Study On Trajectory Tracking Control Of The End Of Six-DOF Manipulator

In this paper, a study on Six-DOF manipulator is done, the kinetic model based onUdwadia-Kalaba equation is used to trajectory tracking control of the Six-DOF manipulator,which provide a theoretical basis for the design of the trajectory tracking controller.As the solving of the Six-DOF manipulator’s forward and inverse kinematics, throughthe method to describe position and orientation in three-dimensional space and the method toestablish coordinate system of the manipulator linkage, the conversion formula is derived foreach manipulator joint coordinate system using DH parameters in order to establish theforward kinematics equations. Bsaed on this, the closed form solution of the manipulatorinverse kinematics is received using bivariate arc tangent function.With the introduced theory of constraints, pseudo-inverse matrix, Lagrange equation andGaussian minimum constraint principle, derived Udwadia-Kalaba equation. Combined withthe constraint violation stability method proposed by Baumgarte can solve the problem thatUdwadia-Kalaba equation does not apply to inconsistent initial condition.According to DH coordinate system, first follow the Lagrangian approach to derive theunconstrained model of the manipulator, and then using the Euler angles describe attitudeconstraints of the end link, and forward kinematics of simultaneous equations, draw attitudeconstraint matrix equation in the form of generalized coordinates, by solving the inverse Eulerangles, build constraint equations describing the manipulator posture to establishe dynamicsmodel of manipulator for trajectory tracking control based on Udwadia-Kalaba equation.Simulation software is Matlab and co-simulation with Adams. Matlab simulationcontains consistent and inconsistent initial condition, fixed and dynamic posture trajectory.Combined simulation considering inconsistent initial condition and dynamic posture trajectory,achieve a stable trajectory tracking control is the validation of theoretical research results.Through these research results the Six-DOF manipulator trajectory tracking controlmethod based on Udwadia-Kalaba equation can track the target trajectory described by theconstraint equations with good accuracy in real time.