Applying Improved Chaotic Sparrow Search Algorithm to SolvingInverse Kinematics of Redundant Manipulator
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摘要: 针对冗余机械臂不满足Pieper准则，无法获得逆运动学封闭解的问题，提出一种自适应混沌麻雀搜索算法（ACSSA）。首先，利用佳点集均匀分布特性生成初始化种群；其次，引入自适应动态权重，用于平衡全局和局部搜索能力，提高种群多样性，改善陷入局部最优的问题；最后，引入高斯变异，加强局部搜索能力，同时产生Tent混沌序列，防止陷入局部最优。将ACSSA应用到冗余机械臂逆向运动学求解中，分别对空间点到点运动和空间连续轨迹跟踪两种工况进行仿真，并与CSSA和SSA进行对比。结果表明：在第一种工况下，ACSSA在收敛精度上提高了2个数量级，在算法稳定性上比CSSA、SSA分别高出2、3个数量级；第二种工况下，在计算值与理论值的绝对误差精度和稳定性这两个评定指标上，ACSSA 较CSSA提高了1个数量级，较SSA提高了6个数量级。充分说明了ACSSA具有精度高、收敛速度快的特性。Abstract: Because a redundant manipulator does not satisfy the Pieper criterion and is not able to obtain a closed inverse kinematics solution, we propose an adaptive chaotic sparrow search algorithm (ACSSA). Firstly, the uniform distribution characteristics of the good point set is used to generate the initial population. Secondly, the adaptive dynamic weight is introduced to balance global and local search capabilities, enhance population diversity and local optimization. Finally, the Gaussian mutation is introduced to strengthen the local search capability, and at the same time to generate a Tent chaotic sequence to prevent falling into local optimization. The ACSSA is applied to solving the inverse kinematics of the redundant manipulator. The two working conditions of spatial point-to-point motion and spatial continuous trajectory tracking are simulated, and compared with the chaotic sparrow search algorithm (CSSA) and the sparrow search algorithm (SSA). The results show that, in the first working condition, the ACSSA improves the convergence accuracy by 2 orders of magnitude, and its stability is 2 or 3 orders of magnitude higher than the CSSA and the SSA respectively. In the second working condition, the ACSSA is one order of magnitude higher than the CSSA and 6 orders of magnitude higher than the SSA in terms of the absolute error accuracy and the stability of calculated value and theoretical value. It fully shows that the ACSSA has the characteristics of high accuracy and fast convergence speed.
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Key words:
- inverse kinematics /
- redundant manipulator /
- best point set /
- dynamic weights /
- sparrow search algorithm
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表 1 冗余机械臂各关节D-H参数
关节i 变量 变量范围/（°） ai-1
/mmαi−1/（°） di/mm 1 θ1 −180 ~ 180 0 −90 580 2 θ2 −100 ~ 100 0 90 0 3 θ3 −180 ~ 180 0 −90 690 4 θ4 −120 ~ 90 90 90 0 5 θ5 −180 ~ 180 0 −90 880 6 θ6 −115 ~ 115 0 90 0 7 θ7 −360 ~ 360 0 0 150 
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表 2 3种算法各自求得的一组逆运动学解
关节角/rad ACSSA CSSA SSA θ1 0.99119 0.97464 1.00012 θ2 1.01189 1.03641 0.99987 θ3 0.99119 1.07177 0.99979 θ4 1.00000 1.00000 0.99991 θ5 0.97462 0.92288 0.99971 θ6 0.99272 0.97841 0.99966
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表 3 3种算法独立运行200次时f1结果
mm 位姿误差f1 ACSSA CSSA SSA 最大值 5.48905 × 10−4 6.42113 × 10−2 0.09787 最小值 5.73837 × 10−6 8.69395 × 10−6 4.17924 × 10−5 平均值 1.93474 × 10−5 1.04144 × 10−3 0.00866 标准差 6.07342 × 10−5 4.64587 × 10−3 0.04744
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表 4 轨迹理论点和实际点位置绝对误差
mm 位置绝对误差 ACSSA CSSA SSA 最大值 9.13618 × 10−4 0.01133 6.82737 × 102 最小值 1.00291 × 10−5 1.00077 × 10−5 47.47253 平均值 4.11963 × 10−5 2.71322 × 10−4 3.60283 × 102 标准差 1.47025 × 10−4 1.66532 × 10−3 1.38841 × 102
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