Related papers: Asymptotically Stable Optimal Multi-rate Rigid Bod…
A deterministic attitude estimator for a rigid body under an attitude dependent potential is studied. This estimator requires only a single direction measurement to a known reference point at each measurement instant. The measurement cannot…
Dynamic state estimation, as opposed to kinematic state estimation, seeks to estimate not only the orientation of a rigid body but also its angular velocity, through Euler's equations of rotational motion. This paper demonstrates that the…
This paper formulates optimal control problems for rigid bodies in a geometric manner and it presents computational procedures based on this geometric formulation for numerically solving these optimal control problems. The dynamics of each…
In this paper, we propose Lagrangian Gaussian Processes (LGPs) for probabilistic and data-efficient learning of dynamics via discrete forced Euler-Lagrange equations. Importantly, the geometric structure of the Lagrange-d'Alembert…
This paper addresses the problem of estimating the attitude of a rigid body, which is subject to high accelerations and equipped with inertial measurement unit (IMU) and sensors providing the body velocity (expressed in the reference frame…
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…
Two nonlinear observers for velocity-aided attitude estimation, relying on gyrometers, accelerometers, magnetometers, and velocity measured in the body-fixed frame, are proposed. As opposed to state-of-the-art body-fixed velocity-aided…
This work is devoted to a systematic exposition of the dynamics of a rigid body, considered as a system with kinematic constraints. Having accepted the variational problem in accordance with this, we no longer need any additional postulates…
This paper provides new results for a robust adaptive tracking control of the attitude dynamics of a rigid body. Both of the attitude dynamics and the proposed control system are globally expressed on the special orthogonal group, to avoid…
We consider the classical problem of estimating the attitude and gyro biases of a rigid body from vector measurements and a triaxial rate gyro. We propose a simple "geometry-free" nonlinear observer with guaranteed uniform global asymptotic…
An unconventional approach for optimal stopping under model ambiguity is introduced. Besides ambiguity itself, we take into account how ambiguity-averse an agent is. This inclusion of ambiguity attitude, via an $\alpha$-maxmin nonlinear…
The problems of optimally estimating a phase, a direction, and the orientation of a Cartesian frame (or trihedron) with general pure states are addressed. Special emphasis is put on estimation schemes that allow for inconclusive answers or…
This paper investigates the problem of continuous attitude estimation on $SO(3)$ using continuous angular velocity and linear acceleration measurements as well as intermittent linear velocity and inertial vector measurements. First, we…
The vortex-induced vibration of multiple spring-mounted bodies free to move in the orthogonal direction of the flow is investigated. In a first step, we derive a Linear Arbitrary Lagrangian Eulerian (L-ALE) method to solve the…
This paper studies a central planner's decision making on behalf of a group of members with diverse discount rates. In the context of optimal stopping, we work with an aggregation preference to incorporate all discount rates via an attitude…
This paper reviews the attitude control problems for rigid-body systems, starting from the attitude representation for rigid body kinematics. Highly redundant rotation matrix defines the attitude orientation globally and uniquely by 9…
This paper addresses the attitude tracking of a rigid body using a quaternion description. Global finite-time attitude controllers are designed with three types of measurements, namely, full states, attitude plus constant-biased angular…
We propose an extension of the principle of virtual work of mechanics to random dynamics of mechanical systems. The total virtual work of the interacting forces and inertial forces on every particle of the system is calculated by…
This paper develops numerical methods for optimal control of mechanical systems in the Lagrangian setting. It extends the theory of discrete mechanics to enable the solutions of optimal control problems through the discretization of…
This paper proposes a novel unit-quaternion observer-based controller for attitude tracking (attitude and angular velocity) with guaranteed transient and steady-state performance. The proposed approach is computationally cheap and can…