYZ axis, and β is the motor installation angle to the horizon. The defined formula in (2) explains that measuring the X¯ via a sensor mounted on the end-effector results in determining the corresponding operating angle value of each motor, which is useful to practically implement position controller approaches on such robots.Figure 1.The Stewart platform mechanism: (a) defined variables and vectors and (b) the top view of the...…”
Section: Equation Of Motionmentioning
confidence: 99%
“…Here, employing the Newton–Euler method, the dynamic formulation of the Stewart platform equipped with six rotary motors is concluded from Van Nguyen and Ha (2018); Szufnarowski (2013). The platform includes, as shown in Figure 1, a moving plate as the end-effector, a sedentary plate as the base, six rotary actuators as manipulators to move the end-effector, and six legs connected to their corresponded motors.…”
Aiming at a more efficient and accurate performance of parallel manipulators in the existence of complex kinematics and dynamics, a robust generalizable methodology is proposed here for an integrated 6-DOF Stewart platform with rotary time-delayed actuators torque control. The suggested method employs a time-delay linear–quadratic integral regulator with online artificial neural network gain adjustment. The unknown time-delay is estimated through a novel robust adaptive estimator. The global asymptotic stability of the estimator is proved via a Lyapunov function. The controller is developed in MATLAB software and implemented on the robot designed in ADAMS software to ensure that the real-time tracking error of a nonlinear system with an unknown time-delay is kept to a minimum. The sensitivity of the controller to the parameter choices is studied via implementing the controller in ADAMS software and is validated by investigating the performance on a naturalistic fabricated robot. The approach is assessed using simulation and experimental tests to show the feasibility, optimum, and zero-error convergence of the technique developed.
“…erefore, it can avoid unnecessary and lengthy calculation compared with the traditional BP neural network. It is proved by numerous literatures that RBF neural networks can approximate any nonlinear function in a compact set [41]. In order to obtain the estimate of the φ, the RBF neural network is utilized to approximate the real value.…”
During the vertical cyclic actuation process of heavy materials handling, the gravitational potential energy will be converted to heat in the form of throttle in the traditional hydraulic system. Therefore, large energy dissipation is inevitable is this process. In order to achieve energy recuperation, as well as precise trajectory tracking, a direct drive and energy recuperation system is developed. To be specific, the function of direct drive and energy recovery is realized via the three-chamber actuator and a hydraulic accumulator. Moreover, the optimized parameters are obtained by the simulated annealing algorithm. To further reduce the energy consumption, the variable supply pressure control circuit is introduced into the system. Furthermore, the prescribed tracking performance is guaranteed by the proposed robust controller. To compensate for the uncertainties, both in the variable supply pressure control circuit and the robust controller, the RBF neural network is employed to approximate the unknown function. The presented approach theoretically possesses the ability to minimize the energy consumption while maintaining satisfied tracking accuracy. The results demonstrate that the proposed approach can save nearly 90 percent of the energy, and the maximum tracking error is 2 mm.
“…Kinematics of the robot with linear manipulator was widely studied in recent years, namely Geng et al (1992); Petrescu et al (2018); and Tajdari et al (2020c), whereas mechanisms with rotary actuators are less studied due to additional complexity of rotation. Thus, in this article, a Stewart robot with rotary manipulator is investigated, owing to the fact that it is faster than a Stewart platform with linear actuators in control responses (Van Nguyen and Ha, 2018). Also, it has less production and maintenance cost, less weight, easier installation procedure (e.g., surgical goals), and powerful ability of integration with other mechanisms (Patel et al, 2018).…”
Aiming at operating optimally minimizing error of tracking and designing control effort, this study presents a novel generalizable methodology of an optimal torque control for a 6-degree-of-freedom Stewart platform with rotary actuators. In the proposed approach, a linear quadratic integral regulator with the least sensitivity to controller parameter choices is designed, associated with an online artificial neural network gain tuning. The nonlinear system is implemented in ADAMS, and the controller is formulated in MATLAB to minimize the real-time tracking error robustly. To validate the controller performance, MATLAB and ADAMS are linked together and the performance of the controller on the simulated system is validated as real time. Practically, the Stewart robot is fabricated and the proposed controller is implemented. The method is assessed by simulation experiments, exhibiting the viability of the developed methodology and highlighting an improvement of 45% averagely, from the optimum and zero-error convergence points of view. Consequently, the experiment results allow demonstrating the robustness of the controller method, in the presence of the motor torque saturation, the uncertainties, and unknown disturbances such as intrinsic properties of the real test bed.
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