Nonlinear Complementary Filters on the Special Orthogonal Group

By Robert E. Mahony, Tarek Hamel, Jean Michel Pflimlin. IEEE Transactions on Automatic Control, 2008

1,847 citations recorded by the source corpus.

This paper considers the problem of obtaining good attitude estimates from measurements obtained from typical low cost inertial measurement units. The outputs of such systems are characterized by high noise levels and time varying additive biases. We formulate the filtering problem as deterministic observer kinematics posed directly on the special orthogonal group SO (3) driven by reconstructed attitude and angular velocity measurements. Lyapunov analysis results for the proposed observers are derived that ensure almost global stability of the observer error. The approach taken leads to an observer that we term the direct complementary filter. By exploiting the geometry of the special orthogonal group a related observer, termed the passive complementary filter, is derived that decouples the gyro measurements from the reconstructed attitude in the observer inputs. Both the direct and passive filters can be extended to estimate gyro bias online. The passive filter is further developed to provide a formulation in terms of the measurement error that avoids any algebraic reconstruction of the attitude. This leads to an observer on SO(3), termed the explicit complementary filter, that requires only accelerometer and gyro outputs; is suitable for implementation on embedded hardware; and provides good attitude estimates as well as estimating the gyro biases online. The performance of the observers are demonstrated with a set of experiments performed on a robotic test-bed and a radio controlled unmanned aerial vehicle.

Subfields: Aerospace Engineering, Artificial Intelligence, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/e660eea77e2417b0b8387408d3da8f39fb1bef9b

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Citations in the corpus

An efficient orientation filter for inertial and inertial / magnetic sensor arrays (2010, background): “Mahony et al [35] developed the complementary filter which is shown to be an efficient and effective solution; however, performance is only validated for an IMU.”
A complementary filter for attitude estimation of a fixed-wing UAV (2008, methodology): “The two methods that are commonly used are extended Kalman filtering (EKF) or some form of constant gain state observer, often termed a complimentary filter due to its frequency filtering properties for linear systems [12].”
A Nonlinear Filtering Approach for the Attitude and Dynamic Body Acceleration Estimation Based on Inertial and Magnetic Sensors: Bio-Logging Application (2011, background): “The three investigated experiments are carried out with low and high moving acceleration as follows.”
Trends Supporting the In-Field Use of Wearable Inertial Sensors for Sport Performance Evaluation: A Systematic Review (2018, methodology): “Examples of sensor fusion approaches are stochastic filtering, often implemented in the form of an Extended Kalman Filter [21,35] and complementary filtering [36,37].”
Estimation of IMU and MARG orientation using a gradient descent algorithm (2011, methodology): “Modern techniques [25], [ 26 ], [38] have focused on simpler algorithms that ameliorate the computational load and parameter tuning burdens associated with conventional Kalman-based approaches.”
Using Inertial Sensors for Position and Orientation Estimation (2017, positive): “Two wellknown complementary filter implementations to estimate the orientation q are presented in [90] and [89].”
Aerodynamics and Control of Quadrotors (2017, methodology): “It is given by Mahony et al. [2012]; Martin and Salaun [2010]; Mellinger et al.”
The Navigation and Control technology inside the AR.Drone micro UAV (2011, neutral): “Pounds et al. [2006], Hoffmann et al.”
Survey of Motion Tracking Methods Based on Inertial Sensors: A Focus on Upper Limb Human Motion (2017, methodology): “Two nonlinear CFs are proposed in [75,76] to fuse accelerometer, magnetometer and gyroscope measurements to obtain an attitude quaternion estimation.”
Quadrotors and Accelerometers: State Estimation with an Improved Dynamic Model (2014, background): “The second filter is the explicit nonlinear complementary (NC) filter developed in [26].”
Globally exponentially stable cascade observers for attitude estimation (2012, background): “This assumption is necessary for attitude estimation with constant vectors in inertial coordinates, see e.g. Mahony et al. (2008) and Batista et al. (2009), and therefore it carries no conservativeness whatsoever.”
Build Your Own Quadrotor: Open-Source Projects on Unmanned Aerial Vehicles (2012, methodology): “…reveals that poles are located in the right-half plane SEPTEMBER 2012 • IEEE ROBOTICS & AUTOMATIONMAGAZINE • 39 Previous Page | Contents | Zoom in | Zoom out | Front Cover | Search Issue | Next Page IEEE M AGAZ INE obotics utomation Previous Page | Contents | Zoom in | Zoom out | Front Cover |…”
The true role of accelerometer feedback in quadrotor control (2010, methodology): “Accordingly, the pitch and roll angles are estimated from gyroscope and accelorometer measurements thanks to some sensor fusion algorithm: Extended Kalman Filter (EKF) [2]; complementary filter, linear [3], [7] or nonlinear [10] (see [ 15 ], [16], [17] for an account of such nonlinear filters and re”