Computationally Efficient IMU-based Endpoint Position Estimation of a Flexible Manipulator with Transverse and Torsional Displacement Effects

In this paper, a new model for estimating the displacement profile and endpoint position of a one-link planar flexible manipulator arm subject to transverse and torsional vibration effects is proposed, which enables convenient application of lightweight and energy-efficient flexible structures that require high-precision real-time measurement. Both objectives are satisfied based on limited feedback information using a measurement network of inertial measurement units (IMUs), which provide angular velocity and linear acceleration information of corresponding elements at the cost of significant bias, measurement noise, and drift over time. Issues pertaining to IMU measurement signals are resolved using a complementary filtering algorithm, which in this work is further developed to analyze the transverse and torsional motion effects specific to the flexible link. Processed IMU-based measurements are subsequently used to estimate the displacement profile of a flexible manipulator as a set of interconnected rigid links. This scheme enables the efficient calculation of the manipulator endpoint's position in the vertical plane based on inverse kinematic analysis without the need to incorporate intensive solution methods for the partial differential equations describing system dynamics or mode shape estimations, which would be required for the finite-element models. The feasibility of the proposed method is verified using the experimental tests for a flexible manipulator setup, and their precision is evaluated based on comparisons with an optic camerabased ground-truth system.