High-Order Small-Time Local Controllability

A quadrotor-like autonomous underwater vehicle that is similar to, yet different from quadrotor unmanned aerial vehicles, has been reported recently. This article investigates the stability and nonlinear controllability properties of the vehicle. First, the 12-degree-of-freedom model of the vehicle deploying an X shape actuation system is developed. Then, a stability property is investigated showing that the vehicle cannot be stabilized by a time invariant smooth state feedback law. After that, by adopting a nonlinear controllability analysis tool in geometric control theory, the small-time local controllability of the vehicle is analyzed for a variety of cases, including the vertical plane motion, the horizontal plane motion, and the three-dimensional space motion. Finally, different small-time local controllability conditions for different cases are developed. The result shows that the small-time local controllability holds for vertical plane motion and horizontal plane motion. However, the full degree of freedom kinodynamics model (i.e. 12 states) of the vehicle does not satisfy the small-time local controllability from zero-velocity states.

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Quadratic obstructions to small-time local controllability for scalar-input systems

Journal of Differential Equations ◽

10.1016/j.jde.2017.11.028 ◽

2018 ◽

Vol 264 (5) ◽

pp. 3704-3774 ◽

Cited By ~ 2

Author(s):

Karine Beauchard ◽

Frédéric Marbach

Keyword(s):

Small Time ◽

Local Controllability ◽

Scalar Input

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On the relation between small-time local controllability and normal self-reachability

Mathematics of Control Signals and Systems ◽

10.1007/bf01211975 ◽

1992 ◽

Vol 5 (1) ◽

pp. 41-66 ◽

Cited By ~ 10

Author(s):

Kevin A. Grasse

Keyword(s):

Small Time ◽

Local Controllability

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Comparison of Higher-Order Numerical Schemes and Several Filtering Methods Applied to Navier-Stokes Equations with Applications to Computational Aeroacoustics

Journal of Algorithms & Computational Technology ◽

10.1260/174830108788251746 ◽

2009 ◽

Vol 3 (3) ◽

pp. 443-459

Author(s):

L.S. Lai ◽

G.S. Djambazov ◽

C.-H. Lai ◽

K.A. Pericleous

Keyword(s):

Stokes Equations ◽

Small Time ◽

High Order ◽

Navier Stokes ◽

Acoustic Analogy ◽

Time Step ◽

Navier Stokes Equations ◽

Flow Equations ◽

High Order Schemes ◽

Fine Mesh

In computational acoustics, fluid-acoustic coupling methods for the computation of sound have been widely used by researchers for the last five decades. In the first part of the coupling procedure, the fully unsteady incompressible or compressible flow equations for the near-field of the unsteady flow are solved by using a Computational Fluid Dynamics (CFD) technique, such as Direct Numerical Simulation (DNS), Large Eddy Simulation (LES) or unsteady Reynolds averaged Navier-Stokes equations (RANS) the CFD predictions are then used to calculate sound sources using the acoustic analogy or solving a set of acoustic perturbation equations (APE) leading to the solution of the acoustic field. It is possible to use a 2-D reduced problem to provide a preliminary understanding of many acoustic problems. Unfortunately 2-D CFD simulations using a fine-mesh-small-time-step-LES-alike numerical method cannot be considered as LES, which applies to 3-D simulations only. Therefore it is necessary to understand the similarities and the effect between filters applied to unsteady compressible Navier-Stokes equations and the combined effect of high-order schemes and mesh size. The aim of this study is to provide suitable LES-alike methods for 2-D simulations. An efficient software implementation of high-order schemes is also proposed. Numerical examples are provided to illustrate these statistical similarities.

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