Sliding mode observer to estimate both the attitude and the gyro-bias by using low-cost sensors A. El Hadri and A. Benallegue Abstract— This paper presents a nonlinear observer algo- rithm for attitude estimation that improves the quality of measures obtained by using low-cost inertial measurements (IMU). It is based on sliding mode observer that provides both the estimates of the gyro-bias and the actual attitude of the rigid body. The algorithm was developed in order to address the well-known problem of the weak dynamics of the tilt sensors and magnetometers, which can be modeled by low pass filters, and of the measurement bias of the gyros. In its design the observer uses the real measurements given by the low- cost attitude sensors (inclinometers and magnetometers) and the gyros, the filters modeling the sensors and the kinematics equation of the rigid body. The asymptotic convergence of the estimation of the attitude and bias-gyros was proven using Lyapunov stability method. The effectiveness of the algorithm has been shown from experimental tests using a rotary platform equipped with several sensors with axes of rotation coincide with orientation of the rigid body. Also, tests for comparison with a linear complementary filter are given. I. INTRODUCTION The attitude control problem of rigid bodies (Walking Robots, Unmanned Aerial Vehicles, Autonomous Vehicles, ...) has been widely studied in literature (control, aerospace and robotics), and several control strategies have been pro- posed [4], [8], [14], [17]. The effectiveness of these controls depends on the availability and reliability of measurements. In most applications in this field, these measurements are derived from sensors such as rate gyros, inclinometers, accelerometers and magnetometers. These sensors are used to perform the attitude estimation. If these sensors are of very high quality, then on the one hand the use of information from accelerometer or inclinometer and magnetometer can provide very accurate estimation of attitude that is valid only on low bandwidth. In the other hand, the rate gyros can be used to derive attitude by integrating the kinematic equations of the rigid body. Such high quality-sensors are very expensive and not suitable for commercial applications. Nowadays, the progress in micro electro-mechanical sys- tem (MEMS) and technology of the anisotropic magneto- resistive has enabled the development of low-cost inertial measurement units (IMU). However, these low-cost sensors (gyroscopes, accelerometers and magnetometers) are usually noisy and provide a biased measurement. The multiplication of the applications using low-quality sensors has lead to a strong interest in attitude estimation algorithms in order to improve the performance. Several authors in the literature A. El Hadri and A. Benallegue are with Laboratory of Sys- tems Engineering (LISV), Versailles University, 10-12 Avenue de l’Europe, 78140 V´ elizy, France elhadri@lisv.uvsq.fr / benalleg@lisv.uvsq.fr proposed estimation algorithms providing an estimation of the bias assuming that the attitude is well known [10], [16]. In case of small angles variation, a linear complementary filtering technique can be used to provide relatively accurate attitude estimation obtained through the fusion process [2], [14]. A nonlinear complementary filtering approach with gyro-bias estimation has been proposed in [10]. A Survey of nonlinear attitude estimation methods is proposed in [5]. A high gain observer based on a low-pass sensors model and Euler equations of a rigid body has been studied for roll and pitch angles estimation by combining sensors data from gyros and inclinometers [11]. In [12], the authors show an experimental evaluation of this observer compared with a standard extended Kalman filter. In [1], the authors formulated the rigid body attitude control with state estima- tion using Rodrigues parameters and assuming measurements from gyros and low-pass inclinometers. In [15], a model with quaternion parameterization using a first-order low-pass filter on a ”virtual” angular velocity is used to design an observer combined with complementary filter for providing estimates for the gyro-bias and the actual attitude. Several other authors in literature have used the Kalman filter or extended Kalman filter to estimate the attitude of the rigid body with low-cost sensors (see for example [9], [18]). In this paper, we consider the problem of rigid body attitude estimation with gyro-bias compensation based on low-cost sensors. In fact, in order to improve the quality of measurements, we combine the measurements derived from inclinometers and magnetometers and rate-gyros with an estimation algorithm based on a nonlinear observer for providing estimates of the gyro-bias and the real attitude of the rigid body. In practice the orientation of the rigid body is obtained using low-pass sensors such as inclinometers (based on accelerometers) and magnetometers. These sensors with generally very close bandwidth provide relatively accurate attitude measurements at low frequencies. On other hand, the gyros have often large bandwidth but the angular velocity measurement is biased. To develop the algorithm for estimating the attitude that covers a wide frequency range, we consider that the sensors measuring the attitude at low frequencies can be modeled as a low pass filter like as proposed in [11] and then using the kinematics equation of a rigid body we propose a nonlinear observer based on sliding mode technique (see [13]) to recon- struct the true attitude and provide an estimate of the gyro- bias. By using Lyapunov analysis stability of the observer, we show the asymptotic convergence of the estimation of the attitude and gyro-bias. This one is considered constant The 2009 IEEE/RSJ International Conference on Intelligent Robots and Systems October 11-15, 2009 St. Louis, USA 978-1-4244-3804-4/09/$25.00 ©2009 IEEE 2867