Simultaneous localization and mapping (SLAM) is a process wherein a robotic system acquires a map of its environment while simultaneously localizing itself relative to this map. A common solution to the SLAM problem involves the use of the extended Kalman filter (EKF). This filter is used to calculate the posterior probability of the robot pose and map given observations and control inputs. From the EKF, one estimates the mean and error covariance of the robot pose and map features by using nonlinear motion and observation models. In this article, the conditions required for the convergence of the errors in the EKF estimates obtained by linearizing the nonlinear system equations are studied and applied to the SLAM problem. In particular, the observability condition of the system describing the typical SLAM problem is studied. Numerical studies are carried out to compare the accuracy of the EKF estimates for a representative SLAM formulation which is not observable with a SLAM formulation that satisfies the observability condition.
In the simultaneous localization and mapping (SLAM) problem, it is required for a robotic system to acquire
the map of its environment while simultaneously localizing itself relative to this evolving map. In order to solve
the SLAM problem, given observations of the environment and control inputs, the joint posterior probability
of the robot pose and the map are estimated by using recursive filters such as the extended Kalman filter
(EKF) and the particle filter. The implementation of these filters requires a motion model to describe the
evolution of the robot pose with control inputs, and additionally, an observation model to describe the relations
between the robot pose and measurements of the environment. In general, the motion model is derived from
the kinematics of the robotic system, without taking the system dynamics into account. In this article, the
authors investigate the performance and efficacy of standard SLAM algorithms when the dynamics of the
robotic system is taken into account in the motion model and provide experimental results to complement the
simulation findings.
In the simultaneous localization and mapping (SLAM) problem, one addresses the problem of using mobile sensor platforms or robotic systems to map unknown environments while simultaneously localizing the mobile systems relative to the map. Applications include mapping in oil storage tanks, oil pipes, search and rescue operations, surveillance operations, exploration operations. In this effort, a previously proposed multi-robot localization algorithm is extended to implement SLAM. The decentralized algorithm is demonstrated to work in dynamic robot networks. Experimental and numerical studies conducted with multiple networked mobile platforms are also discussed to validate the analytical findings.
In this article, localization of a static source by using a mobile sensor platform is studied. With appropriate
assumptions on the system dynamics, the noise robustness of a previously proposed localization algorithm1 is
examined. By using Lyapunov analysis, it is demonstrated that if the noise uncertainty is constant and bounded,
the adaptive localization algorithm results in bounded localization errors. The analytical results are validated
through numerical simulations.
A major concern in the development of microelectromechanical systems (MEMS) is the presence of residual stress. This
stress, which is produced during the fabrication of multi-layer thin-film structures, can significantly affect the
performance of micro-scale devices. Though experimental measurement techniques are accurate, actual stress
measurements can vary dramatically from run to run and wafer to wafer. For this reason, the modeling of this stress can
be a challenging task. Past work has often focused on experimental, static techniques for determining residual-stress
levels in single-layer and bi-layer structures. In addition, in prior studies, the focus has primarily been on residual-stress
measurements in thin films as they are being deposited and prior to the release of a particular device. In this effort,
residual stresses in MEMS resonators are characterized pre- and post-micro-machining and release of the structures.
This is accomplished by applying three residual-stress identification techniques. The first technique, which is based on
wafer-bow measurements and Stoney's formula, is suited for determining the residual stresses in thin film layers as they
are being deposited and before the occurrence of a micro-machining or release process. In the second technique, a static
parametric identification technique, device deflection data is made use of to approximate individual device residual
stress immediately after release of a structure. The third technique, a dynamic parametric identification technique, which
can be based on linear or nonlinear frequency response data can be used to estimate device residual stress immediately
after release and after the device has been polarized. The results obtained by using these techniques are used to develop
an understanding of how geometry, fabrication, release and polarization of resonators affect the stress state in a
piezoelectric device. The results, which show that the stress levels can be quite different after a device has been released
and poled, point to the importance of considering parameter identification schemes such as those described in this effort
for identifying residual stresses in multi-layer, micro-structures.
In this article, theoretical and the experimental studies are reported on the adaptive control of vibration transmission in a
strut system subjected to a longitudinal pulse train excitation. In the control scheme, a magneto-strictive actuator is
employed at the downstream transmission point in the secondary path. The actuator dynamics is taken into account.
The system boundary parameters are first estimated off-line, and later employed to simulate the system dynamics. A
Delayed-X Filtered-E spectral algorithm is proposed and implemented in real time. The underlying mechanics based
filter construction allows for the time varying system dynamics to be taken into account. This work should be of interest
for active control of vibration and noise transmission in helicopter gearbox support struts and other systems.
A major concern in the development of microelectromechanical systems (MEMS) is the presence of residual stress.
Residual stress, which is produced during the fabrication of multi-layer thin-film structures, can significantly affect the
performance of micro-scale devices. Though experimental measurement techniques are accurate, actual stress
measurements can vary dramatically from run to run and wafer to wafer. For this reason, the modeling of this stress can
be a challenging task. Past work has often focused on experimental, static techniques for determining residual stress
levels in single-layer and bi-layer structures. In addition, these past studies have concentrated on residual stress
measurements in thin films as they are being deposited and prior to the release of a particular device. In this effort, three
techniques are used for determining residual stress levels in four-layer piezoelectrically driven cantilevers and resonator
structures. The first technique is a static technique that is based on wafer bow measurements and Stoney's formula. The
second technique is a dynamic technique that is based on parameter identification from nonlinear frequency-response
data. The third technique is also a static technique based on parameter identification from static device deflection
measurements. The devices studied, which are piezoelectric devices, are fabricated with varying lengths and widths.
The results obtained from these three techniques will be compared and discussed, and it is expected that this work will
enable the characterization of residual stress in micro-structures after they have been released.
Nonlinear phenomena such as mode localization have been studied for a number of years in the solid-state physics literature. Energy can become localized at a specific location in a discrete system as a result of the nonlinearity of the system and not due to any defects or impurities within the considered systems. Intrinsic Localized Modes (ILMs), which are defined as localization due to strong intrinsic nonlinearity within an array of perfect, periodically repeating oscillators, are of interest to the present work. Here, such localization is studied in the context of micro-cantilever arrays and micro-resonator arrays, and it is explored if an ILM can be realized as a nonlinear normal mode or nonlinear vibration mode. The method of multiple scales and methods to determine nonlinear normal modes are used to study the nonlinear vibrations of the resonator arrays. Preliminary investigations reported in this article suggest that it is possible to realize an ILM as a nonlinear vibration mode. These results are believed to be important for future designs of microresonator arrays intended for signal processing, communication, and sensor applications.
KEYWORDS: Control systems, Control systems design, Wave propagation, Feedback control, Signal attenuation, Sensors, Actuators, Waveguides, Systems modeling, Composites
A new scheme for designing closed-loop control of dispersive waves in elastic structures is reported in this article. This scheme takes advantage of the dissipative characteristics of visco-elastic materials, and the isospectral properties of the visco-elastic system are used to design the feedback controller for the undamped structural system to realize the desired characteristics of the closed-loop system. Numerical results are presented in the form of frequency-response and wave-transmission characteristics, and these results show the promise of the proposed scheme.
A computational multi-field mechanics model of composite micromechanical systems (MEMS) with piezoelectric actuation and sensing has been developed as a design tool for micro-resonators. These devices are to be used for filters and other signal processing applications. The developed dynamic model of MEMS resonators accounts for structural properties and the electromechanical coupling effect through finite element analysis. It is assumed that the deflection is large and that the geometric nonlinearity must be included. The mechanical strain is assumed to be small so that the linear constitutive relations are valid. The dynamic admittance model is derived by combining the linear piezoelectric constitutive equations with the modal transfer function of the micro-resonator structure. The resonator receptance matrix is constructed through modal summation by considering only a limited number of dominant modes. The electromechanical coupling determination at the input and output ports makes use of the converse and direct piezoelectric effects. In the development of the finite-element models, boundary conditions, electrodes shaping, and factors such as varying elastic modulus across the length of the beam for the multilayered structure are taken into account. The coupled model can be used to carry out sensitivity studies with respect to the following: i) resonator thickness and length; ii) influence of constant axial forces on the transverse vibrations of clamped-clamped micro-resonators; geometry of the drive and sense electrodes; and iii) imperfect boundary conditions due to mask imperfections and fabrication procedure. The developed model has been validated by comparing the predictions with results available in the literature for clamped-clamped resonators.
In this article, recent investigations into the dynamic behavior of a sensor diaphragm under initial tension are presented. A comprehensive mechanics model based on a plate with in-plane tension is presented and analyzed to examine the transition from plate behavior to membrane behavior. It is shown that, for certain tension parameter values, it is appropriate to model the diaphragm as a plate-membrane structure rather than as a membrane. In the nonlinear analysis, the effect of cubic nonlinearity is studied when the excitation frequency is either close to one-third of the first natural frequency or the first natural frequency. The nonlinear effects limit the sensor bandwidth and dynamic range. The study shows that both of the nonlinear effects can be attenuated by decreasing the diaphragm thickness and applying an appropriate tension to realize the desired first natural frequency while reducing the strength of the nonlinearity. The analyses and related results should be valuable for carrying out the design of circular diaphragms for various sensor applications, in particular, for designing sensors on small scales.
Forced oscillations of piezoelectric, micro-electromechanical (MEMS) resonators fabricated as clamped-clamped composite structures are studied in this effort. Piezoelectric actuation is used to excite these structures on the input side and piezoelectric sensing is carried out on the output side. Each resonator structure is modeled as an Euler-Bernoulli beam with axially varying properties across the length and distributed actuation. A nonlinear integro-partial differential system is derived to describe the micro-resonator. For weak damping and weak forcing, the method of multiple scales is used to obtain an approximate solution of the system about a post-buckling position. The different modeling assumptions are presented and discussed, and the analytical prediction is compared with experimental observation.
In designing a controller, one way to avoid an energy spillover is to use what is called the zero spillover scheme. However, practical limitations may make such a controller impossible to realize, and one will need to implement a relaxed version of this controller called a relaxed zero spillover controller (RZSC). Here, analytical and experimental investigations into a RZSC scheme are presented. This controller has been used for active structural acoustic control (ASAC) of sound transmission into an enclosure. Noise is transmitted through the flexible boundary of the enclosure, and piezoceramic patches, mounted on the flexible boundary, are used as actuators. Polyvinylidene fluoride sensors are used on the flexible boundary and condenser microphone sensors are used inside and outside the enclosure. The stability of the chosen RZSC scheme for a single input, single output system and the extension to multiple input, multiple output systems are discussed along with other issues.
KEYWORDS: Actuators, Sensors, Control systems, Digital signal processing, Signal attenuation, Finite element methods, Model-based design, Modal analysis, Interfaces, Chemical elements
Experimental studies of closed-loop control of longitudinal wave transmission through a hollow cylinder are presented in this article. Model studies coupled with experimental modal analysis are used to understand and characterize the actuator-strut ensemble, and a boundary control algorithm, which falls under the class of feedforward control schemes, is experimentally implemented. The algorithm is based on a partial differential equations (PDE) model of the strut-actuator system, and a combination of strain and acceleration measurements are used to solve the boundary-value problem in the implementation. Harmonic vibratory disturbances are transmitted in the frequency range extending up to 1 kHz, and it has been demonstrated that a vibration attenuation of up to 16 dB can be achieved by using a magnetostrictive actuator in this model-based control scheme.
In this paper, analytical and experimental investigations conducted into the design and use of fiber-tip based Fabry-Perot sensors for control of structural acoustics are presented. Noise is transmitted into the enclosure through a flexible boundary, and the fiber-tip sensors are designed for acoustic pressure and air particle velocity measurements inside and outside the enclosure as well as panel acceleration measurements. The benefits of these sensors for realizing zero spillover control schemes and other schemes are discussed.
In designing a controller, one way to avoid energy spillover is to use what is called the zero spillover control scheme. Here, this scheme is studied for actively controlling sound fields inside an enclosure with a flexible boundary. Noise is transmitted into the enclosure through the flexible boundary, and piezoceramic patches, which are mounted on the flexible boundary, are used as actuators. Polyvinylidene fluoride sensors are used on the flexible boundary and microphone sensors are used inside and outside the enclosure. The locations of the sensors needed to construct a zero spillover controller are discussed along with other issues.
Experimental investigations conducted into active control of longitudinal waves transmitted through a hollow cylindrical strut are presented in this article. Following along the lines of our previous work, an active strut of finite extent length, instrumented with sensors, piezoelectric, and magnetostrictive actuators, is studied in the frequency range of 10 Hz to 2 kHz. Single and multiple actuator arrangements are employed in open loop control investigations, and the effectiveness of the control effort in minimizing longitudinal harmonic disturbances transmitted through the strut is experimentally investigated. Initial efforts towards development of feedforward and feedback boundary control algorithms for reducing longitudinal vibratory loads in finite length cylinders is also presented. For the feedback controller development, the strut-actuator ensemble is modeled by using the one dimensional wave equation and the direct method of Liapunov is used. The feedforward control algorithm is based on the previous model of the active strut and relies on measurements of axial strains and accelerations at the strut ends. The influence of the boundary conditions and static forces applied to the strut are also investigated. The relevance of the current work to control of structure-borne helicopter cabin interior noise is also discussed.
Experimental and analytical investigations conducted into active control of longitudinal and flexural waves transmitted through a cylindrical gearbox strut are presented in this article. The development of an experimental model of a finite length active cylindrical strut instrumented with sensors, piezoelectric, and magnetostrictive actuators is described. The strut is included in an experimental arrangement where vibratory loads are applied along the strut's longitudinal and transverse directions while it is subjected to an axial static loading. Modal analysis studies are carried out in the frequency range of 10 Hz to 5 kHz with a finite element model of the cylindrical strut and the experimental model. During wave transmission through the strut, coupling between different types of modes is predicted by analysis and observed in the experiments. Actuator and sensor systems issues are discussed with relevance for control of vibrations transmitted through helicopter gearbox struts.
The influence of piezoceramic actuator nonlinearities on the response of a panel-enclosure system is examined. As an extension of our earlier work, hysteresis effect is also included in the nonlinear relationship between the free strain experienced by a piezoceramic patch and the applied electric field. The responses of the system with the hysteretic effect are discussed and compared with experimental results.
KEYWORDS: Actuators, Wave propagation, Signal attenuation, Control systems, Systems modeling, Mechanics, Matrices, Feedback control, Smart structures, System integration
In this study, the problem of controlling flexural waves transmitted through a cylindrical strut is addressed. This cylindrical strut is representative of a helicopter gearbox strut, which is attached at one end to the gearbox and at the other end to the fuselage. The primary disturbance is assumed to be transmitted from the end attached to the gearbox. Secondary forces are generated by a set of carefully positioned piezoelectric actuators, and feedforward and feedback schemes are used to determine the appropriate current inputs into these actuators. In one case, the control inputs to the actuators are chosen based on a performance function that includes the power supplied by the actuators to the strut. The abilities of the considered active control schemes to effectively attenuate the flexural displacements at the fuselage attachment end are examined and discussed. Future considerations for this work are also presented.
Analytical and numerical investigations into active control of longitudinal and flexural waves transmitted through a cylindrical strut are presented in this article. Following along the lines of our previous work, a mechanics based model for a cylindrical strut fitted with magnetostrictive actuators is developed. For harmonic disturbances, a linear dynamic formulation, which describes the motion of the actuator, is integrated with the formulation describing wave transmission through the strut. The resulting system is studied in the frequency domain, and numerical simulations are used to examine the open-loop system. For disturbances transmitted over the frequency range of 10 Hz to 6 kHz, comparisons are made between the system based on piezoelectric actuators and the system based on magnetostrictive actuators. A closed-loop control scheme based on the developed model is proposed for controlling longitudinal vibrations.
Nonlinear oscillations of a thin, isotropic panel bearing piezoceramic patches are studied in this work. The thin panel, which is clamped along all four edges, forms one of the boundaries of an enclosure. Rigid walls form the other boundaries of the enclosure. The piezoceramic patches are located symmetrically on the top and bottom surfaces of the flexible panel. Nonlinear relationship between the free strain experienced by a piezoceramic patch and the applied electric field is considered along with panel nonlinear elasticity to derive the equations of motion of the plate-enclosure system. It is shown that a voltage input into a piezoceramic actuator pair results in both parametric and external excitations to the panel. For harmonic excitations, the features of the nonlinear responses obtained in the simulations show good agreement with related experimental results. It is seen that for the cases considered, the actuator nonlinearities have a stronger influence on the response than the panel nonlinear elasticity.
We report recent work on acoustic measurements using a Bragg grating based Fabry-Perot sensor system. A single Fabry-Perot sensor using a path matched Michelson interferometer was developed, and a digital demodulation scheme based on the phase stepping technique was used to measure acoustic sound pressure from 100 Hz to 600 Hz. This sensor is designed to work in a multiplexed architecture to provide inputs to a feed-forward adaptive control system. This control system will be used to actively control the sound pressure level within an enclosure. A series of experiments were performed to investigate the possibility and potential use of this sensor system for acoustic noise detection. In this paper, we present initial test data from the prototype optical sensor microphone. We also illustrate the envisioned multiplexed sensor scheme and control system.
The present work is a continuation of our previous efforts, in which active control of deterministic bandlimited and tonal disturbances in an enclosure with a flexible boundary has been addressed. Multiple tones in the bandwidth of 40 Hz to 1000 Hz are transmitted into the enclosure and local noise control is attempted by using a multi-input, multi- output, digital feedforward control scheme. The specific focus of the current work is on actuator grouping, and this issue is explored through numerical and experimental investigations. It is demonstrated that actuator grouping can be beneficial for controlling enclosed sound fields dominated by widely separated tones.
In this work, analytical investigations into active control of longitudinal and flexural vibrations transmitted through a cylindrical strut are conducted. A mechanics based model for a strut fitted with a piezoelectric actuator is developed. For harmonic disturbances, a linear dynamic formulation describing the motion of the actuator is integrated with the formulation describing wave transmission through the strut, and the resulting system is studied in the frequency domain. Open-loop studies are conducted with the aid of numerical simulations, and the potential of active control schemes to attenuate the transmitted vibrations over the frequency range of 10 Hz to 6000 Hz is examined. The relevance of the current work to control of helicopter cabin interior noise is also discussed.
Analytical and experimental investigations into active control of sound fields within a 3D enclosure are presented for tonal and bandlimited disturbances. Lead Zirconate Titanate patches mounted on the flexible wall of the enclosure are used as distributed actuators, and polyvinylidene fluoride film mounted on the flexible wall and condenser microphones are used as sensors. The sensors and actuators are used in a digital, adaptive feedforward control scheme to realize `local' noise and vibration control. For tonal disturbances, the developed analytical model is found to yield results that are in good agreement with the experimental observations. Different cases of bandlimited disturbances are considered in the experiments. These cases include multiple panel and/or enclosure resonances. For bandlimited disturbances, the control scheme is found to be effective in identifying the dominant resonances and realizing significant noise reductions at the dominant modes. However, the local noise reductions realized for bandlimited disturbances are not as high as those realized for tonal disturbances. Issues such as performance functions are also explored in the investigations.
Extensions of our previous analytical and experimental investigations into active control of bandlimited disturbances in a three-dimensional enclosure are presented. The frequency range of the bandlimited disturbance is chosen to encompass structural and/or enclosure resonances. Distributed piezoceramic actuators and distributed polyvinylidene fluoride (PVDF) sensors are mounted on one of the enclosure boundaries. Acoustic sensors are used inside and outside the enclosure. An analytical formulation based on a state-space model is developed for local vibration control on an enclosure boundary and/or local noise control inside the enclosure for bandlimited disturbances. The error sensor signals are minimized by using digital feedforward control schemes based on filtered-U gradient descent algorithms. Analytical predictions from the current work are compared with the results obtained in our previous experimental investigations and discussed.
KEYWORDS: Actuators, Sensors, Control systems, Ferroelectric materials, Scanning probe lithography, Acoustics, Denoising, Electronic filtering, Digital signal processing, Digital filtering
Experimental investigations into the control of noise in the interior of a three-dimensional enclosure with a flexible wall are presented for harmonic and multiple frequency disturbances. Lead zirconate titanate (PZT) patches mounted on the flexible wall are used as actuators and condenser microphones are used as acoustic sensors in a digital feedforward control scheme. The control system is effective in identifying the dominant resonances and achieving significant noise reduction for the dominant modes. Based on the studies on the effect of actuator redundancy on noise reduction, it is found that less noise reduction is achieved when there are more number of actuators than sensors. Modal spillover is also observed in some of the controlled cases.
Numerical studies undertaken to determine the structural intensity for active vibration of plates bonded with piezoceramic patches are presented. The formulation, which is based on finite- difference schemes, allows for thin isotropic plates with general boundary conditions. Active and reactive intensities are computed for the different cases, in which the considered plate is excited by a planar sound field and/or one or more piezoceramic patches. The numerical results indicate the importance of considering reactive intensities for active vibration control applications.
Analytical and experimental studies undertaken for controlling noise in the interior of a 3D enclosure with a flexible boundary are presented. The rigid boundaries are constructed from acrylic material, and the flexible boundary is constructed from aluminum materia. Noise generated by an external speaker is transmitted into the enclosure through the flexible boundary and active control is realized by using Lead Zirconate Titanate piezoelectric actuators bonded to the flexible boundary. Condenser microphones are used for noise measurements. For panel and cavity controller modes, analog controllers based on feedforward schemes using acoustic error signals are developed and discussed.
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