Matching Items (6)
Filtering by
- All Subjects: Control Theory
- All Subjects: Optimization
- Creators: Mignolet, Marc
Description
As robots are increasingly migrating out of factories and research laboratories and into our everyday lives, they should move and act in environments designed for humans. For this reason, the need of anthropomorphic movements is of utmost importance. The objective of this thesis is to solve the inverse kinematics problem of redundant robot arms that results to anthropomorphic configurations. The swivel angle of the elbow was used as a human arm motion parameter for the robot arm to mimic. The swivel angle is defined as the rotation angle of the plane defined by the upper and lower arm around a virtual axis that connects the shoulder and wrist joints. Using kinematic data recorded from human subjects during every-day life tasks, the linear sensorimotor transformation model was validated and used to estimate the swivel angle, given the desired end-effector position. Defining the desired swivel angle simplifies the kinematic redundancy of the robot arm. The proposed method was tested with an anthropomorphic redundant robot arm and the computed motion profiles were compared to the ones of the human subjects. This thesis shows that the method computes anthropomorphic configurations for the robot arm, even if the robot arm has different link lengths than the human arm and starts its motion at random configurations.
ContributorsWang, Yuting (Author) / Artemiadis, Panagiotis (Thesis advisor) / Mignolet, Marc (Committee member) / Santos, Veronica J (Committee member) / Arizona State University (Publisher)
Created2013
Description
All structures suffer wear and tear because of impact, excessive load, fatigue, corrosion, etc. in addition to inherent defects during their manufacturing processes and their exposure to various environmental effects. These structural degradations are often imperceptible, but they can severely affect the structural performance of a component, thereby severely decreasing its service life. Although previous studies of Structural Health Monitoring (SHM) have revealed extensive prior knowledge on the parts of SHM processes, such as the operational evaluation, data processing, and feature extraction, few studies have been conducted from a systematical perspective, the statistical model development.
The first part of this dissertation, the characteristics of inverse scattering problems, such as ill-posedness and nonlinearity, reviews ultrasonic guided wave-based structural health monitoring problems. The distinctive features and the selection of the domain analysis are investigated by analytically searching the conditions of the uniqueness solutions for ill-posedness and are validated experimentally.
Based on the distinctive features, a novel wave packet tracing (WPT) method for damage localization and size quantification is presented. This method involves creating time-space representations of the guided Lamb waves (GLWs), collected at a series of locations, with a spatially dense distribution along paths at pre-selected angles with respect to the direction, normal to the direction of wave propagation. The fringe patterns due to wave dispersion, which depends on the phase velocity, are selected as the primary features that carry information, regarding the wave propagation and scattering.
The following part of this dissertation presents a novel damage-localization framework, using a fully automated process. In order to construct the statistical model for autonomous damage localization deep-learning techniques, such as restricted Boltzmann machine and deep belief network, are trained and utilized to interpret nonlinear far-field wave patterns.
Next, a novel bridge scour estimation approach that comprises advantages of both empirical and data-driven models is developed. Two field datasets from the literature are used, and a Support Vector Machine (SVM), a machine-learning algorithm, is used to fuse the field data samples and classify the data with physical phenomena. The Fast Non-dominated Sorting Genetic Algorithm (NSGA-II) is evaluated on the model performance objective functions to search for Pareto optimal fronts.
The first part of this dissertation, the characteristics of inverse scattering problems, such as ill-posedness and nonlinearity, reviews ultrasonic guided wave-based structural health monitoring problems. The distinctive features and the selection of the domain analysis are investigated by analytically searching the conditions of the uniqueness solutions for ill-posedness and are validated experimentally.
Based on the distinctive features, a novel wave packet tracing (WPT) method for damage localization and size quantification is presented. This method involves creating time-space representations of the guided Lamb waves (GLWs), collected at a series of locations, with a spatially dense distribution along paths at pre-selected angles with respect to the direction, normal to the direction of wave propagation. The fringe patterns due to wave dispersion, which depends on the phase velocity, are selected as the primary features that carry information, regarding the wave propagation and scattering.
The following part of this dissertation presents a novel damage-localization framework, using a fully automated process. In order to construct the statistical model for autonomous damage localization deep-learning techniques, such as restricted Boltzmann machine and deep belief network, are trained and utilized to interpret nonlinear far-field wave patterns.
Next, a novel bridge scour estimation approach that comprises advantages of both empirical and data-driven models is developed. Two field datasets from the literature are used, and a Support Vector Machine (SVM), a machine-learning algorithm, is used to fuse the field data samples and classify the data with physical phenomena. The Fast Non-dominated Sorting Genetic Algorithm (NSGA-II) is evaluated on the model performance objective functions to search for Pareto optimal fronts.
ContributorsKim, Inho (Author) / Chattopadhyay, Aditi (Thesis advisor) / Jiang, Hanqing (Committee member) / Liu, Yongming (Committee member) / Mignolet, Marc (Committee member) / Rajadas, John (Committee member) / Arizona State University (Publisher)
Created2016
Description
Numerous works have addressed the control of multi-robot systems for coverage, mapping, navigation, and task allocation problems. In addition to classical microscopic approaches to multi-robot problems, which model the actions and decisions of individual robots, lately, there has been a focus on macroscopic or Eulerian approaches. In these approaches, the population of robots is represented as a continuum that evolves according to a mean-field model, which is directly designed such that the corresponding robot control policies produce target collective behaviours.
This dissertation presents a control-theoretic analysis of three types of mean-field models proposed in the literature for modelling and control of large-scale multi-agent systems, including robotic swarms. These mean-field models are Kolmogorov forward equations of stochastic processes, and their analysis is motivated by the fact that as the number of agents tends to infinity, the empirical measure associated with the agents converges to the solution of these models. Hence, the problem of transporting a swarm of agents from one distribution to another can be posed as a control problem for the forward equation of the process that determines the time evolution of the swarm density.
First, this thesis considers the case in which the agents' states evolve on a finite state space according to a continuous-time Markov chain (CTMC), and the forward equation is an ordinary differential equation (ODE). Defining the agents' task transition rates as the control parameters, the finite-time controllability, asymptotic controllability, and stabilization of the forward equation are investigated. Second, the controllability and stabilization problem for systems of advection-diffusion-reaction partial differential equations (PDEs) is studied in the case where the control parameters include the agents' velocity as well as transition rates. Third, this thesis considers a controllability and optimal control problem for the forward equation in the more general case where the agent dynamics are given by a nonlinear discrete-time control system. Beyond these theoretical results, this thesis also considers numerical optimal transport for control-affine systems. It is shown that finite-volume approximations of the associated PDEs lead to well-posed transport problems on graphs as long as the control system is controllable everywhere.
This dissertation presents a control-theoretic analysis of three types of mean-field models proposed in the literature for modelling and control of large-scale multi-agent systems, including robotic swarms. These mean-field models are Kolmogorov forward equations of stochastic processes, and their analysis is motivated by the fact that as the number of agents tends to infinity, the empirical measure associated with the agents converges to the solution of these models. Hence, the problem of transporting a swarm of agents from one distribution to another can be posed as a control problem for the forward equation of the process that determines the time evolution of the swarm density.
First, this thesis considers the case in which the agents' states evolve on a finite state space according to a continuous-time Markov chain (CTMC), and the forward equation is an ordinary differential equation (ODE). Defining the agents' task transition rates as the control parameters, the finite-time controllability, asymptotic controllability, and stabilization of the forward equation are investigated. Second, the controllability and stabilization problem for systems of advection-diffusion-reaction partial differential equations (PDEs) is studied in the case where the control parameters include the agents' velocity as well as transition rates. Third, this thesis considers a controllability and optimal control problem for the forward equation in the more general case where the agent dynamics are given by a nonlinear discrete-time control system. Beyond these theoretical results, this thesis also considers numerical optimal transport for control-affine systems. It is shown that finite-volume approximations of the associated PDEs lead to well-posed transport problems on graphs as long as the control system is controllable everywhere.
ContributorsElamvazhuthi, Karthik (Author) / Berman, Spring Melody (Thesis advisor) / Kawski, Matthias (Committee member) / Kuiper, Hendrik (Committee member) / Mignolet, Marc (Committee member) / Peet, Matthew (Committee member) / Arizona State University (Publisher)
Created2019
Description
The problem of modeling and controlling the distribution of a multi-agent system has recently evolved into an interdisciplinary effort. When the agent population is very large, i.e., at least on the order of hundreds of agents, it is important that techniques for analyzing and controlling the system scale well with the number of agents. One scalable approach to characterizing the behavior of a multi-agent system is possible when the agents' states evolve over time according to a Markov process. In this case, the density of agents over space and time is governed by a set of difference or differential equations known as a {\it mean-field model}, whose parameters determine the stochastic control policies of the individual agents. These models often have the advantage of being easier to analyze than the individual agent dynamics. Mean-field models have been used to describe the behavior of chemical reaction networks, biological collectives such as social insect colonies, and more recently, swarms of robots that, like natural swarms, consist of hundreds or thousands of agents that are individually limited in capability but can coordinate to achieve a particular collective goal.
This dissertation presents a control-theoretic analysis of mean-field models for which the agent dynamics are governed by either a continuous-time Markov chain on an arbitrary state space, or a discrete-time Markov chain on a continuous state space. Three main problems are investigated. First, the problem of stabilization is addressed, that is, the design of transition probabilities/rates of the Markov process (the agent control parameters) that make a target distribution, satisfying certain conditions, invariant. Such a control approach could be used to achieve desired multi-agent distributions for spatial coverage and task allocation. However, the convergence of the multi-agent distribution to the designed equilibrium does not imply the convergence of the individual agents to fixed states. To prevent the agents from continuing to transition between states once the target distribution is reached, and thus potentially waste energy, the second problem addressed within this dissertation is the construction of feedback control laws that prevent agents from transitioning once the equilibrium distribution is reached. The third problem addressed is the computation of optimized transition probabilities/rates that maximize the speed at which the system converges to the target distribution.
This dissertation presents a control-theoretic analysis of mean-field models for which the agent dynamics are governed by either a continuous-time Markov chain on an arbitrary state space, or a discrete-time Markov chain on a continuous state space. Three main problems are investigated. First, the problem of stabilization is addressed, that is, the design of transition probabilities/rates of the Markov process (the agent control parameters) that make a target distribution, satisfying certain conditions, invariant. Such a control approach could be used to achieve desired multi-agent distributions for spatial coverage and task allocation. However, the convergence of the multi-agent distribution to the designed equilibrium does not imply the convergence of the individual agents to fixed states. To prevent the agents from continuing to transition between states once the target distribution is reached, and thus potentially waste energy, the second problem addressed within this dissertation is the construction of feedback control laws that prevent agents from transitioning once the equilibrium distribution is reached. The third problem addressed is the computation of optimized transition probabilities/rates that maximize the speed at which the system converges to the target distribution.
ContributorsBiswal, Shiba (Author) / Berman, Spring (Thesis advisor) / Fainekos, Georgios (Committee member) / Lanchier, Nicolas (Committee member) / Mignolet, Marc (Committee member) / Peet, Matthew (Committee member) / Arizona State University (Publisher)
Created2020
Description
The focus of this dissertation is first on understanding the difficulties involved in constructing reduced order models of structures that exhibit a strong nonlinearity/strongly nonlinear events such as snap-through, buckling (local or global), mode switching, symmetry breaking. Next, based on this understanding, it is desired to modify/extend the current Nonlinear Reduced Order Modeling (NLROM) methodology, basis selection and/or identification methodology, to obtain reliable reduced order models of these structures. Focusing on these goals, the work carried out addressed more specifically the following issues:
i) optimization of the basis to capture at best the response in the smallest number of modes,
ii) improved identification of the reduced order model stiffness coefficients,
iii) detection of strongly nonlinear events using NLROM.
For the first issue, an approach was proposed to rotate a limited number of linear modes to become more dominant in the response of the structure. This step was achieved through a proper orthogonal decomposition of the projection on these linear modes of a series of representative nonlinear displacements. This rotation does not expand the modal space but renders that part of the basis more efficient, the identification of stiffness coefficients more reliable, and the selection of dual modes more compact. In fact, a separate approach was also proposed for an independent optimization of the duals. Regarding the second issue, two tuning approaches of the stiffness coefficients were proposed to improve the identification of a limited set of critical coefficients based on independent response data of the structure. Both approaches led to a significant improvement of the static prediction for the clamped-clamped curved beam model. Extensive validations of the NLROMs based on the above novel approaches was carried out by comparisons with full finite element response data. The third issue, the detection of nonlinear events, was finally addressed by building connections between the eigenvalues of the finite element software (Nastran here) and NLROM tangent stiffness matrices and the occurrence of the ‘events’ which is further extended to the assessment of the accuracy with which the NLROM captures the full finite element behavior after the event has occurred.
i) optimization of the basis to capture at best the response in the smallest number of modes,
ii) improved identification of the reduced order model stiffness coefficients,
iii) detection of strongly nonlinear events using NLROM.
For the first issue, an approach was proposed to rotate a limited number of linear modes to become more dominant in the response of the structure. This step was achieved through a proper orthogonal decomposition of the projection on these linear modes of a series of representative nonlinear displacements. This rotation does not expand the modal space but renders that part of the basis more efficient, the identification of stiffness coefficients more reliable, and the selection of dual modes more compact. In fact, a separate approach was also proposed for an independent optimization of the duals. Regarding the second issue, two tuning approaches of the stiffness coefficients were proposed to improve the identification of a limited set of critical coefficients based on independent response data of the structure. Both approaches led to a significant improvement of the static prediction for the clamped-clamped curved beam model. Extensive validations of the NLROMs based on the above novel approaches was carried out by comparisons with full finite element response data. The third issue, the detection of nonlinear events, was finally addressed by building connections between the eigenvalues of the finite element software (Nastran here) and NLROM tangent stiffness matrices and the occurrence of the ‘events’ which is further extended to the assessment of the accuracy with which the NLROM captures the full finite element behavior after the event has occurred.
ContributorsLin, Jinshan (Author) / Mignolet, Marc (Thesis advisor) / Jiang, Hanqing (Committee member) / Oswald, Jay (Committee member) / Spottswood, Stephen (Committee member) / Rajan, Subramaniam D. (Committee member) / Arizona State University (Publisher)
Created2020
Description
Modern life is full of challenging optimization problems that we unknowingly attempt to solve. For instance, a common dilemma often encountered is the decision of picking a parking spot while trying to minimize both the distance to the goal destination and time spent searching for parking; one strategy is to drive as close as possible to the goal destination but risk a penalty cost if no parking spaces can be found. Optimization problems of this class all have underlying time-varying processes that can be altered by a decision/input to minimize some cost. Such optimization problems are commonly solved by a class of methods called Dynamic Programming (DP) that breaks down a complex optimization problem into a simpler family of sub-problems. In the 1950s Richard Bellman introduced a class of DP methods that broke down Multi-Stage Optimization Problems (MSOP) into a nested sequence of ``tail problems”. Bellman showed that for any MSOP with a cost function that satisfies a condition called additive separability, the solution to the tail problem of the MSOP initialized at time-stage k>0 can be used to solve the tail problem initialized at time-stage k-1. Therefore, by recursively solving each tail problem of the MSOP, a solution to the original MSOP can be found. This dissertation extends Bellman`s theory to a broader class of MSOPs involving non-additively separable costs by introducing a new state augmentation solution method and generalizing the Bellman Equation. This dissertation also considers the analogous continuous-time counterpart to discrete-time MSOPs, called Optimal Control Problems (OCPs). OCPs can be solved by solving a nonlinear Partial Differential Equation (PDE) called the Hamilton-Jacobi-Bellman (HJB) PDE. Unfortunately, it is rarely possible to obtain an analytical solution to the HJB PDE. This dissertation proposes a method for approximately solving the HJB PDE based on Sum-Of-Squares (SOS) programming. This SOS algorithm can be used to synthesize controllers, hence solving the OCP, and also compute outer bounds of reachable sets of dynamical systems. This methodology is then extended to infinite time horizons, by proposing SOS algorithms that yield Lyapunov functions that can approximate regions of attraction and attractor sets of nonlinear dynamical systems arbitrarily well.
ContributorsJones, Morgan (Author) / Peet, Matthew M (Thesis advisor) / Nedich, Angelia (Committee member) / Kawski, Matthias (Committee member) / Mignolet, Marc (Committee member) / Berman, Spring (Committee member) / Arizona State University (Publisher)
Created2021