24 research outputs found
Robust control of redundantly actuated dynamical systems
The eigenstructure assignment scheme for robust multivariable feedback control
is extended to redundantly actuated dynamical systems. It is shown that an orthonormal
set of close loop eigenvectors is always exactly assignable in the case of
redundant actuation proving the inherent robustness in the control design methodology.
A choice of close loop eigenvector set to minimize the feedback gain matrix
is suggested. Partial Eigenstructure Assignment methodology is proposed for second
order mechanical systems. A methodology for coordinated actuation of redundant
actuator sets by a trained weighted minimum norm solution is presented. To apply
the methodology to hyper-redundant actuator arrays, for application to smart actuator
arrays, a novel adaptive discretization algorithm is proposed. The adaptive
aggregation strategy, based on the physics of the system, introduces nodes, to optimize
a performance index of the overall plant model. The dimensionality of the
inputs thus reduces to a finite number, making it a candidate plant for control by
the robust redundant control scheme. The adaptive aggregation together with robust
redundant control methodology is demonstrated on a finite element model of a novel
morphing wing. This schema unifies the traditionally disparate methods of modeling
and controller design
System Identification: Time Varying and Nonlinear Methods
Novel methods of system identification are developed in this dissertation. First
set of methods are designed to realize time varying linear dynamical system models from
input-output experimental data. The preliminary results obtained in a recent paper by the
author are extended to establish a new algorithm called the Time Varying Eigensystem
Realization Algorithm (TVERA). The central aim of this algorithm is to obtain a linear,
time varying, discrete time model sequence of the dynamic system directly from the
input-output data. Important results relating to concepts concerning coordinate systems
for linear time varying systems are developed (discrete time theory) and an intuitive
understanding of equivalent realizations is provided. A procedure to develop first few
time step models is detailed, providing a unified solution to the time varying
identification problem.
The practical problem of identifying the time varying generalized Markov
parameters required for TVERA is presented as the next result. In the process, we
generalize the classical time invariant input output AutoRegressive model with an
eXogenous input (ARX) models to the time varying case and realize an asymptotically stable observer as a byproduct of the calculations. It is further found that the choice of
the generalized time varying ARX model (GTV-ARX) can be set to realize a time
varying dead beat observer.
Methods to use the developed algorithm(s) in this research are then considered
for application to the identification of system models that are bilinear in nature. The fact
that bilinear plant models become linear for constant inputs is used in the development
of an algorithm that generalizes the classical developments of Juang.
An intercept problem is considered as a candidate for application of the time
varying identification scheme, where departure motion dynamics model sequence is
calculated about a nominal trajectory with suboptimal performance owing to the
presence of unstructured perturbations. Control application is subsequently
demonstrated.
The dynamics of a particle in a rotating tube is considered next for identification
using the time varying eigensystem realization algorithm. Continuous time bilinear
system identification method is demonstrated using the particle example and the
identification of an automobile brake model
Differentiable Rendering for Pose Estimation in Proximity Operations
Differentiable rendering aims to compute the derivative of the image
rendering function with respect to the rendering parameters. This paper
presents a novel algorithm for 6-DoF pose estimation through gradient-based
optimization using a differentiable rendering pipeline. We emphasize two key
contributions: (1) instead of solving the conventional 2D to 3D correspondence
problem and computing reprojection errors, images (rendered using the 3D model)
are compared only in the 2D feature space via sparse 2D feature
correspondences. (2) Instead of an analytical image formation model, we compute
an approximate local gradient of the rendering process through online learning.
The learning data consists of image features extracted from multi-viewpoint
renders at small perturbations in the pose neighborhood. The gradients are
propagated through the rendering pipeline for the 6-DoF pose estimation using
nonlinear least squares. This gradient-based optimization regresses directly
upon the pose parameters by aligning the 3D model to reproduce a reference
image shape. Using representative experiments, we demonstrate the application
of our approach to pose estimation in proximity operations.Comment: AIAA SciTech Forum 2023, 13 pages, 9 figure
NaRPA: Navigation and Rendering Pipeline for Astronautics
This paper presents Navigation and Rendering Pipeline for Astronautics
(NaRPA) - a novel ray-tracing-based computer graphics engine to model and
simulate light transport for space-borne imaging. NaRPA incorporates lighting
models with attention to atmospheric and shading effects for the synthesis of
space-to-space and ground-to-space virtual observations. In addition to image
rendering, the engine also possesses point cloud, depth, and contour map
generation capabilities to simulate passive and active vision-based sensors and
to facilitate the designing, testing, or verification of visual navigation
algorithms. Physically based rendering capabilities of NaRPA and the efficacy
of the proposed rendering algorithm are demonstrated using applications in
representative space-based environments. A key demonstration includes NaRPA as
a tool for generating stereo imagery and application in 3D coordinate
estimation using triangulation. Another prominent application of NaRPA includes
a novel differentiable rendering approach for image-based attitude estimation
is proposed to highlight the efficacy of the NaRPA engine for simulating
vision-based navigation and guidance operations.Comment: 49 pages, 22 figure
Doppler Measurement of Modulated Light for High Speed Vehicles
Technical details associated with a novel relative motion sensor system are elaborated in the paper. By utilizing the Doppler effect, the optical sensor system estimates the relative motion rates between the sensor and the moving object equipped with modulating light sources and relatively inexpensive electrical components. A transimpedance amplifier (TIA) sensing circuit is employed to measure the Doppler shift exhibited by the amplitude modulated light sources on the moving platform. Implementation details associated with the amplitude modulation and photo-detection processes are discussed using representative hardware elements. A heterodyne mixing process with a reference signal is shown to improve the signal-to-noise ratios of the Doppler shift estimation processing pipeline. Benchtop prototype experiments are used to demonstrate the utility of the proposed technology for relative motion estimation applications