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Definition of Intermediate coordinate system defined by orthogonal basis {ê a , ˆ e b , ˆ e c }  

Definition of Intermediate coordinate system defined by orthogonal basis {ê a , ˆ e b , ˆ e c }  

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Conference Paper
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Inclination measurement for purpose of balancing of robots has traditionally been accomplished using Inertial Measurement Units (IMUs) which use linear acceleration measurement and gyroscope data. This provides inclination measurement relative to an absolute axis (or coordinate system) and is subject to drift. The Vestibular Dynamic Inclinometer (V...

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Citations

... This also allows for measurement of base link inclination parameters, which is instantaneously in contact with the ground and experiencing planar motion. The planar Vestibular Dynamic Inclinometer (pVDI) is an inclination sensor that measures inclination parameters for links/robots having five degree-of-freedom [21]. ...
... So, given the accelerometer and gyroscope inputs, the Equations 3-12 can be summarized as a pVDI i function as denoted in Figure 3. More details of the analysis are given in [21]. ...
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A novel approach of dynamic, non-contact measurement of joint parameters using the planar Vestibular Dynamic Inclinometer (pVDI) is proposed in this paper. The gravity-invariant planar Vestibular Dynamic Inclinometer (pVDI) is a non-contact sensor that consists of symmetrically placed four dual-axis accelerometers and one tri-axial gyroscope. The deployment of the non-contact sensor is strategic and need not be at the joints. The paper proposes measurement of joint parameters — base angle, joint angle, angular velocity and angular acceleration, that are independent of integration errors/drift.