Related papers: Deterministic filtering and dimensionality reducti…
Successful control of a rigid-body rotating in three dimensional space requires accurate estimation of its attitude. The attitude dynamics are highly nonlinear and are posed on the Special Orthogonal Group $SO(3)$. In addition, measurements…
We revisit the nonlinear complimentary filter on $SO(3)$, previously proposed in the literature, and provide the (time-explicit) solution to the matrix ODE governing the attitude estimation error in the absence of measurement errors. The…
This work proposes a nonlinear stochastic filter evolved on the Special Orthogonal Group SO(3) as a solution to the attitude filtering problem. One of the most common potential functions for nonlinear deterministic attitude observers is…
A robust (deterministic) filtering approach to the problem of optimal sensor selection is considered herein. For a given system with several sensors, at each time step the output of one of the sensors must be chosen in order to obtain the…
The problem of $H_{\infty}$ filtering for attitude estimation using rotation matrices and vector measurements is studied. Starting from a storage function on the Special Orthogonal Group $SO(3)$, a dissipation inequality is considered, and…
Nonlinear attitude filters have been recognized to have simpler structure and better tracking performance when compared with Gaussian attitude filters and other methods of attitude determination. A key element of nonlinear attitude filter…
The design of deterministic filters can be cast as a problem of minimizing an associated cost function for an optimal control problem. Employing the min-plus linearity property of the dynamic programming operator (associated with the…
We revisit the gradient based nonlinear attitude complementary filters (observers) on the Special Orthogonal group SO(3) and provide explicit solutions of the norm of the attitude estimation error dynamics. One smooth and two non-smooth…
This article approaches deterministic filtering via an application of the min-plus linearity of the corresponding dynamic programming operator. This filter design method yields a set-valued state estimator for discrete-time nonlinear…
This paper introduces two novel nonlinear stochastic attitude estimators developed on the Special Orthogonal Group \mathbb{SO}\left(3\right) with the tracking error of the normalized Euclidean distance meeting predefined transient and…
This paper proposes two novel nonlinear attitude filters evolved directly on the Special Orthogonal Group SO(3) able to ensure prescribed measures of transient and steady-state performance. The tracking performance of the normalized…
This paper proposes a novel geometric nonlinear filter for attitude and bias estimation on the Special Orthogonal Group $SO(3)$ using matrix measurements. The structure of the proposed filter is similar to that of the continuous-time…
There are several attitude estimation algorithms in existence, all of which use local coordinate representations for the group of rigid body orientations. All local coordinate representations of the group of orientations have associated…
This paper presents theory, application, and comparisons of the feedback particle filter (FPF) algorithm for the problem of attitude estimation. The paper builds upon our recent work on the exact FPF solution of the continuous-time…
An efficient and accurate computational approach is proposed for optimal attitude control of a rigid body. The problem is formulated directly as a discrete time optimization problem using a Lie group variational integrator. Discrete…
Ordinary Differential Equations are a simple but powerful framework for modeling complex systems. Parameter estimation from times series can be done by Nonlinear Least Squares (or other classical approaches), but this can give…
Two nonlinear stochastic complimentary filters are developed on SO(3). They guarantee that errors in the Rodriguez vector and estimates are semi-globally uniformly ultimately bounded in mean square, and they converge to a small neighborhood…
The problem of attitude tracking using rotation matrices is addressed using an approach which combines inverse optimality and $\mathcal{L}_{2}$ disturbance attenuation. Conditions are provided which solve the inverse optimal nonlinear…
In this article, we discuss two algorithms tailored to discrete-time deterministic finite-horizon nonlinear optimal control problems or so-called deterministic trajectory optimization problems. Both algorithms can be derived from an…
We propose a zero-order optimization method for sequential min-max problems based on two populations of interacting particles. The systems are coupled so that one population aims to solve the inner maximization problem, while the other aims…