| 6R industrial manipulators are widely used in high-demanded Cartesian trajectory tracking tasks.Inverse kinematics affects the precision and real-time performance of trajectory tracking control.There is still a lack of a unified and efficient method to find the inverse solution of the 6R industrial manipulator.In addition,in Cartesian trajectory tracking,multiple solution selections,singularity and pose error compensation affect the speed and accuracy of the inverse solution.Therefore,studying and solving the inverse solution problems of the 6R industrial manipulator for its Cartesian trajectory tracking task is significant.To solve the above problems,based on the improved disconnection-reconnection method,unique domain method and pose error compensation method,the inverse solution of nominal model,multiple solution selection of inverse kinematics,inverse solution of singular pose and inverse solution of calibrated manipulator were studied.The main research content of this dissertation:（1）An improved disconnection-reconnection method for inverse solution of 6R industrial manipulator.Aiming at the problem that the forward kinematic equation of the 6R industrial manipulator needs to be transformed several times to find the closure equations which can derive the inverse solution,the geometric feature that the adjacent axes of the industrial manipulator intersect at one point is fully utilized.Six independent equations can be determined by the constraints only after one deformation of the forward kinematics equation.On this basis,the analytical solution of the 6R industrial manipulator can be obtained directly,or the inverse solution problem can be transformed into a one-dimensional nonlinear equation root-finding problem.（2）Multi-solution selection of inverse kinematics for 6R industrial manipulator based on the unique domain.Aiming at selecting multiple inverse kinematics solutions in the Cartesian trajectory tracking of 6R industrial manipulator,the feasibility of selecting inverse solution by unique domain method and the deficiency of selecting inverse solution by minimum joint motion criterion were analyzed theoretically.The numerical results show that the unique domain method is more suitable for selecting the inverse solution of the 6R industrial manipulator than the minimum joint motion criterion in the Cartesian trajectory tracking task,and the solution speed is faster.（3）A new analytical method for the singular pose of the 6R industrial manipulator.Aiming at the inverse solution of the singular pose in the Cartesian trajectory tracking of the 6R industrial manipulator,a new analytical formula is derived based on the improved separation and reconnection method.Compared with the existing analytical methods,the analytic formula derived by the new method can integrate the pose,velocity and acceleration of the target trajectory and improve the inverse solution accuracy of the singular pose.Numerical experimental results show that the new analytical method can accurately obtain the inverse solution of the singular pose in Cartesian trajectory.（4）Inverse solution of the calibrated 6R industrial manipulator based on command pose error compensation.To solve the inverse problem of the calibrated 6R industrial manipulator,the error between the calibrated model pose and the desired pose compensates for the instruction pose.The inverse solution of the new instruction was solved using the inverse solution algorithm of the nominal model and substituted into the calibrated model.Repeat the above steps until the termination condition is met.The results show that the proposed method can converge the pose error norm to the order of 10-10 in finite iterations,and the solving speed is about 2.44 times that of the damped least square method.（5）Inverse solution experiment of Cartesian trajectory tracking for 6R industrial manipulator.To verify the effectiveness and feasibility of the proposed inverse solution algorithm,Cartesian trajectory tracking experiments were carried out on ABB IRB6700 industrial manipulator.The proposed inverse solution algorithm is simulated and verified on Robot Studio.The ABB IRB6700 industrial manipulator’s inverse solution was obtained using the proposed algorithm"online".Experimental results show that the inverse solution based on unique domain selection can make the manipulator end-track the target trajectory.The new analytical method can make the manipulator’s end pass through the singular position without path mutation.This dissertation studies the Cartesian trajectory tracking of the 6R industrial manipulator.An improved disconnection and reconnection method,a new method for selecting multiple solutions,a new analytical method for the singular pose,and an inverse kinematics method for calibrated manipulators are proposed,improving the inverse solution’s speed and accuracy.It provides new methods and theory for advancing 6R industrial manipulators to carry out Cartesian trajectory tracking tasks. |
