Abstract
The control algorithm of robotic manipulator (RM) movement along the program trajectory by the method of Lyapunov function is obtained. The method uses the decomposition of original multiply-connected nonlinear system into subsystems and realizes the possibility of decentralized control of each of moving RM links. The control signal is formed taking into account the dynamics of RM mechanical system and electric drives. When constructing the control system, the coefficients of nonlinear system dynamics equations a constructed in the form of the Lagrange – Maxwell equations are calculated. The control for the initial nonlinear system is obtained explicitly. The stability of dynamical system in entire phase space and its dissipativity in region of phase space are investigated with a significant influence of disturbing moments in operating conditions. To compensate for them, an adaptive signal-type additive has been introduced into the control law, which ensures system performance at significant rates of change in power moments on the output shafts of drives. The influence of measurement errors of RM state vector on the formation of control is taken into account. In the Acsocad software according to the mathematical model of RM link, a block diagram is made up with subsystems of gradient tuning and signal adjustment. The movement of one link along the program trajectory is considered. To take into account the influence of measurement noise on the values of current, speed and position, blocks with adding a random signal having a normal distribution are added to system. Simulation was performed in the absence and influence of noise on measurements both at constant values of adjustable coefficients, and using the coefficient gradient tuning method. Constructed curves of coefficients optimal values to obtain the minimum deviation value from the program trajectory. The efficiency of using the gradient tuning and signal adjustment methods when RM is moving in conditions of incomplete information is shown.
Highlights
A manipulation robot is a mechanical system whose dynamics is described by Lagrange's differential equations
When solving the problem of synthesis of the control moments of robot manipulator (RM) by this method, a function that reflects the change in the total energy of the dynamic system can be chosen as a Lyapunov function that allows to study the behavior of the phase trajectories of the system in the entire phase space
The object of the study is a three-link robot manipulator with electric drives, the full model of which dynamics is constructed in the form of Lagrange – Maxwell equations [16, 17] and according to the well-known rules [21] is reduced to a non-linear model by the form of the relationship between its input and output parameters, defined by the vector differential x F x,U,v, (1)
Summary
A manipulation robot is a mechanical system whose dynamics is described by Lagrange's differential equations. When solving the problem of synthesis of the control moments of robot manipulator (RM) by this method, a function that reflects the change in the total energy of the dynamic system can be chosen as a Lyapunov function that allows to study the behavior of the phase trajectories of the system in the entire phase space. With this approach, the Lyapunov function is selected from the first integrals of the motion of the system. К задаче улучшения точности позиционирования робота-манипулятора в условиях неполноты информации
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