Review of Attitude Representations Used for Aircraft Kinematics

Phillips, Warren F.; Hailey, Christine E.; Gebert, Glenn

doi:10.2514/2.2824

Cited by 107 publications

(20 citation statements)

References 82 publications

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“…However, since these problems arise from identification of local linearizations using data local to x 0 , it is often the case that X is a wide matrix, that is p > n. This causes problems because the matrix inverse (X X) −1 does not exist. Also, researchers have noticed that in some systems, the trajectory data often lies on a manifold with dimension lower than that of the state-space, and a classical example of this is gimbal lock [22]. This is a similar situation because once again: (X X) −1 does not exist.…”

Section: A Statistical Challengesmentioning

confidence: 89%

Statistics for sparse, high-dimensional, and nonparametric system identification

Aswani

Bickel

Tomlin

2009

2009 IEEE International Conference on Robotics and Automation

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Local linearization techniques are an important class of nonparametric system identification. Identifying local linearizations in practice involves solving a linear regression problem that is ill-posed. The problem can be ill-posed either if the dynamics of the system lie on a manifold of lower dimension than the ambient space or if there are not enough measurements of all the modes of the dynamics of the system. We describe a set of linear regression estimators that can handle data lying on a lower-dimension manifold. These estimators differ from previous estimators, because these estimators are able to improve estimator performance by exploiting the sparsity of the system -the existence of direct interconnections between only some of the states -and can work in the "large p, small n" setting in which the number of states is comparable to the number of data points. We describe our system identification procedure, which consists of a presmoothing step and a regression step, and then we apply this procedure to data taken from a quadrotor helicopter. We use this data set to compare our procedure with existing procedures.

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Section: A Statistical Challengesmentioning

confidence: 89%

Statistics for sparse, high-dimensional, and nonparametric system identification

Aswani

Bickel

Tomlin

2009

2009 IEEE International Conference on Robotics and Automation

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“…It should be pointed out that equations (1) to (4), (22), (23), (25), and (32) to (35) constitute the closedloop system.…”

Section: Attitude Tracking Control Law Designmentioning

confidence: 99%

“…For the command filter (25), if setting the damping ratio and choosing large enough ! n , then the error between the filter output and input is sufficiently small, i.e.…”

Section: Propositionmentioning

confidence: 99%

“…Step 3: Compute the command attitude trajectory r c , _ r c , € r c from equation (25), and compute the attitude tracking error r e and angular velocity tracking error x e from equation (29);…”

Section: Brief Summary Of Control Algorithmmentioning

confidence: 99%

“…n are the damping ratio and frequency, respectively. The initial conditions for equation (25) are set as…”

Section: Command Attitude Trajectory Calculationmentioning

confidence: 99%

See 2 more Smart Citations

Nonlinear adaptive trajectory tracking control for a quad-rotor with parametric uncertainty

Sun

2014

Proceedings of the Institution of Mechanical Engineers, Part G:

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A novel adaptive control algorithm to trajectory tracking control problem for a quad-rotor with uncertain mass and inertial parameters is presented based on the noncertainty equivalence principle. The estimation laws for quad-rotor mass and inertial parameters are developed with the introduction of stable attracting manifolds into the position-loop and attitude-loop adaptation process, respectively. The position and attitude trajectory tracking control algorithms are constructed through a unified immersion and invariance adaptive control technology. With extracting the desired attitude trajectory from the position-loop, the desired attitude trajectory for the attitude-loop is calculated from a command filter. The ultimately uniformly boundedness of the closed-loop system signals is derived for the quad-rotor under the proposed control algorithm. Simulation results demonstrate the performance of the proposed approach.

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Liquid fluidization with cylindrical particles: Highly resolved simulations

Derksen

2019

AIChE Journal

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We perform three-dimensional, time-dependent simulations of dense, fluidized suspensions of solid cylindrical particles in a Newtonian liquid in fully periodic domains. The resolution of the flow field is an order of magnitude finer than the diameter of the cylindrical particles. At their surfaces no-slip conditions are applied through an immersed boundary method (IBM), coupled to the lattice-Boltzmann method that is used as the fluid flow solver. The marker points of the IBM are also used to detect and perform collisions between the cylinders. With these particle-resolved simulations, we study the effects of the aspect ratio of the cylinders and the solids volume fraction on the superficial slip velocity between fluid and solids, on the solids velocity fluctuations, as well as on the orientation of the cylinders. The aspect ratio (length over diameter of the cylinders) ranges from 0.5 to 4, the solids volume fraction goes up to 0.48. Reynolds numbers based on average settling velocity are of the order of 1-10. At constant Archimedes number, we observe only minor sensitivities of the settling Reynolds number on the aspect ratio.

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Review of Attitude Representations Used for Aircraft Kinematics

Cited by 107 publications

References 82 publications

Statistics for sparse, high-dimensional, and nonparametric system identification

Statistics for sparse, high-dimensional, and nonparametric system identification

Nonlinear adaptive trajectory tracking control for a quad-rotor with parametric uncertainty

Liquid fluidization with cylindrical particles: Highly resolved simulations

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