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Related papers: Solving Cosserat Rod Models via Collocation and th…

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The Magnus expansion provides an exponential representation of one-parameter operator families, expressed as a series expansion in its generators. This is useful for example in quantum mechanics for expressing a unitary evolution determined…

Quantum Physics · Physics 2025-09-24 Harriet Apel , Toby Cubitt , Emilio Onorati

We address the motion planning problem for large multi-agent systems, utilizing Cosserat rod theory to model the dynamic behavior of vehicle formations. The problem is formulated as an optimal control problem over partial differential…

Optimization and Control · Mathematics 2024-06-13 Amirreza Fahim Golestaneh , Maxwell Hammond , Venanzio Cichella

A special purpose solver, based on the Magnus expansion, well suited for the integration of the linear three neutrino oscillations equations in matter is proposed. The computations are speeded up to two orders of magnitude with respect to a…

Computational Physics · Physics 2017-01-23 Fernando Casas , Jose Angel Oteo , Juan Carlos D'Olivo

The characteristic ``in-plane" bending associated with soft robots' deformation make them preferred over rigid robots in sophisticated manipulation and movement tasks. Executing such motion strategies to precision in soft deformable robots…

Robotics · Computer Science 2023-12-12 Lekan Molu , Shaoru Chen , Audrey Sedal

We derive the stochastic version of the Magnus expansion for linear systems of stochastic differential equations (SDEs). The main novelty with respect to the related literature is that we consider SDEs in the It\^o sense, with progressively…

Probability · Mathematics 2022-05-23 Kevin Kamm , Stefano Pagliarani , Andrea Pascucci

We present a theoretical and numerical framework to compute bifurcations of equilibria and stability of slender elastic rods. The 3D kinematics of the rod is treated in a geometrically exact way by parameterizing the position of the…

Soft Condensed Matter · Physics 2012-12-27 A. Lazarus , J. T. Miller , P. M. Reis

In the recent past, several sampling-based algorithms have been proposed to compute trajectories that are collision-free and dynamically-feasible. However, the outputs of such algorithms are notoriously jagged. In this paper, by focusing on…

Robotics · Computer Science 2015-10-28 Zhijie Zhu , Edward Schmerling , Marco Pavone

Caging is a promising tool which allows a robot to manipulate an object without directly reasoning about the contact dynamics involved. Furthermore, caging also provides useful guarantees in terms of robustness to uncertainty, and often…

Robotics · Computer Science 2019-08-05 Bernardo Aceituno-Cabezas , Hongkai Dai , Alberto Rodriguez

This article deals with the mathematical derivation and the validation over benchmark examples of a numerical method for the solution of a finite-strain holonomic (rate-independent) Cosserat plasticity problem for materials, possibly with…

Computational Engineering, Finance, and Science · Computer Science 2019-06-20 Thomas Blesgen , Ada Amendola

We consider numerical approximation to the solution of non-autonomous evolution equations. The order of convergence of the simplest possible Magnus method will be investigated.

Functional Analysis · Mathematics 2011-11-23 András Bátkai , Eszter Sikolya

This extended abstract introduces a novel method for continuous state estimation of continuum robots. We formulate the estimation problem as a factor-graph optimization problem using a novel Gaussian-process prior that is parameterized over…

Robotics · Computer Science 2024-09-20 Spencer Teetaert , Sven Lilge , Jessica Burgner-Kahrs , Timothy D. Barfoot

Accurate and efficient tracking of surgical instruments is fundamental for Robot-Assisted Minimally Invasive Surgery. Although vision-based robot pose estimation has enabled markerless calibration without tedious physical setups, reliable…

Robotics · Computer Science 2026-03-16 Hanyang Hu , Zekai Liang , Florian Richter , Michael C. Yip

This paper is concerned with the problem of estimating (interpolating and smoothing) the shape (pose and the six modes of deformation) of a slender flexible body from multiple camera measurements. This problem is important in both biology,…

In this work, we develop reduced order models (ROMs) to predict solutions to a multiscale kinetic transport equation with a diffusion limit under the parametric setting. When the underlying scattering effect is not sufficiently strong, the…

Numerical Analysis · Mathematics 2025-05-14 Tianyu Jin , Zhichao Peng , Yang Xiang

In this paper, we use the optimal control methodology to control a flexible, elastic Cosserat rod. An inspiration comes from stereotypical movement patterns in octopus arms, which are observed in a variety of manipulation tasks, such as…

Optimization and Control · Mathematics 2023-04-25 Tixian Wang , Udit Halder , Heng-Sheng Chang , Mattia Gazzola , Prashant G. Mehta

The linearization of the equations of motion of a robotics system about a given state-input trajectory, including a controlled equilibrium state, is a valuable tool for model-based planning, closed-loop control, gain tuning, and state…

Robotics · Computer Science 2022-04-20 Martijn Bos , Silvio Traversaro , Daniele Pucci , Alessandro Saccon

In this paper, we derive the continuous space-time equations of motion of a three-dimensional geometrically exact rod, or the Cosserat rod, incorporating planar cross-sectional deformation. We then adopt the Lie group variational integrator…

Systems and Control · Electrical Eng. & Systems 2026-02-12 Srishti Siddharth , Vivek Natarajan , Ravi N. Banavar

In this paper, we show how the It\^o-stochastic Magnus expansion can be used to efficiently solve stochastic partial differential equations (SPDE) with two space variables numerically. To this end, we will first discretize the SPDE in space…

Numerical Analysis · Mathematics 2024-03-27 Kevin Kamm , Stefano Pagliarani , Andrea Pascucci

In the following, we discuss nonlinear simulations of nonlinear dynamical systems, which are applied in technical and biological models. We deal with different ideas to overcome the treatment of the nonlinearities and discuss a novel…

Numerical Analysis · Mathematics 2014-12-01 Juergen Geiser , Vahid Yaghoubi

Traditional motion planning approaches for multi-legged locomotion divide the problem into several stages, such as contact search and trajectory generation. However, reasoning about contacts and motions simultaneously is crucial for the…