Matching Items (12)
Description
This thesis considers two problems in the control of robotic swarms. Firstly, it addresses a trajectory planning and task allocation problem for a swarm of resource-constrained robots that cannot localize or communicate with each other and that exhibit stochasticity in their motion and task switching policies. We model the population dynamics of the robotic swarm as a set of advection-diffusion- reaction (ADR) partial differential equations (PDEs).
Specifically, we consider a linear parabolic PDE model that is bilinear in the robots' velocity and task-switching rates. These parameters constitute a set of time-dependent control variables that can be optimized and transmitted to the robots prior to their deployment or broadcasted in real time. The planning and allocation problem can then be formulated as a PDE-constrained optimization problem, which we solve using techniques from optimal control. Simulations of a commercial pollination scenario validate the ability of our control approach to drive a robotic swarm to achieve predefined spatial distributions of activity over a closed domain, which may contain obstacles. Secondly, we consider a mapping problem wherein a robotic swarm is deployed over a closed domain and it is necessary to reconstruct the unknown spatial distribution of a feature of interest. The ADR-based primitives result in a coefficient identification problem for the corresponding system of PDEs. To deal with the inherent ill-posedness of the problem, we frame it as an optimization problem. We validate our approach through simulations and show that reconstruction of the spatially-dependent coefficient can be achieved with considerable accuracy using temporal information alone.
Specifically, we consider a linear parabolic PDE model that is bilinear in the robots' velocity and task-switching rates. These parameters constitute a set of time-dependent control variables that can be optimized and transmitted to the robots prior to their deployment or broadcasted in real time. The planning and allocation problem can then be formulated as a PDE-constrained optimization problem, which we solve using techniques from optimal control. Simulations of a commercial pollination scenario validate the ability of our control approach to drive a robotic swarm to achieve predefined spatial distributions of activity over a closed domain, which may contain obstacles. Secondly, we consider a mapping problem wherein a robotic swarm is deployed over a closed domain and it is necessary to reconstruct the unknown spatial distribution of a feature of interest. The ADR-based primitives result in a coefficient identification problem for the corresponding system of PDEs. To deal with the inherent ill-posedness of the problem, we frame it as an optimization problem. We validate our approach through simulations and show that reconstruction of the spatially-dependent coefficient can be achieved with considerable accuracy using temporal information alone.
ContributorsElamvazhuthi, Karthik (Author) / Berman, Spring Melody (Thesis advisor) / Peet, Matthew Monnig (Committee member) / Mittelmann, Hans (Committee member) / Arizona State University (Publisher)
Created2014
Description
In this paper, optimal control routines are applied to an existing problem of electron state transfer to determine if spin information can successfully be moved across a chain of donor atoms in silicon. The additional spin degrees of freedom are introduced into the formulation of the problem as well as the control optimization algorithm. We find a timescale of transfer for spin quantum information across the chain fitting with a t > π/A and t > 2π/A transfer pulse time corresponding with rotation of states on the electron Bloch sphere where A is the electron-nuclear coupling constant. Introduction of a magnetic field weakens transfer
efficiencies at high field strengths and prohibits anti-aligned nuclear states from transferring. We also develop a rudimentary theoretical model based on simulated results and partially validate the characteristic transfer times for spin states. This model also establishes a framework for future work including the introduction of a magnetic field.
efficiencies at high field strengths and prohibits anti-aligned nuclear states from transferring. We also develop a rudimentary theoretical model based on simulated results and partially validate the characteristic transfer times for spin states. This model also establishes a framework for future work including the introduction of a magnetic field.
ContributorsMorgan, Eric Robert (Author) / Treacy, Michael (Thesis director) / Whaley, K. Birgitta (Committee member) / Greenman, Loren (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Department of Physics (Contributor)
Created2015-05
Description
Pharmacokinetics describes the movement and processing of a drug in a body, while Pharmacodynamics describes the drug's effect on a given subject. Pharmacokinetic/Pharmacodynamic(Pk/Pd) models have become a fundamental tool when predicting bacterial behavior and drug development. In November of 2009, Katsube et al. published their paper detailing their Pk/Pd model for the drug Doripenem and the bacteria P. aeruginosa. In their paper, they determined that there is a dependent relationship between the drug's effectiveness and the dosing strategy of the drug. Therefore, this thesis has applied optimal control in order to optimize the drug's effectiveness, while not burdening the subject with the side effects of the drug. Optimal Control is a mathematical tool used to balance two competing factors. As a result, it has become a useful tool used to make decisions involving complex behavior. By using Optimal Control, the model will maximize the drug's effect on the bacterial population of P. aeruginosa, while minimizing the drug concentration of Doripenem. In doing so, our research will enable doctors and clinicians to maximize a drug's effectiveness on the body, while minimizing side effects.
ContributorsSawkins, Bryan Thomas (Author) / Camacho, Erika (Thesis director) / Wirkus, Stephen (Committee member) / School of Mathematical and Natural Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
Description
Unmanned aerial vehicles have received increased attention in the last decade due to their versatility, as well as the availability of inexpensive sensors (e.g. GPS, IMU) for their navigation and control. Multirotor vehicles, specifically quadrotors, have formed a fast growing field in robotics, with the range of applications spanning from surveil- lance and reconnaissance to agriculture and large area mapping. Although in most applications single quadrotors are used, there is an increasing interest in architectures controlling multiple quadrotors executing a collaborative task. This thesis introduces a new concept of control involving more than one quadrotors, according to which two quadrotors can be physically coupled in mid-flight. This concept equips the quadro- tors with new capabilities, e.g. increased payload or pursuit and capturing of other quadrotors. A comprehensive simulation of the approach is built to simulate coupled quadrotors. The dynamics and modeling of the coupled system is presented together with a discussion regarding the coupling mechanism, impact modeling and additional considerations that have been investigated. Simulation results are presented for cases of static coupling as well as enemy quadrotor pursuit and capture, together with an analysis of control methodology and gain tuning. Practical implementations are introduced as results show the feasibility of this design.
ContributorsLarsson, Daniel (Author) / Artemiadis, Panagiotis (Thesis advisor) / Marvi, Hamidreza (Committee member) / Berman, Spring (Committee member) / Arizona State University (Publisher)
Created2016
Description
Infectious diseases are a leading cause of death worldwide. With the development of drugs, vaccines and antibiotics, it was believed that for the first time in human history diseases would no longer be a major cause of mortality. Newly emerging diseases, re-emerging diseases and the emergence of microorganisms resistant to existing treatment have forced us to re-evaluate our optimistic perspective. In this study, a simple mathematical framework for super-infection is considered in order to explore the transmission dynamics of drug-resistance. Through its theoretical analysis, we identify the conditions necessary for the coexistence between sensitive strains and drug-resistant strains. Farther, in order to investigate the effectiveness of control measures, the model is extended so as to include vaccination and treatment. The impact that these preventive and control measures may have on its disease dynamics is evaluated. Theoretical results being confirmed via numerical simulations. Our theoretical results on two-strain drug-resistance models are applied in the context of Malaria, antimalarial drugs, and the administration of a possible partially effective vaccine. The objective is to develop a monitoring epidemiological framework that help evaluate the impact of antimalarial drugs and partially-effective vaccine in reducing the disease burden at the population level. Optimal control theory is applied in the context of this framework in order to assess the impact of time dependent cost-effective treatment efforts. It is shown that cost-effective combinations of treatment efforts depend on the population size, cost of implementing treatment controls, and the parameters of the model. We use these results to identify optimal control strategies for several scenarios.
ContributorsUrdapilleta, Alicia (Author) / Castillo-Chavez, Carlos (Thesis advisor) / Wang, Xiaohong (Thesis advisor) / Wirkus, Stephen (Committee member) / Camacho, Erika (Committee member) / Arizona State University (Publisher)
Created2011
Energy efficient optimal formation control of a multiple quadrotor UAV system with uncertain payload
Description
This thesis presents the design and simulation of an energy efficient controller for a system of three drones transporting a payload in a net. The object ensnared in the net is represented as a mass connected by massless stiff springs to each drone. Both a pole-placement approach and an optimal control approach are used to design a trajectory controller for the system. Results are simulated for a single drone and the three drone system both without and with payload.
ContributorsHayden, Alexander (Author) / Grewal, Anoop (Thesis director) / Berman, Spring (Committee member) / Barrett, The Honors College (Contributor) / Mechanical and Aerospace Engineering Program (Contributor) / Historical, Philosophical & Religious Studies, Sch (Contributor)
Created2022-05
Description
Multi-segment manipulators and mobile robot collectives are examples of multi-agent robotic systems, in which each segment or robot can be considered an agent. Fundamental motion control problems for such systems include the stabilization of one or more agents to target configurations or trajectories while preventing inter-agent collisions, agent collisions with obstacles, and deadlocks. Despite extensive research on these control problems, there are still challenges in designing controllers that (1) are scalable with the number of agents; (2) have theoretical guarantees on collision-free agent navigation; and (3) can be used when the states of the agents and the environment are only partially observable. Existing centralized and distributed control architectures have limited scalability due to their computational complexity and communication requirements, while decentralized control architectures are often effective only under impractical assumptions that do not hold in real-world implementations. The main objective of this dissertation is to develop and evaluate decentralized approaches for multi-agent motion control that enable agents to use their onboard sensors and computational resources to decide how to move through their environment, with limited or absent inter-agent communication and external supervision. Specifically, control approaches are designed for multi-segment manipulators and mobile robot collectives to achieve position and pose (position and orientation) stabilization, trajectory tracking, and collision and deadlock avoidance. These control approaches are validated in both simulations and physical experiments to show that they can be implemented in real-time while remaining computationally tractable. First, kinematic controllers are proposed for position stabilization and trajectory tracking control of two- or three-dimensional hyper-redundant multi-segment manipulators. Next, robust and gradient-based feedback controllers are presented for individual holonomic and nonholonomic mobile robots that achieve position stabilization, trajectory tracking control, and obstacle avoidance. Then, nonlinear Model Predictive Control methods are developed for collision-free, deadlock-free pose stabilization and trajectory tracking control of multiple nonholonomic mobile robots in known and unknown environments with obstacles, both static and dynamic. Finally, a feedforward proportional-derivative controller is defined for collision-free velocity tracking of a moving ground target by multiple unmanned aerial vehicles.
ContributorsSalimi Lafmejani, Amir (Author) / Berman, Spring (Thesis advisor) / Tsakalis, Konstantinos (Thesis advisor) / Papandreou-Suppappola, Antonia (Committee member) / Marvi, Hamidreza (Committee member) / Arizona State University (Publisher)
Created2022
Description
This dissertation discusses continuous-time reinforcement learning (CT-RL) for control of affine nonlinear systems. Continuous-time nonlinear optimal control problems hold great promise in real-world applications. After decades of development, reinforcement learning (RL) has achieved some of the greatest successes as a general nonlinear control design method. Yet as RL control has developed, CT-RL results have greatly lagged their discrete-time RL (DT-RL) counterparts, especially in regards to real-world applications. Current CT-RL algorithms generally fall into two classes: adaptive dynamic programming (ADP), and actor-critic deep RL (DRL). The first school of ADP methods features elegant theoretical results stemming from adaptive and optimal control. Yet, they have not been shown effectively synthesizing meaningful controllers. The second school of DRL has shown impressive learning solutions, yet theoretical guarantees are still to be developed. A substantive analysis uncovering the quantitative causes of the fundamental gap between CT and DT remains to be conducted. Thus, this work develops a first-of-its kind quantitative evaluation framework to diagnose the performance limitations of the leading CT-RL methods. This dissertation also introduces a suite of new CT-RL algorithms which offers both theoretical and synthesis guarantees. The proposed design approach relies on three important factors. First, for physical systems that feature physically-motivated dynamical partitions into distinct loops, the proposed decentralization method breaks the optimal control problem into smaller subproblems. Second, the work introduces a new excitation framework to improve persistence of excitation (PE) and numerical conditioning via classical input/output insights. Third, the method scales the learning problem via design-motivated invertible transformations of the system state variables in order to modulate the algorithm learning regression for further increases in numerical stability. This dissertation introduces a suite of (decentralized) excitable integral reinforcement learning (EIRL) algorithms implementing these paradigms. It rigorously proves convergence, optimality, and closed-loop stability guarantees of the proposed methods, which are demonstrated in comprehensive comparative studies with the leading methods in ADP on a significant application problem of controlling an unstable, nonminimum phase hypersonic vehicle (HSV). It also conducts comprehensive comparative studies with the leading DRL methods on three state-of-the-art (SOTA) environments, revealing new performance/design insights.
ContributorsWallace, Brent Abraham (Author) / Si, Jennie (Thesis advisor) / Berman, Spring M (Committee member) / Bertsekas, Dimitri P (Committee member) / Tsakalis, Konstantinos S (Committee member) / Arizona State University (Publisher)
Created2024
Description
There has been a vast increase in applications of Unmanned Aerial Vehicles (UAVs) in civilian domains. To operate in the civilian airspace, a UAV must be able to sense and avoid both static and moving obstacles for flight safety. While indoor and low-altitude environments are mainly occupied by static obstacles, risks in space of higher altitude primarily come from moving obstacles such as other aircraft or flying vehicles in the airspace. Therefore, the ability to avoid moving obstacles becomes a necessity
for Unmanned Aerial Vehicles.
Towards enabling a UAV to autonomously sense and avoid moving obstacles, this thesis makes the following contributions. Initially, an image-based reactive motion planner is developed for a quadrotor to avoid a fast approaching obstacle. Furthermore, A Dubin’s curve based geometry method is developed as a global path planner for a fixed-wing UAV to avoid collisions with aircraft. The image-based method is unable to produce an optimal path and the geometry method uses a simplified UAV model. To compensate
these two disadvantages, a series of algorithms built upon the Closed-Loop Rapid Exploratory Random Tree are developed as global path planners to generate collision avoidance paths in real time. The algorithms are validated in Software-In-the-Loop (SITL) and Hardware-In-the-Loop (HIL) simulations using a fixed-wing UAV model and in real flight experiments using quadrotors. It is observed that the algorithm enables a UAV to avoid moving obstacles approaching to it with different directions and speeds.
for Unmanned Aerial Vehicles.
Towards enabling a UAV to autonomously sense and avoid moving obstacles, this thesis makes the following contributions. Initially, an image-based reactive motion planner is developed for a quadrotor to avoid a fast approaching obstacle. Furthermore, A Dubin’s curve based geometry method is developed as a global path planner for a fixed-wing UAV to avoid collisions with aircraft. The image-based method is unable to produce an optimal path and the geometry method uses a simplified UAV model. To compensate
these two disadvantages, a series of algorithms built upon the Closed-Loop Rapid Exploratory Random Tree are developed as global path planners to generate collision avoidance paths in real time. The algorithms are validated in Software-In-the-Loop (SITL) and Hardware-In-the-Loop (HIL) simulations using a fixed-wing UAV model and in real flight experiments using quadrotors. It is observed that the algorithm enables a UAV to avoid moving obstacles approaching to it with different directions and speeds.
ContributorsLin, Yucong (Author) / Saripalli, Srikanth (Thesis advisor) / Scowen, Paul (Committee member) / Fainekos, Georgios (Committee member) / Thangavelautham, Jekanthan (Committee member) / Youngbull, Cody (Committee member) / Arizona State University (Publisher)
Created2015
Description
The 2009-10 influenza and the 2014-15 Ebola pandemics brought once again urgency to an old question: What are the limits on prediction and what can be proposed that is useful in the face of an epidemic outbreak?
This thesis looks first at the impact that limited access to vaccine stockpiles may have on a single influenza outbreak. The purpose is to highlight the challenges faced by populations embedded in inadequate health systems and to identify and assess ways of ameliorating the impact of resource limitations on public health policy.
Age-specific per capita constraint rates play an important role on the dynamics of communicable diseases and, influenza is, of course, no exception. Yet the challenges associated with estimating age-specific contact rates have not been decisively met. And so, this thesis attempts to connect contact theory with age-specific contact data in the context of influenza outbreaks in practical ways. In mathematical epidemiology, proportionate mixing is used as the preferred theoretical mixing structure and so, the frame of discussion of this dissertation follows this specific theoretical framework. The questions that drive this dissertation, in the context of influenza dynamics, proportionate mixing, and control, are:
I. What is the role of age-aggregation on the dynamics of a single outbreak? Or simply speaking, does the number and length of the age-classes used to model a population make a significant difference on quantitative predictions?
II. What would the age-specific optimal influenza vaccination policies be? Or, what are the age-specific vaccination policies needed to control an outbreak in the presence of limited or unlimited vaccine stockpiles?
Intertwined with the above questions are issues of resilience and uncertainty including, whether or not data collected on mixing (by social scientists) can be used effectively to address both questions in the context of influenza and proportionate mixing. The objective is to provide answers to these questions by assessing the role of aggregation (number and length of age classes) and model robustness (does the aggregation scheme selected makes a difference on influenza dynamics and control) via comparisons between purely data-driven model and proportionate mixing models.
This thesis looks first at the impact that limited access to vaccine stockpiles may have on a single influenza outbreak. The purpose is to highlight the challenges faced by populations embedded in inadequate health systems and to identify and assess ways of ameliorating the impact of resource limitations on public health policy.
Age-specific per capita constraint rates play an important role on the dynamics of communicable diseases and, influenza is, of course, no exception. Yet the challenges associated with estimating age-specific contact rates have not been decisively met. And so, this thesis attempts to connect contact theory with age-specific contact data in the context of influenza outbreaks in practical ways. In mathematical epidemiology, proportionate mixing is used as the preferred theoretical mixing structure and so, the frame of discussion of this dissertation follows this specific theoretical framework. The questions that drive this dissertation, in the context of influenza dynamics, proportionate mixing, and control, are:
I. What is the role of age-aggregation on the dynamics of a single outbreak? Or simply speaking, does the number and length of the age-classes used to model a population make a significant difference on quantitative predictions?
II. What would the age-specific optimal influenza vaccination policies be? Or, what are the age-specific vaccination policies needed to control an outbreak in the presence of limited or unlimited vaccine stockpiles?
Intertwined with the above questions are issues of resilience and uncertainty including, whether or not data collected on mixing (by social scientists) can be used effectively to address both questions in the context of influenza and proportionate mixing. The objective is to provide answers to these questions by assessing the role of aggregation (number and length of age classes) and model robustness (does the aggregation scheme selected makes a difference on influenza dynamics and control) via comparisons between purely data-driven model and proportionate mixing models.
ContributorsMorales, Romarie (Author) / Castillo-Chavez, Carlos (Thesis advisor) / Mubayi, Anuj (Thesis advisor) / Towers, Sherry (Committee member) / Arizona State University (Publisher)
Created2016