Research On Orientation Interpolation And Optimal Trajectory Of Industrial Robot

While the applications of industrial robot increase greatly, the motion planningis required more and more strictly. The smooth trajectory of robot can improve theprecision and performance of industrial robot. For this consideration, the smoothorientation interpolation algorithm and smooth minimum time trajectoryoptimization are studied in this paper.Firstly, the kinematic and dynamic model of6-DOF arc welding robot werebuild up. Based on DH coordinate system, the forward kinematic and the inversekinematics were derived, the inverse kinematic was modified with a method that isjust three times of inversion to simplify the analytic deduction process and improvethe efficiency of deduction. Also, three forms of orientation expression of the robot,matrix, Euler angle system, unit quaternion, were analyzed to find out the meritsand drawbacks of them. Lagrange dynamic method was employed to derive thedynamic model of6-DOF arc welding robot. The motion simulation platform of6-DOF arc welding robot which included the modules of the kinematic, dynamicand motion planning was build up in MATLAB/SIMULINK.Then, the interpolation algorithm based on unit quaternion was studied.Derived from the physical significance and the multiplication of unit quaternion, theunit quaternion orientation curve in S3was transformed to the curve on unit spherein Euclidean space and the orientation interpolation expression on sphere was buildup. Based on that transformation, interpolation between two orientations expressedby unit quaternion was formed. The sine-jerk motion planning was designed tointerpolate the angle of two orientations.The comparison between Euler anglesystem and SLERP in simulation platform of6-DOF arc welding robot shows thatthe interpolation using unit quaternion shows a better performance of motioncontrol and smoothness. At last, the multi-orientations interpolation algorithm basedon unit quaternion was studied because of the requirement of complex curve andplane in manufacture. The interpolation curve on unit sphere of three orientationswas constructed with the help of mapping between S3and Euclidean space.Compared with SQUAD, the orientation interpolation was more smooth at theinterpolation points of orientations.At last, minimum time optimization with smooth trajectory was studied. Thetime optimization model of industrial robot was built up and transformed tocoordinate space. To get smooth optimal trajectory, the smooth constraints ofcontrol variables were added to the optimal model. Cubic B-spline was employed toconstruct the smooth constraints of optimal variables and was transformed to equivalent equation constrains. Then the optimal problem was rewritten as SOCPproblem and solved with SOCP solver SeDuMi. The comparsion with optimalproblem without smooth constrains shows that the optimal result are smooth enoughfor motion.