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Model-Free Optimal Estimation and Sensor Placement Framework for Elastic Kinematic Chain

We propose a novel model-free optimal estimation and sensor placement framework for a high-DOF (degree-of-freedom) EKC (elastic kinematic chain) with only a limited number of IMU (inertial measurement unit) sensors based on POD (proper orthogonal decomposition) and MAP (maximum a posteriori) estimation. First, we (off-line) excite the system richly enough, collect the data and perform the POD to extract dominant and non-dominant modes. We then decide the minimum number of IMUs according to the dominant modes, and construct the prior distribution of the output (i.e., top-end position of EKC) based on the singular value of each POD mode. We also formulate the MAP estimation given the prior distribution and different placements of the IMUs and choose the optimal IMU placement to maximize the posterior probability. This optimal placement is then used for real-time output estimation of the EKC. Experiments are also performed to verify the theory.