基于傅里叶级数的最优能量运动轨迹优化方法
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摘要
从机器人关节空间出发,以单关节系统为例,针对机器人关节空间能量最优的运动轨迹优化方法进行了研究。在基于Stribeck摩擦模型构造单关节系统动力学模型的基础上,建立了以傅里叶级数表征任意位置和规律的运动轨迹规划方案。以能量作为优化目标,通过添加边界位置、速度及加速度等约束条件,构建了运动轨迹优化的理论模型。基于遗传算法对傅里叶级数的最优系数进行搜索,从而形成以能量最优为目标的运动轨迹优化方法。通过具体算例分析了傅里叶级数系数的数量对于优化后的轨迹作用于关节系统能耗及运动学性能等方面的影响,并与多项式运动规律进行对比分析,结果表明该运动轨迹优化方法对于降低关节系统能耗具有显著作用。
With the single-joint system as an example,research is conducted on the method of optimal-energy motion trajectory planning in the robot joint space. Based on the Stribeck model of single-joint systematic dynamics,the scheme of motion trajectory planning is formulated,with the positions and their laws represented by Fourier Series. For the sake of optimal energy,the model of motion-trajectory optimization is built up,with the position,velocity and acceleration on the boundary as the constraints. By means of GA,measures are taken to identify the optimal coefficients of Fourier Series and establish the theoretical model of optimal-energy motion trajectory. Based on the analysis on several examples,the effects of Fourier Series coefficients on energy consumption and kinematic performance are identified. Based on the comparison with the polynomial motion law,the results show that the method has a significant effect in reducing the energy consumption of the joint system.
With the single-joint system as an example,research is conducted on the method of optimal-energy motion trajectory planning in the robot joint space. Based on the Stribeck model of single-joint systematic dynamics,the scheme of motion trajectory planning is formulated,with the positions and their laws represented by Fourier Series. For the sake of optimal energy,the model of motion-trajectory optimization is built up,with the position,velocity and acceleration on the boundary as the constraints. By means of GA,measures are taken to identify the optimal coefficients of Fourier Series and establish the theoretical model of optimal-energy motion trajectory. Based on the analysis on several examples,the effects of Fourier Series coefficients on energy consumption and kinematic performance are identified. Based on the comparison with the polynomial motion law,the results show that the method has a significant effect in reducing the energy consumption of the joint system.
引文
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[3] Shin K,McKay N. A dynamic programming approach to trajectory planning of robotic manipulators[J]. IEEE Transactions on Automatic Control,1986,31(6):491-500.
[4]丛明,熊永康,刘冬,等.一种并联机械手操作空间最优时间轨迹规划方法[J].机械设计,2016,33(2):7-13.
[5] Westk覿mper E,Schraft R D,Schweizer M,et al. Task-oriented programming of large redundant robot motion[J]. Robotics and Computer-Integrated Manufacturing,1998,14(5):363-375.
[6] Wu C,Jou C. Design of a controlled spatial curve trajectory for robot manipulations[J]. Journal of Dynamic Systems,MeaSurement&Control,1991,113(2):248-258.
[7]任敬轶,孙汉旭.一种新颖的笛卡尔空间轨迹规划方法[J].机器人,2002,24(3):217-221.
[8]王攀峰,梅江平,黄田.高速并联机械手抓放操作时间最优轨迹规划[J].天津大学学报,2007,40(10):1139-1145.
[9] Piazzi A,Visioli A. Global minimum-time trajectory planning of mechanical manipulators using interval analysis[J]. International Journal of Control,1998,71(4):631-652.
[10]王喆,曾侠,刘松涛,等.一种2自由度高速并联机械手的轨迹规划方法[J].天津大学学报:自然科学与工程技术版,2016(7):687-694.
[11]邓乾旺,罗正平,张丽科,等.点焊机器人轨迹能耗模型及其优化算法研究[J].中国机械工程,2016,27(1):14-20.
[12] Paes K,Dewulf W,Elst K V,et al. Energy efficient trajectories for an industrial ABB robot[J]. Procedia Cirp,2014,15:105-110.
[13]刘鹏程,艾廷华,毕旭.傅立叶级数支持下的等高线多尺度表达模型[J].武汉大学学报:信息科学版,2013,38(2):221-224.
[14]褚金奎,孙建伟.基于傅里叶级数理论的连杆机构轨迹综合方法[J].机械工程学报,2010,46(13):31-41.
[15]刘维仲,张大森.傅里叶级数的曲线仿真应用及算法[J].天津大学学报,1996,29(1):108-112.
[16] Craig J. Introduction to robotics[M]. New York:AddisonWesley Publishing Company,1986.