This paper presents a novel framework for estimating the position and orientation of flexible manipulators undergoing vertical motion using multiple inertial measurement units (IMUs), optimized and calibrated with ground truth data. The flexible links are modeled as a series of rigid segments, with joint angles estimated from accelerometer and gyroscope measurements acquired by cost-effective IMUs. A complementary filter is employed to fuse the measurements, with its parameters optimized through particle swarm optimization (PSO) to mitigate noise and delay. To further improve estimation accuracy, residual errors in position and orientation are compensated using radial basis function neural networks (RBFNN). Experimental results validate the effectiveness of the proposed intelligent multi-IMU kinematic estimation method, achieving root mean square errors (RMSE) of 0.00021~m, 0.00041~m, and 0.00024~rad for $y$, $z$, and $\theta$, respectively.
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