Proceedings of the 2002 IEEE International Conference on Robotics & Automation Washington, DC • May 2002
Attitude Calibration of an Accelerometer Array Kourosh Parsa, Jorge Angeles, and Arun K. Misra Department of Mechanical Engineering and Centre for Intelligent Machines McGill University Montreal, Canada kourosh|angeles|
[email protected]
Abstract— An accelerometer-array attitude-calibration method is proposed here. Being based on the compatibility of rigid-body point accelerations, this method can be applied to determine and account for the accelerometer installation errors with a high degree of accuracy. It is assumed that the number of three-axis accelerometers in the array is redundant in order to help reduce the effect of sensor noise, thereby obviating the Kalman-filtering of the signals. Procedures are developed to calculate the angular velocity and acceleration as well as the attitude of the body, all in the body frame. It is demonstrated that even large attitude errors can be dealt with via off-line iterative applications of the scheme. Keywords— Angular-velocity estimation, attitude calibration, attitude estimation, inertial navigation, three-axis accelerometers.
I. I NTRODUCTION Accelerometers have long been used beside rate gyros, inclinometers, or combinations thereof in inertial navigation systems to determine the pose and twist of moving bodies. In such systems, the rate gyro is used to measure absolute angular velocity, whose numerical integration yields the body attitude. With the attitude estimated at each instant, by reading the accelerometer signals, the navigation system can determine the absolute acceleration of the system in an inertial frame, and then integrate this acceleration to infer the body twist and pose—translational and angular velocity of a rigid body constitute its twist, its point position and attitude (orientation in a given frame) constituting its pose. Since different types of sensors are used in these systems, sensory-data fusion becomes an issue; the accelerometer being a part of the sensory system, its readouts are fused with the signals from another sensor through the applicable kinematic relations and noise models [1–4]. Shown in Fig. 1 is the rendering of an accelerometer array, currently under deveopment at McGill’s Centre for Intelligent Machines. The array consists of a set of triaxial accelerometers that would measure the acceleration of multiple points of a rigid body. The idea of using an accelerometer array to obtain the angular acceleration of a rigid body and then infer its twist and pose was proposed in [5]. Subsequently, the problem of sensor noise in multiaccelerometer measurement systems was addressed in [6], where it was suggested that, using redundant acceleration measurements, the effect of the measurement noise on the final results could be filtered. No matter what the method used to filter the noise is, the 0-7803-7272-7/02/$17.00 © 2002 IEEE
Fig. 1. An accelerometer array
attitude of an individual accelerometer of the array, must be known accurately enough; else, even small angular misalignments will cause a drift in the results, as shown in [7], where the drifts due to misalignments were found to be fatal to the success of even integrating the angular acceleration to obtain the angular velocity, let alone the attitude. We demonstrated in [7] that, by means of another pose sensor, one can stabilize both the pose and the twist estimations. Note that the drifts caused by such attitude errors are indeed deterministic. The attitude calibration of an accelerometer array is the focus of this paper. This is achieved through an iterative procedure that can be performed off-line by processing the acceleration readouts recorded over a long-enough, arbitrary motion of the body. Furthermore, unlike [7], where error in the angular-velocity estimate was accumulative because it was calculated by numerically integrating the angular acceleration inferred from point-acceleration data, the angular velocity is determined directly from the accelerometer data by solving a simple system of nonlinear equations. 129
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