基于NURBS算法的工业机器人轨迹规划研究
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摘要
轨迹规划是工业机器人研究领域的重要内容之一。为解决使用直线与圆弧逼近不规则曲线方法带来较大误差的问题,提出使用NURBS拟合自由曲线,并使用S形速度曲线来控制机器人末端的运动速度和加速度,使各个插补点的位置、速度和加速度能够连续,将之反推到关节空间可以得到各个关节的角度、角速度和角加速度。最后以IRB2600工业机器人为仿真本体,通过MATLAB仿真证明:NURBS和S形速度曲线相结合的方法可以得到在关节空间连续、平稳的运行轨迹、速度曲线、加速度曲线,减弱了因各关节角度、角速度、角加速度突变带来的冲击影响,优化了机器人运行轨迹。
Trajectory planning is one of the important contents in industrial robot research field. In order to solve the problem of large error caused by the method of linear and arc approximating irregular curve, a NURBS fitting free curve was proposed and the velocity and acceleration of the end of the robot were controlled by using the S-shape speed curve, so that the position, speed and acceleration of each interpolation point could be continuous. The angle, angular velocity and angular acceleration of each joint could be obtained by pushing it back into joint space. Finally, with the IRB2600 industrial robot as the simulation ontology, the MATLAB simulation proves that the combination of NURBS and S-shape velocity curve can get continuous and steady trajectory, the velocity curve and the acceleration curve of the joint space. The impact caused by mutation of the joint angle, angular velocity, angular acceleration is weaken and the trajectory of the robot is optimized.
Trajectory planning is one of the important contents in industrial robot research field. In order to solve the problem of large error caused by the method of linear and arc approximating irregular curve, a NURBS fitting free curve was proposed and the velocity and acceleration of the end of the robot were controlled by using the S-shape speed curve, so that the position, speed and acceleration of each interpolation point could be continuous. The angle, angular velocity and angular acceleration of each joint could be obtained by pushing it back into joint space. Finally, with the IRB2600 industrial robot as the simulation ontology, the MATLAB simulation proves that the combination of NURBS and S-shape velocity curve can get continuous and steady trajectory, the velocity curve and the acceleration curve of the joint space. The impact caused by mutation of the joint angle, angular velocity, angular acceleration is weaken and the trajectory of the robot is optimized.
引文
[1]叶仁平,曾德怀.基于NURBS曲线自适应实时前瞻插补算法研究[J].机床与液压,2017,44(13):46-52.YE R P,ZENG D H.Research on Interpolation Algorithm of Adaptive Real-time Look-ahead Based on NURBS Curve[J].Machine Tool & Hydraulics,2017,44(13):46-52.
[2]韩庆瑶,赵忠华.基于NURBS的复杂曲线多轴运动控制轨迹生成的研究[J].机床与液压,2014,42(8):106-109.HAN Q Y,ZHAO Z H.Study of Multi-axis Motion Controlled Trajectory Generation of Complex Curves Based on NURBS[J].Machine Tool & Hydraulics,2014,42(8):106-109.
[3]黄国辉.基于DSP的NURBS曲线高速高精度实时插补算法的研究与实现[D].广州:广东工业大学,2013.
[4]王允森,盖荣丽,孙一兰,等.面向高质量加工的NURBS曲线插补算法[J].计算机辅助设计与图形学学报,2013,25(10):1549-1556.WANG Y S,GAI R L,SUN Y L,et al.NURBS Interpolation Algorithm for High-Quality Machining[J].Journal of Computer-Aided Design & Computer Graphics,2013,25(10):1549-1556.
[5]翟静涛,赵国勇,庄丙远,等.椭圆曲线回转类零件NURBS插补算法研究[J].组合机床与自动化加工技术,2016(2):112-114.ZHAI J T,ZHAO G Y,ZHUANG B Y,et al.Research on NURBS Interpolation Algorithm for Rotational Parts with Elliptic Curve[J].Modular Machine Tool & Automatic Manufacturing Technique,2016(2):112-114.
[6]BEDI S,ALI I,QUAN N.Advanced Interpolation Techniques for CNC Machines[J].ASME Journal of Engineering for Industry,1993,115(1):329-336.
[7]NAM S H,YANG M Y.A Study on Generalized Parametric Interpolator with Real-time Jerk-limited Acceleration[J].Computer-Aided Design,2004,36(1):27-36.
[8]乐英,王颖.基于NURBS插补算法的汽轮机叶片数控加工[J].组合机床与自动化加工技术,2017(1):78-81.YUE Y,WANG Y.NURBS Interpolation Algorithm for Turbine Blade in NC Machining[J].Modular Machine Tool & Automatic Manufacturing Technique,2017(1):78-81.
[9]杨锦涛,姜文刚,林永才.工业机器人冲击最优的轨迹规划算法[J].科学技术与工程,2014,14(28):64-69.YANG J T,JIANG W G,LIN Y C.Jerk-optimal Trajectory Planning Algorithm of Industry Robot[J].Science Technology and Engineering,2014,14(28):64-69.
[10]CORKEP.A Robotics Toolbox for MATLAB[J].Robotics and Automation Magazine,1996,3(1):24-32.
[2]韩庆瑶,赵忠华.基于NURBS的复杂曲线多轴运动控制轨迹生成的研究[J].机床与液压,2014,42(8):106-109.HAN Q Y,ZHAO Z H.Study of Multi-axis Motion Controlled Trajectory Generation of Complex Curves Based on NURBS[J].Machine Tool & Hydraulics,2014,42(8):106-109.
[3]黄国辉.基于DSP的NURBS曲线高速高精度实时插补算法的研究与实现[D].广州:广东工业大学,2013.
[4]王允森,盖荣丽,孙一兰,等.面向高质量加工的NURBS曲线插补算法[J].计算机辅助设计与图形学学报,2013,25(10):1549-1556.WANG Y S,GAI R L,SUN Y L,et al.NURBS Interpolation Algorithm for High-Quality Machining[J].Journal of Computer-Aided Design & Computer Graphics,2013,25(10):1549-1556.
[5]翟静涛,赵国勇,庄丙远,等.椭圆曲线回转类零件NURBS插补算法研究[J].组合机床与自动化加工技术,2016(2):112-114.ZHAI J T,ZHAO G Y,ZHUANG B Y,et al.Research on NURBS Interpolation Algorithm for Rotational Parts with Elliptic Curve[J].Modular Machine Tool & Automatic Manufacturing Technique,2016(2):112-114.
[6]BEDI S,ALI I,QUAN N.Advanced Interpolation Techniques for CNC Machines[J].ASME Journal of Engineering for Industry,1993,115(1):329-336.
[7]NAM S H,YANG M Y.A Study on Generalized Parametric Interpolator with Real-time Jerk-limited Acceleration[J].Computer-Aided Design,2004,36(1):27-36.
[8]乐英,王颖.基于NURBS插补算法的汽轮机叶片数控加工[J].组合机床与自动化加工技术,2017(1):78-81.YUE Y,WANG Y.NURBS Interpolation Algorithm for Turbine Blade in NC Machining[J].Modular Machine Tool & Automatic Manufacturing Technique,2017(1):78-81.
[9]杨锦涛,姜文刚,林永才.工业机器人冲击最优的轨迹规划算法[J].科学技术与工程,2014,14(28):64-69.YANG J T,JIANG W G,LIN Y C.Jerk-optimal Trajectory Planning Algorithm of Industry Robot[J].Science Technology and Engineering,2014,14(28):64-69.
[10]CORKEP.A Robotics Toolbox for MATLAB[J].Robotics and Automation Magazine,1996,3(1):24-32.