Mathematical Modeling Of The Robot Manipulator Motion

The complexity of the mechanical system manipulator, as well as some significant features, inherent the robot as an object of control(elastic compliance of links and transmission mechanisms, mutual influence degrees of freedom, ambiguity of the solution some tasks, the presence of various types restrictions) often leads to the extreme complexity of the obtained models that complicates the control tasks manipulators. Therefore, the creation of effective methods and control algorithms is very relevant.In the process of studying a number of issues, associated with the complexity of the obtained models and algorithms control systems manipulators, associated with a complexity of the obtained models and algorithms control systems manipulators, which are more fully take account multilink structure, nonlinear, non-stationary program motions, delay in the feedback loop and other factors, faced a number of problems. In particular, with a system of nonlinear differential equations of high-level dimension, this is expressed by mathematical models of complex mechanical systems. As a result, the search for possible solutions and analysis of the existing literature on this topic, by the decision to this problem was the idea decoupling, that is the idea of full compensation dynamic mutual influence between subsystems. During the study of the works on the treatment of decoupling, was chosen for the study of control algorithm with piecewise constant coefficients, which allowed output system from the initial area in the mode decoupling, which provides an exponential stabilization of programmed motion. Were investigated modern methods of modeling manipulators and other robotic systems; analyzed modern methods of describing the kinematics and dynamics of manipulators When finished with the theoretical part, the results used in subsequent chapters for constructing of control algorithms manipulators; the investigated problem of control manipulators, which can be modeled as a coupled rigid bodies system. Has tentatively accepted that the model is described the Lagrange equations of the second kind.The main contents are as follows.In the first chapter of the thesis presents research on modeling of manipulators and other robotic and controlled mechanical systems. Analyzed modern methods with describe kinematics and dynamics of manipulators. The results of the first chapter apply to the following chapters for constructing algorithms control manipulators.The second chapter research problem of manipulator control that can be modeled as a system of coupled rigid bodies. In the first paragraph it is assumed, that model is described the Lagrange equations of the second kind. In the second paragraph consider the problem of constructing control for manipulator, which modeled as a system of coupled rigid bodies with a leading body, which implementation the defined motion. In the third paragraph consider a problem of constructing control for manipulator, which represented as a free system of coupled rigid bodies. Develop appropriate control algorithms for such modeling.In the third chapter substantiates new control models, which provide stabilization of program motions of two- and three-link manipulators.