Dynamics and control analysis of a single flexible link robot with translational joints

Modern design always aims at reducing mass, simplifying the structure, and reducing the energy consumption of the system especially in robotics. These targets could lead to lowing cost of the material and increasing the operating capacity. The priority direction in robot design is optimal structures with longer lengths of the links, smaller and thinner links, more economical still warranting ability to work. However, all of these structures such as flexible robots are reducing rigidity and motion accuracy because of the effect of elastic deformations. Therefore, taking the effects of elastic factor into consideration is absolutely necessary for kinematic, dynamic modeling, analyzing, and controlling flexible robots. Because of the complexity of modeling and controlling flexible robots, the single-link and two-link flexible robots with only rotational joints are mainly mentioned and studied by most researchers. It is easy to realize that combining the different types of joints of flexible robots can extend their applications, flexibility, and types of structure. However, the models consisting of rotational and translational joints will make the kinematic, dynamic modeling, and control becomes more complex than models that have only rotational joints. This study focuses on the dynamics model and optimal controller based on genetic algorithms (GA) for a single flexible link robot (FLR) with a rigid translational joint. The motion equations of the FLR are built based on the Finite Element Method (FEM) and Lagrange Equations (LE). The difference between flexible manipulators that have only rotational joints and others with the translational joint is presented through boundary conditions. A PID controller is designed with parameters that are optimized by the GA algorithm. The cost function is established based on errors signal of translational joint, elastic displacements of the End-Point (EP) of the FLR. Simulation results show that the errors of the joint variable, the elastic displacements (ED) are destructed in a short time when the system is controlled following the reference point. The results of this study can be basic to research other flexible robots with more joint or combine joint styles.