Sérgio Bras

A Nonlinear Attitude Observer Based on Active Vision and Inertial Measurements

This paper presents an experimentally evaluated solution to the problem of estimating the attitude of a rigid body using rate gyros and a pan-tilt camera. A nonlinear attitude observer combines angular velocity measurements obtained from rate gyros with images of a planar scene provided by the camera. By directly exploiting the sensor information, a stabilizing feedback law is introduced, and exponential convergence to the origin of the estimation errors is shown. Additionally, an active-vision system is proposed that relies on an image-based exponentially input-to-state-stable control law for the pan and tilt angular rates of the camera to keep the features in the image plane. Using recent results in geometric numerical integration, a multirate implementation of the observer is proposed, which exploits the complementary bandwidth of the sensors. Practical considerations, such as the lens-distortion compensation and the computation of suitable observer feedback gains, are considered. Experimental results obtained with a high-accuracy motion rate table demonstrate the high level of performance attained by the proposed solution.

Nonlinear observer for 3D rigid body motion

Observer design for rigid body translational and rotational motion has important applications to unmanned or manned vehicles operating in air, underwater, or in space. An observer design for pose and velocity estimation for three-dimensional rigid body motion, in the framework of geometric mechanics, is presented here. Resorting to convenient defined Lyapunov function, a nonlinear observer on the Special Euclidean Group (SE(3)) is derived. This observer is based on the exponential coordinates, which are used to represent the group of rigid body motions. Exponential convergence of the estimation errors is shown and boundedness of the estimation error under bounded unmodeled torques and forces is established. Since exponential coordinates can describe uniquely almost the entire group of rigid body motions, the resulting observer design is almost globally exponentially convergent. The observer is then applied to the free dynamics of a rigid vehicle. Numerical simulation results are presented to show the performance of this observer, both in the absence and with unmodeled forces and torques.

Nonlinear Attitude Observer Based on Range and Inertial Measurements

We address the problem of attitude and rate gyro bias estimation based on inertial and range data. Range measurements are obtained from beacons installed in an inertial frame and acoustic sensors fixed in the moving body reference frame. A nonlinear observer is proposed and its stability and performance properties are studied using Lyapunov techniques. In the presence of constant bias on the rate gyro measurements, the attitude and bias estimates are shown to converge exponentially to the desired values inside an almost global region of attraction. For time-varying bias with bounded derivative, a local result of ultimate boundedness is provided. The performance of the proposed nonlinear observer is validated experimentally using a high-accuracy calibration table, which provides ground-truth signals for comparison with the resulting estimates.

Fault Detection and Isolation in Inertial Measurement Units Based on Bounding Sets

This work addresses the problem of Fault Detection and Isolation (FDI) for navigation systems equipped with sensors providing inertial measurements and vector observations. Assuming upper bounded sensor noise, two strategies are proposed: i) the first one takes advantage of existing hardware redundancy, requiring at least five sensor measurements to isolate faults; ii) the second approach exploits the analytical redundancy between the angular velocity measurements and the vector observations, by resorting to set-valued observers (SVOs). Necessary and sufficient conditions on the magnitude of the faults are provided, in order to guarantee successful detection and isolation, when hardware redundancy is available. Due to the set-based construction of the methods, none of the solutions generates false detections and no decision threshold is required. Using a simulation scenario, the proposed strategies are compared with two alternatives available in the literature.

Global attitude and gyro bias estimation based on set-valued observers

a b s t r a c t The problem of attitude and rate gyro bias estimation is addressed by resorting to measurements acquired from rate gyros and vector observations. A Set-Valued Observer (SVO) is proposed that has no singulari- ties and that, for any initial conditions, provides a bounding set with guarantees of containing the actual (unknown) rotation matrix. The sensor readings are assumed to be corrupted by bounded measurement noise and constant gyro bias. Conditions for the boundedness of the estimated sets are established and implementation details are discussed. The feasibility of the technique is demonstrated in simulation.

Experimental evaluation of a nonlinear attitude observer based on image and inertial measurements

This paper presents an experimentally tested solution to the problem of estimating the attitude of a rigid body using rate gyros and a pan and tilt camera. An exponential input-to-state stable pan and tilt control law is used to keep the visual features in the image plane. A multi-rate implementation of the nonlinear attitude observer that uses recent results in geometric numeric integration is proposed. Practical aspects, such as the computation of suitable observer feedback gains, are considered. Experimental results obtained with a high accuracy motion rate table demonstrate the high level of performance attained by the proposed solution.

Fault Detection and Isolation for Inertial Measurement Units

This paper addresses the problem of Fault Detection and Isolation (FDI) for navigation systems equipped with sensors providing inertial measurements and vector observations. Two strategies are proposed. The first one takes advantage of existing hardware redundancy, providing sufficient conditions for the isolation of faults. The second approach exploits the analytical redundancy between the angular velocity measurements and the vector observations, by resorting to Set-Valued Observers (SVOs). The behavior of both strategies are illustrated in simulation.

Integrated solution to quadrotor stabilization and attitude estimation using a pan and tilt camera

This work proposes a cascaded architecture comprising a nonlinear attitude observer and a nonlinear controller for position and attitude stabilization of a quadrotor. The attitude estimates are obtained from rate gyros measurements, corrupted by bias, and image coordinates from a set of landmarks on the terrain, obtained by a controllable pan and tilt camera. Lateral-longitudinal stabilization is achieved with a nested saturation control law by feedback of the image measurements, estimated body attitude, and corrected rate gyros measurements. The vehicle is stabilized vertically using an additional vertical position sensor. Due to the input-to-state stability property of controller, the quadrotor position and attitude are shown to converge to the desired equilibrium point and the convergence is robust to the estimation errors. Additionally, the pan and tilt camera is actively actuated to keep the landmarks visible in the image sensor for most operating conditions. The performance of the proposed ensemble is illustrated with some simulation results.

Set-Valued Observers for attitude and rate gyro bias estimation

This paper addresses the problem of attitude and rate gyro bias estimation using Set-Valued Observers (SVOs). We propose a singularity-free solution that exploits rate gyro measurements and vector observations corrupted by bounded noise providing bounds on the attitude of the rigid body and on the bias of the rate gyros. The sensor readings are fused directly by the SVO, without intermediate attitude computation. By taking advantage of the powerful new multi-core processors it is possible to increase the estimator convergence rate without compromising the execution time. The feasibility of the technique is demonstrated in simulation.

Optimal attitude estimation using Set-Valued Observers

An optimal Set-Valued Observer (SVO) for attitude estimation that merges rate gyro readings with body frame vectorial observations is proposed. The observer provides singularity-free estimates and considers sensor readings corrupted by bounded (but unknown) measurement noise. The suggested solution is an alternative method to the ones available in the literature, with the guarantee that the state is inside the estimated set. Optimal estimates are obtained, provided that there is no uncertainty in the angular velocity measurements, whereas the case with noisy rate gyros measurements is addressed by resorting to a relaxation of the problem. The sensor readings are exploited directly in the observer, without intermediate attitude estimate computation. Moreover, the feasibility of the technique is demonstrated in simulation.