Estimating the angular velocity of a rigid body moving in the plane from tangential and centripetal acceleration measurements |
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Authors: | Philippe Cardou Jorge Angeles |
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Affiliation: | (1) Macdonald Engineering Building, Department of Mechanical Engineering, Centre for Intelligent Machines, McGill University, 817 Sherbrooke Street West, Montreal, Quebec, H3A 2K6, Canada |
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Abstract: | Two methods are available for the estimation of the angular velocity of a rigid body from point-acceleration measurements:
(i) the time-integration of the angular acceleration and (ii) the square-rooting of the centripetal acceleration. The inaccuracy
of the first method is due mainly to the accumulation of the error on the angular acceleration throughout the time-integration
process, which does not prevent that it be used successfully in crash tests with dummies, since these experiments never last
more than one second. On the other hand, the error resulting from the second method is stable through time, but becomes inaccurate
whenever the rigid body angular velocity approaches zero, which occurs in many applications. In order to take advantage of
the complementarity of these two methods, a fusion of their estimates is proposed. To this end, the accelerometer measurements
are modeled as exact signals contaminated with bias errors and Gaussian white noise. The relations between the variables at
stake are written in the form of a nonlinear state-space system in which the angular velocity and the angular acceleration
are state variables. Consequently, a minimum-variance-error estimate of the state vector is obtained by means of extended
Kalman filtering. The performance of the proposed estimation method is assessed by means of simulation. Apparently, the resulting
estimation method is more robust than the existing accelerometer-only methods and competitive with gyroscope measurements.
Moreover, it allows the identification and the compensation of any bias error in the accelerometer measurements, which is
a significant advantage over gyroscopes. |
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Keywords: | Camera stabilization Angular velocity Accelerometer Inertial measurement unit Mobile robot Angular acceleration Rigid body motion Kinematics Acceleration |
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