V. Vikas and C.D. Crane III (USA)

Inclination estimation, Inertial measurement, Inclinometer,Dynamic Equilibrium Axis.

The balance of robots has traditionally been accomplished using Inertial Measurement Units [IMUs] which use linear accelerations and gyroscope data to track the orientation of the vertical direction in inertial space. A novel approach, motivated by the human vestibular system in the human ear, is presented in this paper. It discusses the use of two linear dual-axis accelerometers and a single-axis gyroscope per axis to obtain the magnitude of acceleration acting on the body, angular acceleration, angular velocity, and inclination of a body. It introduces a novel con cept of Dynamic Equilibrium Axis(DEA), the axis along which the robot/body is at equilibrium. The inclination angle obtained from the sensor is relative to this equilibrium axis. The two parts of the vestibular organ - otolith organs and semicircular canals are interpreted as a dual-axis linear accelerometer and a single-axis gyroscope respectively. Kinematic analysis shows that combining these vestibular readings properly yields in the general case, irrespective of acceleration acting on the body or sensor array location, a fully effective dynamic inclinometer, which continually senses the inclination from the axis of stability (DEA), and is not subject to drift or integration errors or acceleration acting on the body. Further, kinematic analysis shows that magnitude of acceleration acting on the body can also be sensed from the sensor. The design is powerful as it outputs dynamic inclination of a body with respect to the DEA without requiring signiﬁcant computational burden, irrespective of the acceleration acting on the body or the sensor array location, and is not subject to drift or integration errors. The Vestibular Dynamic Inclinometer (VDI), as presented here, gives inclination from the equilibrium axis for the cases when the robot is static (inertial platform) or accelerating (noninertial platform). Estimation of all the parameters is done through kinematic analysis, and thus is independent of the dynamics of robot. Finally, for all these reasons, the cost of making the VDI is greatly reduced relative to IMUs. The calculations discussed in the paper are for a planar case and can be extended to three dimensions.

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