An almost globally convergent observer for visual SLAM without persistent excitation

In this paper we propose a novel observer to solve the problem of visual simultaneous localization and mapping (SLAM), only using the information from a single monocular camera and an inertial measurement unit (IMU). The system state evolves on the manifold $SE(3)\times \mathbb{R}^{3n}$, on which we design dynamic extensions carefully in order to generate an invariant foliation, such that the problem is reformulated into online \emph{constant parameter} identification. Then, following the recently introduced parameter estimation-based observer (PEBO) and the dynamic regressor extension and mixing (DREM) procedure, we provide a new simple solution. A notable merit is that the proposed observer guarantees almost global asymptotic stability requiring neither persistency of excitation nor uniform complete observability, which, however, are widely adopted in most existing works with guaranteed stability

Observers for invariant systems on Lie groups with biased input measurements and homogeneous outputs

This paper provides a new observer design methodology for invariant systems whose state evolves on a Lie group with outputs in a collection of related homogeneous spaces and where the measurement of system input is corrupted by an unknown constant bias. The key contribution of the paper is to study the combined state and input bias estimation problem in the general setting of Lie groups, a question for which only case studies of specific Lie groups are currently available. We show that any candidate observer (with the same state space dimension as the observed system) results in non-autonomous error dynamics, except in the trivial case where the Lie-group is Abelian. This precludes the application of the standard non-linear observer design methodologies available in the literature and leads us to propose a new design methodology based on employing invariant cost functions and general gain mappings. We provide a rigorous and general stability analysis for the case where the underlying Lie group allows a faithful matrix representation. We demonstrate our theory in the example of rigid body pose estimation and show that the proposed approach unifies two competing pose observers published in prior literature.Comment: 11 page

Hybrid Controller for Robot Manipulators in Task-Space with Visual-Inertial Feedback

This paper presents a visual-inertial-based control strategy to address the task space control problem of robot manipulators. To this end, an observer-based hybrid controller is employed to control end-effector motion. In addition, a hybrid observer is introduced for a visual-inertial navigation system to close the control loop directly at the Cartesian space by estimating the end-effector pose. Accordingly, the robot tip is equipped with an inertial measurement unit (IMU) and a stereo camera to provide task-space feedback information for the proposed observer. It is demonstrated through the Lyapunov stability theorem that the resulting closed-loop system under the proposed observer-based controller is globally asymptotically stable. Besides this notable merit (global asymptotic stability), the proposed control method eliminates the need to compute inverse kinematics and increases trajectory tracking accuracy in task-space. The effectiveness and accuracy of the proposed control scheme are evaluated through computer simulations, where the proposed control structure is applied to a 6 degrees-of-freedom long-reach hydraulic robot manipulator

Rigid Body Attitude Estimation: An Overview and Comparative Study

The attitude estimation of rigid body systems has attracted the attention of many researchers over the years. The development of efficient estimation algorithms that can accurately estimate the orientation of a rigid body is a crucial step towards a reliable implementation of control schemes for underwater and flying vehicles. The primary focus of this thesis consists in investigating various attitude estimation techniques and their applications. Two major classes are discussed. The first class consists of the earliest static attitude determination techniques relying solely on a set of body vector measurements of known vectors in the inertial frame. The second class consists of dynamic attitude estimation and filtering techniques, relying on body vector measurements as well other measurements, and using the dynamical equations of the system under consideration. Various attitude estimation algorithms, including the latest nonlinear attitude observers, are presented and discussed, providing a survey that covers the evolution and structural differences of these estimation methods. Simulation results have been carried out for a selected number of such attitude estimators. Their performance in the presence of noisy measurements, as well as their advantages and disadvantages are discussed

Three-dimensional structure from motion recovery of a moving object with noisy measurement

In this paper, a Nonlinear Unknown Input Observer (NLUIO) based approach is proposed for three-dimensional (3-D) structure from motion identification. Unlike the previous studies that require prior knowledge of either the motion parameters or scene geometry, the proposed approach assumes that the object motion is imperfectly known and considered as an unknown input to the perspective dynamical system. The reconstruction of the 3-D structure of the moving objects can be achieved using just two-dimensional (2-D) images of a monocular vision system. The proposed scheme is illustrated with a numerical example in the presence of measurement noise for both static and dynamic scenes. Those results are used to clearly demonstrate the advantages of the proposed NLUIO