Researched On Collaborate Robot Trajectory Planning Based On B-spline Curve

In the field of cooperative robots’ motion control,common planning methods were divided into joint space trajectory planning and end position trajectory planning,end position trajectory planning was commonly includes linear,circular and circle trajectory.In the application scenarios of robot spraying,grinding,massage and assembly for complex curves and surfaces tracking,the common planning method was inconvenience and ineffective.In this paper,based on the principle of B-spline curve,extending B-spline to multi-dimensional space is proposed,and the method of sampling speed look-ahead algorithm matching convolution calculation is proposed to generate speed planning.Finally,the complete trajectory is generated by adaptive compensation interpolation parameter calculation method based on first-order Taylor expansion and a modular Bspline trajectory planning process is summarized.Specific research work and achievements are as follows:(1)In order to solve the problem that cooperative robots’ conventional motion planning can not adapt to complex curve tracking,the properties and characteristics of various B-spline curves were studied.And cubic quasi-uniform rational B-spline curves was selected as the research objects.It was proposed to extend the B-spline curve to multidimensional to achieve synchronous planning position and posture,and to extend the Bspline parameter equation to the form of matrix calculation.So that it can adapt to computer programming and calculation.(2)To enable the cooperative robot can move follow the curve,speed planning of Bspline curve is required.In this paper,three kinds of conventional speed planning were studied.There were some shortcomings in speed planning of B-spline curve with variable curvature.Therefore,convolution method is proposed for speed planning.This method is capable of continuously handling frequently changing speed requirements,generating high-order smooth speed curves with very small computational loads,and also provides a framework for apply speed look-ahead algorithm.(3)Changing the vector direction will impact the servo control system when the end of the cooperative robot runs fast with loads.Therefore,feature extraction is required for the fitted B-spline curve.And speed constraints on its curvature and angular velocity are processed to obtain sampling speed constraints everywhere on the curve.Because the selected cubic quasi-uniform B-spline curve is smooth and its curvature changes continuously,an adaptive speed look-ahead algorithm using uniform parameter sampling and speed limitation dispersed functions of curvature and posture change angle is proposed.Then the speed limitation is obtained by using two convolution calculations to obtain the speed planning of the whole curve,which eliminates the load of sectional planning and iteration calculation and improves the real-time performance.It smoothies speed change impact and reduces the loads to servo system.(4)Because the B-spline curve is a non-time-dependent parameter equation,interpolation points can not be given directly.It is necessary to establish a non-linear ordinary differential equation about velocity for the parameter equation of curve and calculate interpolation parameters by numerical iteration.In this study,the first-order Taylor expansion was selected as the calculation method of estimation parameters,and then the bow height error of the parameters was compensated.Proportional compensation correction was adopted after judging that the interpolation speed error exceeds the tolerance.It was verified by experiments that the calculation accuracy is high and the calculation burden is small.The research results is now applied in collaborative robot products.After testing,the plan can effectively adjust the running speed according to the curve shape,the speed curve is smooth,and the interpolation calculation is more efficient than the existing methods,with the speed fluctuation reduced by 98.2% and the accumulated error reduced by 65.6%.This research has theoretical prospects and application value.