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.

/pdf/nonlinear-complementary-filters-on-the-special-orthogonal-ysp0zzaoar.pdf

Nonlinear Complementary Filters on the Special Orthogonal Group

In this paper, we propose a new quaternion-based feedback control scheme for exponential attitude stabilization of a four-rotor vertical takeoff and landing aerial robot known as a quadrotor aircraft. The proposed controller is based upon the compensation of the Coriolis and gyroscopic torques and the use of a PD/sup 2/ feedback structure, where the proportional action is in terms of the vector quaternion and the two derivative actions are in terms of the airframe angular velocity and the vector quaternion velocity. We also show that the model-independent PD controller, where the proportional action is in terms of the vector-quaternion and the derivative action is in terms of the airframe angular velocity, without compensation of the Coriolis and gyroscopic torques, provides asymptotic stability for our problem. The proposed controller as well as some other controllers have been tested experimentally on a small-scale quadrotor aircraft.

Attitude stabilization of a VTOL quadrotor aircraft

In this paper, a quaternion based extended Kalman filter (EKF) is developed for determining the orientation of a rigid body from the outputs of a sensor which is configured as the integration of a tri-axis gyro and an aiding system mechanized using a tri-axis accelerometer and a tri-axis magnetometer. The suggested applications are for studies in the field of human movement. In the proposed EKF, the quaternion associated with the body rotation is included in the state vector together with the bias of the aiding system sensors. Moreover, in addition to the in-line procedure of sensor bias compensation, the measurement noise covariance matrix is adapted, to guard against the effects which body motion and temporary magnetic disturbance may have on the reliability of measurements of gravity and earth's magnetic field, respectively. By computer simulations and experimental validation with human hand orientation motion signals, improvements in the accuracy of orientation estimates are demonstrated for the proposed EKF, as compared with filter implementations where either the in-line calibration procedure, the adaptive mechanism for weighting the measurements of the aiding system sensors, or both are not implemented.

Quaternion-based extended Kalman filter for determining orientation by inertial and magnetic sensing

There are many communication imperfections in networked control systems (NCS) such as varying transmission delays, varying sampling/transmission intervals, packet loss, communication constraints and quantization effects. Most of the available literature on NCS focuses on only some of these aspects, while ignoring the others. In this paper we present a general framework that incorporates communication constraints, varying transmission intervals and varying delays. Based on a newly developed NCS model including all these network phenomena, we will provide an explicit construction of a continuum of Lyapunov functions. Based on this continuum of Lyapunov functions we will derive bounds on the maximally allowable transmission interval (MATI) and the maximally allowable delay (MAD) that guarantee stability of the NCS in the presence of communication constraints. The developed theory includes recently improved results for delay-free NCS as a special case. After considering stability, we also study semi-global practical stability (under weaker conditions) and performance of the NCS in terms of Lp gains from disturbance inputs to controlled outputs. The developed results lead to tradeoff curves between MATI, MAD and performance gains that depend on the used protocol. These tradeoff curves provide quantitative information that supports the network designer when selecting appropriate networks and protocols guaranteeing stability and a desirable level of performance, while being robust to specified variations in delays and transmission intervals. The complete design procedure will be illustrated using a benchmark example.

/pdf/networked-control-systems-with-communication-constraints-5ak0mdbgn7.pdf

Networked Control Systems With Communication Constraints: Tradeoffs Between Transmission Intervals, Delays and Performance

https://www3.nd.edu/~pantsakl/Publications/292-Automatica03.pdf

Brief On the model-based control of networked systems

Drift-free attitude estimation for accelerated rigid bodies

Scheduling of a limited communication channel for optimal control

We study the attitude estimation problem for an accelerated rigid body using gyros and accelerometers. The application in mind is that of a walking robot and particular attention is paid to the large and abrupt changes in accelerations that can be expected in such an environment. We propose a state estimation algorithm that fuses data from rate gyros and accelerometers to give long-term drift free attitude estimates. The algorithm does not use any local parameterization of the rigid body kinematics and can thus be used for a rigid body performing any kind of rotations. The algorithm is a combination of two non-standard, but in a sense linear, Kalman filters between which a trigger based switching takes place. The kinematics representation used makes it possible to construct a linear algorithm that can be shown to give convergent estimates for this nonlinear problem. The state estimator is evaluated in simulations demonstrating how the estimates are long term stable even in the presence of gyrodrift.

/pdf/drift-free-attitude-estimation-for-accelerated-rigid-bodies-40adtclww1.pdf

https://people.kth.se/~hu/papers/scl00.pdf

Nonlinear state estimation for rigid-body motion with low-pass sensors

We prove the convergence of Luenberger-type observers for systems with implicitly defined outputs.

Henrik Rehbinder

Papers

Drift-free attitude estimation for accelerated rigid bodies

Scheduling of a limited communication channel for optimal control

Drift-free attitude estimation for accelerated rigid bodies

Nonlinear state estimation for rigid-body motion with low-pass sensors

Observers for systems with implicit output