Application of Hybrid Mutation Fruit Fly Optimization Algorithm in Inverse Kinematics of Redundant Manipulator
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摘要: 逆运动学问题是冗余度机器人运动控制、轨迹规划和动力学分析的基础, 也是机器人学中最重要的问题之一。针对末端执行器位姿的最小误差为优化目标, 建立了适应度函数, 将冗余度机械手的逆运动学问题转化为一个等价的优化问题, 在种群智能优化算法基础上应用了杂交变异果蝇优化算法(HMFOA)进行冗余度机械手逆运动学问题的求解。采用嗅觉搜索杂交突变机制和视觉搜索的动态实时更新机制, 能有效地解决果蝇优化算法(FOA)的收敛问题, 并提高算法的收敛速度。为进一步验证HMFOA的有效性, 在七自由度机械手上对HMFOA进行了测试, 对其结果与FOA、LGMS-FOA和AE-LGMS-FOA等算法进行了比较, 实验结果表明HMFOA能有效地解决冗余机械手的逆运动学问题。Abstract: Inverse kinematics is the basis of motion control, trajectory planning and dynamics analysis of redundant robots, and it is also one of the most important problems in robotics. Aiming at the minimum error of the position and pose of the end effecter as the optimization objective, the fitness function is established, and the inverse kinematics problem of redundant manipulator is transformed into an equivalent optimization problem. Based on the swarm intelligence optimization algorithm, the hybrid mutation fruit fly optimization algorithm (HMFOA) is applied to solve the inverse kinematics problem of redundant manipulator. Using olfactory search hybrid mutation mechanism and visual search dynamic real-time update mechanism can effectively solve the convergence problem of fruit fly optimization algorithm (FOA) and improve the convergence speed of the algorithm. In order to further verify the effectiveness of HMFOA, HMFOA is tested on a 7-DOF manipulator, and the results are compared with FOA, LGMS-FOA and AE-LGMS-FOA. The experimental results show that HMFOA can effectively solve the inverse kinematics problem of redundant manipulators.
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表 1 机械臂DH参数
i di/
mmθi/
radai/
mmαi/
radli/
radui/
mm1 452 0 -150 -90 -168.5 168.5 2 0 0 -150 90 -143.5 43.5 3 298 0 162 -90 -123.5 80 4 0 -90 162 -90 -290 290 5 470 180 42 -90 -88 138 6 0 0 -42 90 -229 229 7 49 0 0 0 -168.5 168.5 
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表 2 基准函数表达式
测试函数 搜寻空间 优化值 
[-100, 100]D 0 
[-30, 30]D 0 
[-100, 100]D 0 
[-10, 10]D 0 
[-600, 600]D 0 
[-5.12, 5.12]D 0 
[-100, 100]D 0 
[-100, 100]D 0
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表 3 不同算法下的数值统计
名称 FOA LGMS-FOA AE-LGMS-FOA HMFOM 最佳值 2.358 0.008 5 8.175 4×10-4 4.865 1×10-16 最差值 5.878 1.508 2 1.358 8 0.095 8 平均值 5.726 0.455 5 0.312 6 0.000 2 标准差 0.492 0.423 8 0.302 9 0.012 6 SR/% 0 0 0 95.2
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表 4 各算法对应最佳适应度的逆运动学解
θi/rad FOA LGMS-FOA AE-LGMS-FOA HMFOM θ1 0.099 -1.086 -2.622 -2.771 θ2 -1.071 -2.505 -1.358 -1.252 θ3 0.121 -0.425 -0.881 -1.162 θ4 5.021 -4.528 -4.525 1.445 θ5 0.068 1.362 0.004 0.382 θ6 0.092 1.385 3.306 3.426 θ7 0.092 0.375 -1.005 -0.318
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表 5 各算法对应的位置误差
nx, y FOA LGMS-FOA AE-LGMS-FOA HMFOM nx*-nx -7.019×10-1 5.241×10-17 -5.241×10-17 0 ny*-ny -7.112×10-2 -1.111×10-16 0 0 nz*-nz -5.308×10-1 -5.241×10-17 -1.111×10-16 0 ox*-ox -0.235×10-1 -5.241×10-17 -5.241×10-17 -5.241×10-17 oy*-oy 1.485 -2.775×10-17 -8.327×10-17 -1.111×10-16 oz*-oz 1.458 0 1.111×10-16 0 ax*-ax 5.239×10-1 2.231×10-16 1.111×10-16 1.111×10-16 ay*-ay 5.253×10-1 -1.111×10-16 -2.234×10-16 0 az*-az -5.441×10-1 0 -2.782×10-17 2.785×10-17 px*-px 4.654×102 5.326×10-14 -8.015×10-2 -3.551×10-15 py*-py 1.007×102 -8.625×10-1 -2.182×10-6 -1.421×10-14 pz*-pz -2.952×102 3.982×10-3 0 0
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