Related papers: Lie Group Formulation of Recursive Dynamics Algori…
A class of high-order numerical algorithms for Riesz derivatives are established through constructing new generating functions. Such new high-order formulas can be regarded as the modification of the classical (or shifted) Lubich's…
An algorithm for a family of self-starting high-order implicit time integration schemes with controllable numerical dissipation is proposed for both linear and nonlinear transient problems. This work builds on the previous works of the…
Fast prototyping of new SE(3) estimation objectives remains awkward in practice. Modern Lie-group frameworks -- GTSAM, manif, Sophus, SymForce, Ceres -- target first-order workloads through different code-generation and…
Incorporating the Hamiltonian structure of physical dynamics into deep learning models provides a powerful way to improve the interpretability and prediction accuracy. While previous works are mostly limited to the Euclidean spaces, their…
Structured reinforcement learning and stochastic optimization often involve parameters evolving on matrix Lie groups such as rotations and rigid-body transformations. We establish a representation-optimization dichotomy for…
Tracking on the rotation group is a key component of many modern systems for estimation of the motion of rigid bodies. To address this problem, here we describe a Bayesian algorithm that relies on directional measurements for tracking on…
High-order Lie derivatives are essential in nonlinear systems analysis. If done symbolically, their evaluation becomes increasingly expensive as the order increases. We present a compact and efficient numerical approach for computing Lie…
This survey paper discusses behaviour of higher-order correlations for one-parameter dynamical systems and more generally for dynamical systems arising from group actions. In particular, we present a self-contained proof of quantitative…
The integration of the equations of motion in gravitational dynamical systems -- either in our Solar System or for extra-solar planetary system -- being non integrable in the global case, is usually performed by means of numerical…
The details of second-order partial derivatives of rigid-body Inverse/Forward dynamics are provided. Several properties and identities using Spatial Vector Algebra are listed, along with their detailed derivations. The expressions build…
Through assembling the navigation parameters as matrix Lie group state, the corresponding inertial navigation system (INS) kinematic model possesses a group-affine property. The Lie logarithm of the navigation state estimation error…
A four dimensional treatment of nonrelativistic space-time gives a natural frame to deal with objective time derivatives. In this framework some well known objective time derivatives of continuum mechanics appear as Lie-derivatives. Their…
A systematic approach to nonlinear model order reduction (NMOR) of coupled fluid-structureflight dynamics systems of arbitrary fidelity is presented. The technique employs a Taylor series expansion of the nonlinear residual around…
We study the dynamics of the rigid rotator on the group manifold of SU(2) as an instance of dynamics on Lie groups together with a dual model whose carrier space is the Borel group SB(2,C), the Lie Poisson dual of SU(2). We thus introduce a…
In this work, new finite difference schemes are presented for dealing with the upper-convected time derivative in the context of the generalized Lie derivative. The upper-convected time derivative, which is usually encountered in the…
Most of the rigid-body systems which evolve on nonlinear Lie groups where Euclidean control designs lose geometric meaning. In this paper, we introduce a log-linear backstepping control law on SE2(3) that preserves full…
We present a rigorous framework for determining equilibrium configurations of uniformly rotating self-gravitating fluid bodies. This work addresses the longstanding challenge of modeling rotational deformation in celestial objects such as…
This paper is concerned with the efficient evaluation of higher-order derivatives of functions $f$ that are composed of matrix operations. I.e., we want to compute the $D$-th derivative tensor $\nabla^D f(X) \in \mathbb R^{N^D}$, where…
In real-world robotics applications, accurate models of robot dynamics are critical for safe and stable control in rapidly changing operational conditions. This motivates the use of machine learning techniques to approximate robot dynamics…
The development of efficient and robust dynamic models is fundamental in the field of systems and control engineering. In this paper, a new formulation for the dynamic model of nonlinear mechanical systems, that can be applied to different…