Research On Robot Smooth Trajectory Planning Based On Improved S-Curve

In the fields where arc welding and spraying robots are widely used,the unsmooth motion trajectory of the robot will cause processing defects,reduce the trajectory tracking accuracy,cause the impact and vibration of the joints,and accelerate the wear of the transmission components.In order to improve the smoothness of the trajectory planning algorithm,this paper takes the six-degree-of-freedom collaborative robot UR5 as the research object Based on the establishment of its kinematics model,this paper studies the speed planning and attitude planning of the space straight line,and the speed planning of the free curve.The aim is to design and develop a set of trajectory planning algorithms that take into account smoothness and motion efficiency.The main research contents are as follows:First of all,to solve the problems of large amount ofcalculation,poor smoothness and low motion efficiency of straight-line speed planning,an improved S-curve speed planning algorithm with continuous jerk is proposed.Based on the third-order S-curve model and the sine-curve model,a continuous jerk sine S-curve is constructed,and a sine proportion coefficient is proposed to determine the proportion of the sine curve to simplify the process of determining the curve.By analyzing the critical constraint conditions of the four possible contours,the construction of the sinusoidal S-curve is analyzed in detail and a complete analytical solution of the kinematic parameters is given.At the same time,in view of the time period error,the characteristics of the sinusoidal S-curve and the monotonic relationship between the kinematic parameters are analyzed.Based on this,a period rounding method based on upward rounding of time is proposed.Through different kinematic parameter adjustment strategies,the period error compensation is realized and the smoothness of the movement is ensured.Secondly,aiming at the problem of unnatural movement of attitude transformation and sudden changes in velocity,a attitude planning algorithm based on spherical linear interpolation and sinusoidal S-curve is proposed.By analyzing the mapping relationship between unit quaternion space and Euclidean space,a spherical linear interpolation algorithm between the two poses is established.Aiming at the sudden change of angular velocity in isoparametric interpolation,the interpolation parameters are calculated based on the sinusoidal S-curve velocity planning algorithm.The robot’s position and attitude collaborative planning algorithm is discussed to meet the requirements of the beginning and end postures and to ensure the synchronization of the position and attitude movement.Thirdly,in view of the problem that the Non-Uniform Rational B-Spline curve speed planning is difficult to satisfy the full curve contour error constraint,a planning algorithm based on the idea of bidirectional interpolation and sinusoidal S-curve is proposed.Through the analysis of the calculation error of the interpolation point parameters,an accurate solution method with the idea of Predictor-Corrector Interpolation is given.And in the forward-looking stage of speed,the speed extreme point is corrected forward and backward.After finishing the pre-processing,the feed speed is adaptively adjusted based on the sinusoidal S curve in the twoway speed planning process.A detailed analysis of the rendezvous of the forward and reverse interpolation is carried out and the constraint of the contour error of the full curve is satisfied.Finally,based on the above research,a series of algorithm programs are written in Matlab for simulation testing,and the planned trajectory data is transmitted to the UR5 controller through the Robot Operating System framework to verify the proposed smooth trajectory planning algorithm.The results show that the improved S-curve speed planning proposed in this paper has improved the smoothness of the third-order S-curve.The two-way adaptive sinusoidal S velocity planning for Non-Uniform Rational B-Spline satisfies the full curve contour error constraint and has good smoothness.