基于改进差分进化算法的机械臂运动学逆解
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摘要
以9自由度液压机械臂为研究对象,建立求解位姿逆解的非线性方程组.以末端执行器位姿误差最小为优化指标建立目标函数,将非线性方程求解问题转化为最优化问题,并应用差分进化(DE)算法求解该问题.首先,为了避免位置和姿态收敛精度的不同,引入自适应权值系数进行平衡.然后,为克服基本DE算法难以平衡全局探索能力和局部开发能力的缺陷,结合DE/rand/1/bin和DE/best/1/bin两种进化模式,改进自适应变异差分进化(SAMDE)算法,提高了算法的收敛精度和收敛速度.最后,采用对称映射法对不满足关节角边界范围的个体进行处理,提高了收敛精度.开展了与基本DE算法的对比试验,仿真结果表明,该算法的收敛精度和收敛速度优于基本差分进化算法,且能够大幅度提高算法的稳定性.
For a 9-DOF(degree of freedom) hydraulic manipulator, a set of nonlinear equations are established to solve its inverse kinematics of position and orientation. An objective function is proposed to minimize the position and orientation error of the end-effector, and the solution problem of the nonlinear equations is transformed into an optimization problem,which is solved by the differential evolution(DE) algorithm. Firstly, self-adaptive weight coefficients are introduced to avoid the difference of the convergence accuracy of position error and orientation error. In order to overcome the difficulty of the basic DE algorithm in balancing the global and local exploitation abilities, DE/rand/1/bin and DE/best/1/bin, the two evolution models are combined to improve the self-adaptive mutation differential evolution(SAMDE) algorithm, resulting in better convergence accuracy and convergence rate. Finally, the reflection approach is applied to dealing with the individuals exceeding the boundary of the joint angles, and thus the convergence accuracy is improved. Some contrastive experiments with the basic DE algorithm are conducted. The simulation results indicate that the proposed method outperforms the basic DE algorithm in terms of convergence accuracy and convergence rate, and improves the stability significantly.
For a 9-DOF(degree of freedom) hydraulic manipulator, a set of nonlinear equations are established to solve its inverse kinematics of position and orientation. An objective function is proposed to minimize the position and orientation error of the end-effector, and the solution problem of the nonlinear equations is transformed into an optimization problem,which is solved by the differential evolution(DE) algorithm. Firstly, self-adaptive weight coefficients are introduced to avoid the difference of the convergence accuracy of position error and orientation error. In order to overcome the difficulty of the basic DE algorithm in balancing the global and local exploitation abilities, DE/rand/1/bin and DE/best/1/bin, the two evolution models are combined to improve the self-adaptive mutation differential evolution(SAMDE) algorithm, resulting in better convergence accuracy and convergence rate. Finally, the reflection approach is applied to dealing with the individuals exceeding the boundary of the joint angles, and thus the convergence accuracy is improved. Some contrastive experiments with the basic DE algorithm are conducted. The simulation results indicate that the proposed method outperforms the basic DE algorithm in terms of convergence accuracy and convergence rate, and improves the stability significantly.
引文
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[14]Wu L H,Wang Y N,Yuan X F.Design of 2-D recursive filters using self-adaptive mutation differential evolution algorithm[J].International Journal of Computational Intelligence Systems,2011,4(4):644-654.
[15]Ronkkonen J,Kukkonen S,Price K V.Real-parameter optimization with differential evolution[C]//IEEE Congress on Evolutionary Computation.Piscataway,USA:IEEE,2005:506-513.
[2]Starke S,Hendrich N,Magg S,et al.An efficient hybridization of genetic algorithms and particle swarm optimization for inverse kinematics[C]//IEEE International Conference on Robotics and Biomimetics.Piscataway,USA:IEEE,2016:1782-1789.
[3]Jiang G,Luo M,Bai K,et al.A precise positioning method for a puncture robot based on a PSO-optimized BP neural network algorithm[J].Applied Sciences,2017,7(10):969.
[4]Collinsm T J,Shen W M.Particle swarm optimization for highDOF inverse kinematics[C]//IEEE International Conference on Control,Automation and Robotics.Piscataway,USA:IEEE,2017:6pp.
[5]林阳,赵欢,丁汉.基于多种群遗传算法的一般机器人逆运动学求解[J].机械工程学报,2017,53(3):1-8.Lin Y,Zhao H,Ding H.Solution of inverse kinematics for general robot manipulators based on multiple population genetic algorithm[J].Journal of Mechanical Engineering,2017,53(3):1-8.
[6]Tabandeh S,Melek W W,Clark C M.An adaptive niching genetic algorithm approach for generating multiple solutions of serial manipulator inverse kinematics with applications to modular robots[J].Robotica,2010,28(4):493-507.
[7]黄开启,陈荣华,丁问司.凿岩机器人钻臂定位控制交叉精英反向粒子群算法[J].控制理论与应用,2017,34(3):303-311.Huang K Q,Chen R H,Ding W S.Crossover elite oppositionbased particle swarm optimization algorithm for positioning control of rock drilling robotic drilling arm[J].Control Theory&Applications,2017,34(3):303-311.
[8]何兵,车林仙,刘初升,等.空间6R机械臂位置逆解的复合形差分进化算法[J].机械工程学报,2014,50(15):45-52.He B,Che L X,Liu C S,et al.Complex differential evolution algorithm for inverse kinematics of spatial 6R robot manipulators[J].Journal of Mechanical Engineering,2014,50(15):45-52.
[9]Gonzalez C,Blanco D,Moreno L.A memetic approach to the inverse kinematics problem[C]//IEEE International Conference on Mechatronics and Automation.Piscataway,USA:IEEE,2012:180-185.
[10]Uzc′ategui C G,Rojas D B.A memetic differential evolution algorithm for the inverse kinematics problem of robot manipulators[J].International Journal of Mechatronics and Automation,2013,3(2):118-131.
[11]Wang Y,Li H X,Huang T,et al.Differential evolution based on covariance matrix learning and bimodal distribution parameter setting[J].Applied Soft Computing Journal,2014,18(1):232-247.
[12]Storn R,Price K.Differential evolution-A simple and efficient heuristic for global optimization over continuous spaces[J].Journal of Global Optimization,1997,11(4):341-359.
[13]Arabas J,Szczepankiewicz A,Wroniak T.Experimental comparison of methods to handle boundary constraints in differential evolution[C]//International Conference on Parallel Problem Solving from Nature.Berlin,Germany:Springer-Verlag,2010:411-420.
[14]Wu L H,Wang Y N,Yuan X F.Design of 2-D recursive filters using self-adaptive mutation differential evolution algorithm[J].International Journal of Computational Intelligence Systems,2011,4(4):644-654.
[15]Ronkkonen J,Kukkonen S,Price K V.Real-parameter optimization with differential evolution[C]//IEEE Congress on Evolutionary Computation.Piscataway,USA:IEEE,2005:506-513.