基于PSO-BPNN和Newton-Raphson法融合的并联机构正运动学解法

Solution for Forward Kinematics of Parallel Mechanism based on PSO-BPNN and Newton-Raphson Algorithm

以并联机构为研究对象,针对求解正运动学时神经网络法易陷入局部最优及Newton-Raphson法对迭代初值敏感的问题,提出了一种融合PSO-BPNN(Back propagation neural network,BPNN)和Newton-Raphson法的正运动学通用求解算法。建立了并联机构逆运动学方程,得到驱动杆值,以此为训练样本,利用粒子群算法(Particle swarm optimization,PSO)优化BPNN(PSO-BPNN)模型获得位置正解,再以PSO-BPNN的正解值作为Newton-Raphson法的迭代初值对并联机构正运动学问题进行求解。为验证算法的有效性和通用性,给出了3-PCR、3-PPR两种并联机构的算例仿真。结果表明,由于迭代初值选取与目标值相差较大,导致Newton-Raphson法无法收敛;相比于PSO-BPNN算法,PSO-BPNN和Newton-Raphson法相结合得到的绝对误差最少降低了99.68%和99.96%,迭代次数更少;该方法既克服了神经网络法局部收敛性差的缺点,又避免了初值选取对Newton-Raphson法求解精度的影响,具有较好的通用性。

Taking parallel mechanism as a research object,aiming at the problem that neural network algorithm is easy to fall into local optimization and the Newton-Raphson algorithm is sensitive to the initial value of iteration when solving forward kinematics,a general forward kinematics algorithm combining PSO-BPNN and Newton-Raphson algorithm is proposed.The inverse kinematics equation of parallel mechanism is established to obtain the value of the driving rod,which is used as the training sample,and the BPNN model is optimized by PSO to obtain the solution for forward kinematic,which is taken as the initial iterative value of the newton-raphson algorithm to solve the forward kinematics of parallel mechanism.To verify the effectiveness and universality of the algorithm,simulation examples of 3-PCR and 3-PPR parallel mechanisms are given.The simulation results show that Newton-Raphson algorithm does not converge due to the large difference between the initial iteration value and the target value.Compared with the PSO-BPNN algorithm,the absolute error obtained by combining PSO-BPNN and Newton-Raphson algorithm is reduced by at least 99.68%and 99.96%,and the number of iterations is less.PSO-BPNN and Newton-Raphson algorithm not only overcomes the shortcomings of poor local convergence of the neural network algorithm,but also avoids the influence of initial value selection on the accuracy of the Newton-Raphson algorithm,which has good versatility.