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We present a novel approach to estimating physical properties of objects from video. Our approach consists of a physics engine and a correction estimator. Starting from the initial observed state, object behavior is simulated forward in…
The notion of observers' and their measurements is closely tied to the Lorentzian metric geometry of spacetime, which in turn has its roots in the symmetries of Maxwell's theory of electrodynamics. Modifying either the one, the other, or…
This paper considers the design of nonlinear observers for invariant systems posed on finite-dimensional connected Lie groups with measurements generated by a transitive group action on an associated homogeneous space. We consider the case…
This paper proposes a low order geometrically exact flexible beam formulation based on the utilisation of generic beam shape functions to approximate distributed kinematic properties of the deformed structure. The proposed nonlinear beam…
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…
We study the dynamics of gauge theory and general relativity using fields of local observers, thus maintaining local Lorentz symmetry despite a space/time splitting of fields. We start with Yang--Mills theory, where observer fields are…
Aghannan and Rouchon proposed a new design method of asymptotic observers for a class of nonlinear mechanical systems: Lagrangian systems with configuration (position) measurements. The observer is based on the Riemannian structure of the…
An adaptive state observer is proposed for a class of overparametrized uncertain linear time-invariant systems without restrictive requirement of their representation in the observer canonical form. It evolves the method of generalized…
Orientation is a key attribute of objects, crucial for understanding their spatial pose and arrangement in images. However, practical solutions for accurate orientation estimation from a single image remain underexplored. In this work, we…
In this paper we present a framework which provides an analytical (i.e., infinitely differentiable) transformation between spatial coordinates and orbital elements for the solution of the gravitational two-body problem. The formalism omits…
General covariant expressions for measurable angles, distances, velocities, and accelerations are provided in terms of fundamental parameters that can be applied in any setup. The relativistic aberration of light relationship is presented…
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…
Navigation in Global Positioning Systems (GPS)-denied environments requires robust estimators reliant on fusion of inertial sensors able to estimate rigid-body's orientation, position, and linear velocity. Ultra-wideband (UWB) and Inertial…
Motivated by attitude control and attitude estimation problems for a rigid body, computational methods are proposed to propagate uncertainties in the angular velocity and the attitude. The nonlinear attitude flow is determined by…
Relative attitude formation control systems are developed for multiple spacecraft, based on the line-of-sight measurements between spacecraft in formation. The proposed control systems are unique in the sense that they do not require…
We consider the problem of distributed attitude estimation of multi-agent systems, evolving on $SO(3)$, relying on individual angular velocity and relative attitude measurements. The interaction graph topology is assumed to be an undirected…
By employing an accelerated weighting method, we establish arbitrary polynomial and exponential pointwise convergence for multiple ergodic averages under general balancing conditions in both discrete and continuous settings, including…
We estimate the support of a uniform density, when it is assumed to be a convex polytope or, more generally, a convex body in $\R^d$. In the polytopal case, we construct an estimator achieving a rate which does not depend on the dimension…
This work considers a system coupling a viscous Burgers equation (aimed to describe a simplified model of $1D$ fluid flow) with the ODE describing the motion of a point mass moving inside the fluid. The point mass is possibly under the…
In axistationary asymptotically flat spacetimes zero angular momentum observers (ZAMOs) define an absolute standard of non--rotation locally, as can be verified by the absence of any Sagnac effect for these observers. Nevertheless, we argue…