Related papers: Log-linear Dynamic Inversion for Thrusting Spacecr…
This paper presents a novel nonlinear backstepping control law for continuous, low-thrust station-keeping in the Earth-Moon system. Quasi-periodic libration point orbits are targeted under a high-fidelity model of the dynamics. Almost…
The control of a tail-sitter aircraft is a challenging task, especially during transition maneuver where the lift and drag forces are highly nonlinear. In this work, we implement a Neural Network (NN) capable of estimate such…
We study Langevin dynamics with noise projected onto the directions orthogonal to an isometric group action. This mathematical model is introduced to shed new light on the effects of symmetry on stochastic gradient descent for…
This paper proposes to use a newly-derived transformed inertial navigation system (INS) mechanization to fuse INS with other complementary navigation systems. Through formulating the attitude, velocity and position as one group state of…
In this article, a brief description of Discrete Mechanics and Variational Integrators which preserve the symplectic structure of the flow will be provided and a Newton-Raphson algorithm that can be used to solve implicit equations on the…
This paper proposes a nonlinear optimal guidance law that enables a pursuer to enclose a target within arbitrary geometric patterns, which extends beyond conventional circular encirclement. The design operates using only relative state…
Many nonlinear dynamical systems can be written as Lure systems, which are described by a linear time-invariant system interconnected with a diagonal static sector-bounded nonlinearity. Sufficient conditions are derived for the global…
To fuse information from inertial measurement units (IMU) with other sensors one needs an accurate model for IMU error propagation in terms of position, velocity and orientation, a triplet we call extended pose. In this paper we leverage a…
In the study of induced bilinear systems, the classical Lie algebra rank condition (LARC) is known to be impractical since it requires computing the rank everywhere. On the other hand, the transitive Lie algebra condition, while more…
We extend the method of controlled Lagrangians with kinetic shaping to those mechanical systems on semidirect product Lie groups with broken symmetry, more specifically to the Euler--Poincar\'e equations with advected parameters. We find a…
Nonlinear contraction theory is a comparatively recent dynamic control system design tool based on an exact differential analysis of convergence, in essence converting a nonlinear stability problem into a linear time-varying stability…
Successful navigation of a rigid-body traveling with six degrees of freedom (6 DoF) requires accurate estimation of attitude , position, and linear velocity. The true navigation dynamics are highly nonlinear and are modeled on the matrix…
Incorporating prior knowledge of physics laws and structural properties of dynamical systems into the design of deep learning architectures has proven to be a powerful technique for improving their computational efficiency and…
Bayesian estimation with an explicit transitional prior is required for a tracking algorithm to be embedded in most multi-target tracking frameworks. This paper describes a novel approach capable of tracking maneuvering spacecraft with an…
Recent numerical results point to the existence of a conformally invariant twist defect in the critical 3d Ising model. In this note we show that this fact is supported by both epsilon expansion and conformal bootstrap calculations. We find…
Inverted landing in a rapid and robust manner is a challenging feat for aerial robots, especially while depending entirely on onboard sensing and computation. In spite of this, this feat is routinely performed by biological fliers such as…
The reduction of dynamical systems has a rich history, with many important applications related to stability, control and verification. Reduction of nonlinear systems is typically performed in an exact manner - as is the case with…
In our previous paper: K. Kowalski and J. Rembieli\'nski, Groups and nonlinear dynamical systems. Dynamics on the SU(2) group, Physica D 99, 237 (1996), we introduced an abstract Newton-like equation on a general Lie algebra such that…
In this paper one first shows that the slow flow of a mechanical system with one unstable mode coupled to a Nonlinear Energy Sink (NES) can be reduced, in the neighborhood of a fold point of its critical manifold, to a normal form of the…
Non-conservative loads of the follower type are usually believed to be the source of dynamic instabilities such as flutter and divergence. It is shown that these instabilities (including Hopf bifurcation, flutter, divergence, and…