Design and Dynamic Modeling of a 3-RPS Compliant Parallel Robot Driven by Voice Coil Actuators

In order to increase the driving force of the voice coil actuator while reducing its size and mass, the structural parameters of the coil and magnet in the actuator are optimized by combing Biot–Savart law with Lagrangian interpolation. A 30 mm × 30 mm × 42 mm robot based on a 3-RPS parallel mechanism driven by voice coil actuators is designed. The Lagrangian dynamic equation of the robot is established, and the mapping relationship between the driving force and the end pose is explored. The results of dynamic analysis are simulated and verified by the ADAMS software. The mapping relationship between the input current and the end pose is concluded by taking the driving force as the intermediate variable. The robot can bear a load of 10 g. The maximum axial displacement of the robot can reach 9 mm, and the maximum pitch angle and return angle can reach 40 and 35 degrees, respectively. The robot can accomplish forward movement through vibration, and the maximum average velocity can reach 4.1 mm/s.

Controller Design for a Delta Robot Using Lagrangian Multipliers

The novelty of this research is that the study utilizes Lagrangian multipliers for an articulated close-chain robot mechanism as time-varying states to augment an energy-based Lagrangian dynamic model, and the strategy facilitates the system computations while satisfying the forward/inverse dynamics and mechanism constraints simultaneously for the close-chained robot. Then, this article develops a controller based upon the augmented dynamics model for the Delta robot mechanism and drives its moving platform to track prescribed trajectories in space. As a result, the simulation results validate the effectiveness of the augmented system model in undertaking complex dynamics of close-chained robot mechanisms.

Analytical and experimental nonzero-sum differential game-based control of a 7-DOF robotic manipulator

We formulate a Nash-based feedback control law for an Euler–Lagrange system to yield a solution to noncooperative differential game. The robot manipulators are broadly used in industrial units on the account of their reliable, fast, and precise motions, while consuming a significant lumped amount of energy. Therefore, an optimal control strategy needs to be implemented in addressing efficiency issues, while delivering accuracy obligation. As a case study, we here focus on a 7-DOF robot manipulator through formulating a two-player feedback nonzero-sum differential game. First, coupled Euler–Lagrangian dynamic equations of the manipulator are briefly presented. Then, we formulate the feedback Nash equilibrium solution to achieve perfect trajectory tracking. Finally, the performance of the Nash-based feedback controller is analytically and experimentally examined. Simulation and experimental results reveal that the control law yields almost perfect tracking and achieves closed-loop stability.

Experimental and Analytical Nonzero-Sum Differential Game-Based Control of a 7-DOF Robotic Manipulator

We formulate a Nash-based feedback control law for an Euler-Lagrange system to yield a solution to non-cooperative differential game. The robot manipulators are broadly utilized in industrial units on the account of their reliable, fast, and precise motions, while consuming a significant lumped amount of energy. Therefore, an optimal control strategy needs to be implemented in addressing efficiency issues, while delivering accuracy obligation. As a case study, we here focus on a 7-DOF robot manipulator through formulating a two-player feedback nonzero-sum differential game. First, coupled Euler-Lagrangian dynamic equations of the manipulator are briefly presented. Then, we formulate the feedback Nash equilibrium solution in order to achieve perfect trajectory tracking. Finally, the performance of the Nash-based feedback controller is analytically and experimentally examined. Simulation and experimental results reveal that the control law yields almost perfect tracking and achieves closed-loop stability.

Dynamic Parameters and Friction Model Identification of an Industrial Hybrid Robot

To obtain higher performance for an industrial hybrid robot, the dynamic control method is utilized to control the robot. For dynamic control, the control performance is directly affected by the accuracy of the dynamic model. This paper investigated a method to establish and identify an accurate dynamic model. First, based on the Lagrangian dynamic equation and the Stribeck friction model, the unidentified dynamic model of the five-DOF hybrid robot is established. Second, identification experiments are carried out. Each of the driving joints performs frequent reciprocating motions individually. In the meantime, the moving speed is gradually increased to obtain driving torques of the respective joint at different moving speeds. Then the dynamic parameters with lower coupling are identified by using the standard deviation index and the least squares methods until all parameters are gradually determined. Finally, the hybrid robot moves a typical trajectory, while the currents of each joint are collected to obtain the driving forces. The actual driving forces, the identified dynamic model, and the unidentified dynamic model are compared. The results show that the identified method could significantly improve the accuracy of the dynamic model. The method proposed in this paper is general and can be applied to the other robots without adding any sensors.

A Two-Step Taylor Galerkin Smoothed Finite Element Method for Lagrangian Dynamic Problem

In this paper, a two-step Taylor Galerkin smoothed finite element method (TG-SFEM) is presented to deal with the two-dimensional Lagrangian dynamic problems. In this method, the smoothed Galerkin weak form is employed to create discretized system equations, and the cell-based smoothing domains are used to perform the smoothing operation and the numerical integration. The stability and the adaptation of elements aberrations presented in the two-step TG-SFEM are studied through detailed analyses of numerical examples. In the analysis of wave propagation, the proposed method can provide smoother displacement and stress than the common SFEM does, and energy fluctuations are found to be minimal. In the large deformation problems, the TG-SFEM can acclimatize itself to the mesh distortion effectively and stay bounded for long durations because the isoparametric elements are replaced, and area integration over each smoothing cells is recast into line integration along edges and no mapping is needed. Therefore, the stability, flexibility of elements distortion and the property of energy conservation of the TG-SFEM applied on two-dimensional solid problems are well represented and clarified.