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- All Subjects: Applied Mathematics
- Creators: Berman, Spring
Description
High-entropy alloys possessing mechanical, chemical, and electrical properties that far exceed those of conventional alloys have the potential to make a significant impact on many areas of engineering. Identifying element combinations and configurations to form these alloys, however, is a difficult, time-consuming, computationally intensive task. Machine learning has revolutionized many different fields due to its ability to generalize well to different problems and produce computationally efficient, accurate predictions regarding the system of interest. In this thesis, we demonstrate the effectiveness of machine learning models applied to toy cases representative of simplified physics that are relevant to high-entropy alloy simulation. We show these models are effective at learning nonlinear dynamics for single and multi-particle cases and that more work is needed to accurately represent complex cases in which the system dynamics are chaotic. This thesis serves as a demonstration of the potential benefits of machine learning applied to high-entropy alloy simulations to generate fast, accurate predictions of nonlinear dynamics.
ContributorsDaly, John H (Author) / Ren, Yi (Thesis director) / Zhuang, Houlong (Committee member) / Mechanical and Aerospace Engineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2021-05
Description
This thesis presents a process by which a controller used for collective transport tasks is qualitatively studied and probed for presence of undesirable equilibrium states that could entrap the system and prevent it from converging to a target state. Fields of study relevant to this project include dynamic system modeling, modern control theory, script-based system simulation, and autonomous systems design. Simulation and computational software MATLAB and Simulink® were used in this thesis.
To achieve this goal, a model of a swarm performing a collective transport task in a bounded domain featuring convex obstacles was simulated in MATLAB/ Simulink®. The closed-loop dynamic equations of this model were linearized about an equilibrium state with angular acceleration and linear acceleration set to zero. The simulation was run over 30 times to confirm system ability to successfully transport the payload to a goal point without colliding with obstacles and determine ideal operating conditions by testing various orientations of objects in the bounded domain. An additional purely MATLAB simulation was run to identify local minima of the Hessian of the navigation-like potential function. By calculating this Hessian periodically throughout the system’s progress and determining the signs of its eigenvalues, a system could check whether it is trapped in a local minimum, and potentially dislodge itself through implementation of a stochastic term in the robot controllers. The eigenvalues of the Hessian calculated in this research suggested the model local minima were degenerate, indicating an error in the mathematical model for this system, which likely incurred during linearization of this highly nonlinear system.
To achieve this goal, a model of a swarm performing a collective transport task in a bounded domain featuring convex obstacles was simulated in MATLAB/ Simulink®. The closed-loop dynamic equations of this model were linearized about an equilibrium state with angular acceleration and linear acceleration set to zero. The simulation was run over 30 times to confirm system ability to successfully transport the payload to a goal point without colliding with obstacles and determine ideal operating conditions by testing various orientations of objects in the bounded domain. An additional purely MATLAB simulation was run to identify local minima of the Hessian of the navigation-like potential function. By calculating this Hessian periodically throughout the system’s progress and determining the signs of its eigenvalues, a system could check whether it is trapped in a local minimum, and potentially dislodge itself through implementation of a stochastic term in the robot controllers. The eigenvalues of the Hessian calculated in this research suggested the model local minima were degenerate, indicating an error in the mathematical model for this system, which likely incurred during linearization of this highly nonlinear system.
ContributorsBaye-Wallace, Lily Catherine (Author) / Berman, Spring (Thesis director) / Marvi, Hamidreza (Committee member) / Mechanical and Aerospace Engineering Program (Contributor) / School of Music, Dance and Theatre (Contributor) / School for Engineering of Matter,Transport & Enrgy (Contributor) / Barrett, The Honors College (Contributor)
Created2020-12
Description
In the next decade or so, there will be a shift in the industry of transportation across the world. Already today we have autonomous vehicles (AVs) tested in the Greater Phoenix area showing that the technology has improved to a level available to the public eye. Although this technology is not yet released commercially (for the most part), it is being used and will continue to be used to develop a safer future. With a high incidence of human error causing accidents, many expect that autonomous vehicles will be safer than human drivers. They do still require driver attention and sometimes intervention to ensure safety, but for the most part are much safer. In just the United States alone, there were 40,000 deaths due to car accidents last year [1]. If traffic fatalities were considered a disease, this would be an epidemic. The technology behind autonomous vehicles will allow for a much safer environment and increased mobility and independence for people who cannot drive and struggle with public transport. There are many opportunities for autonomous vehicles in the transportation industry. Companies can save a lot more money on shipping by cutting the costs of human drivers and trucks on the road, even allowing for simpler drop shipments should the necessary AI be developed.Research is even being done by several labs at Arizona State University. For example, Dr. Spring Berman’s Autonomous Collective Systems Lab has been collaborating with Dr. Nancy Cooke of Human Systems Engineering to develop a traffic testbed, CHARTopolis, to study the risks of driver-AV interactions and the psychological effects of AVs on human drivers on a small scale. This testbed will be used by researchers from their labs and others to develop testing on reaction, trust, and user experience with AVs in a safe environment that simulates conditions similar to those experienced by full-size AVs. Using a new type of small robot that emulates an AV, developed in Dr. Berman’s lab, participants will be able to remotely drive around a model city environment and interact with other AV-like robots using the cameras and LiDAR sensors on the remotely driven robot to guide them.
Although these commercial and research systems are still in testing, it is important to understand how AVs are being marketed to the general public and how they are perceived, so that one day they may be effectively adopted into everyday life. People do not want to see a car they do not trust on the same roads as them, so the questions are: why don’t people trust them, and how can companies and researchers improve the trustworthiness of the vehicles?
Although these commercial and research systems are still in testing, it is important to understand how AVs are being marketed to the general public and how they are perceived, so that one day they may be effectively adopted into everyday life. People do not want to see a car they do not trust on the same roads as them, so the questions are: why don’t people trust them, and how can companies and researchers improve the trustworthiness of the vehicles?
ContributorsShuster, Daniel Nadav (Author) / Berman, Spring (Thesis director) / Cooke, Nancy (Committee member) / Mechanical and Aerospace Engineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2019-05
Description
This thesis details the design and construction of a torque-controlled robotic gripper for use with the Pheeno swarm robotics platform. This project required expertise from several fields of study including: robotic design, programming, rapid prototyping, and control theory. An electronic Inertial Measurement Unit and a DC Motor were both used along with 3D printed plastic components and an electronic motor control board to develop a functional open-loop controlled gripper for use in collective transportation experiments. Code was developed that effectively acquired and filtered rate of rotation data alongside other code that allows for straightforward control of the DC motor through experimentally derived relationships between the voltage applied to the DC motor and the torque output of the DC motor. Additionally, several versions of the physical components are described through their development.
ContributorsMohr, Brennan (Author) / Berman, Spring (Thesis director) / Ren, Yi (Committee member) / Mechanical and Aerospace Engineering Program (Contributor) / School for Engineering of Matter,Transport & Enrgy (Contributor) / Barrett, The Honors College (Contributor)
Created2019-05
Description
In this paper, we propose an autonomous throwing and catching system to be developed as a preliminary step towards the refinement of a robotic arm capable of improving strength and motor function in the limb. This will be accomplished by first autonomizing simpler movements, such as throwing a ball. In this system, an autonomous thrower will detect a desired target through the use of image processing. The launch angle and direction necessary to hit the target will then be calculated, followed by the launching of the ball. The smart catcher will then detect the ball as it is in the air, calculate its expected landing location based on its initial trajectory, and adjust its position so that the ball lands in the center of the target. The thrower will then proceed to compare the actual landing position with the position where it expected the ball to land, and adjust its calculations accordingly for the next throw. By utilizing this method of feedback, the throwing arm will be able to automatically correct itself. This means that the thrower will ideally be able to hit the target exactly in the center within a few throws, regardless of any additional uncertainty in the system. This project will focus of the controller and image processing components necessary for the autonomous throwing arm to be able to detect the position of the target at which it will be aiming, and for the smart catcher to be able to detect the position of the projectile and estimate its final landing position by tracking its current trajectory.
ContributorsLundberg, Kathie Joy (Co-author) / Thart, Amanda (Co-author) / Rodriguez, Armando (Thesis director) / Berman, Spring (Committee member) / Electrical Engineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
Description
Navigation and mapping in GPS-denied environments, such as coal mines ordilapidated buildings filled with smog or particulate matter, pose a significant challenge
due to the limitations of conventional LiDAR or vision systems. Therefore there
exists a need for a navigation algorithm and mapping strategy which do not use vision
systems but are still able to explore and map the environment. The map can further
be used by first responders and cave explorers to access the environments.
This thesis presents the design of a collision-resilient Unmanned Aerial Vehicle
(UAV), XPLORER that utilizes a novel navigation algorithm for exploration and
simultaneous mapping of the environment. The real-time navigation algorithm uses
the onboard Inertial Measurement Units (IMUs) and arm bending angles for contact
estimation and employs an Explore and Exploit strategy. Additionally, the quadrotor
design is discussed, highlighting its improved stability over the previous design.
The generated map of the environment can be utilized by autonomous vehicles to
navigate the environment. The navigation algorithm is validated in multiple real-time
experiments in different scenarios consisting of concave and convex corners and circular
objects. Furthermore, the developed mapping framework can serve as an auxiliary
input for map generation along with conventional LiDAR or vision-based mapping
algorithms.
Both the navigation and mapping algorithms are designed to be modular, making
them compatible with conventional UAVs also. This research contributes to the
development of navigation and mapping techniques for GPS-denied environments,
enabling safer and more efficient exploration of challenging territories.
ContributorsPandian Saravanakumaran, Aravind Adhith (Author) / Zhang, Wenlong (Thesis advisor) / Das, Jnaneshwar (Committee member) / Berman, Spring (Committee member) / Arizona State University (Publisher)
Created2023
Description
Multibody Dynamic (MBD) models are important tools in motion analysis and are used to represent and accurately predict the behavior of systems in the real-world. These models have a range of applications, including the stowage and deployment of flexible deployables on spacecraft, the dynamic response of vehicles in automotive design and crash testing, and mapping interactions of the human body. An accurate model can aid in the design of a system to ensure the system is effective and meets specified performance criteria when built. A model may have many design parameters, such as geometrical constraints and component mechanical properties, or controller parameters if the system uses an external controller. Varying these parameters and rerunning analyses by hand to find an ideal design can be time consuming for models that take hours or days to run. To reduce the amount of time required to find a set of parameters that produces a desired performance, optimization is necessary. Many papers have discussed methods for optimizing rigid and flexible MBD models, and separately their controllers, using both gradient-based and gradient-free algorithms. However, these optimization methods have not been used to optimize full-scale MBD models and their controllers simultaneously. This thesis presents a method for co-optimizing an MBD model and controller that allows for the flexibility to find model and controller-based solutions for systems with tightly coupled parameters. Specifically, the optimization is performed on a quadrotor drone MBD model undergoing disturbance from a slung load and its position controller to meet specified position error performance criteria. A gradient-free optimization algorithm and multiple objective approach is used due to the many local optima from the tradeoffs between the model and controller parameters. The thesis uses nine different quadrotor cases with three different position error formulations. The results are used to determine the effectiveness of the optimization and the ability to converge on a single optimal design. After reviewing the results, the optimization limitations are discussed as well as the ability to transition the optimization to work with different MBD models and their controllers.
ContributorsGambatese, Marcus (Author) / Zhang, Wenlong (Thesis advisor) / Berman, Spring (Committee member) / Inoyama, Daisaku (Committee member) / Arizona State University (Publisher)
Created2022
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
Description
National Airspace Systems (NAS) are complex cyber-physical systems that require swift air traffic management (ATM) to ensure flight safety and efficiency. With the surging demand for air travel and the increasing intricacy of aviation systems, the need for advanced technologies to support air traffic management and air traffic control (ATC) service has become more crucial than ever. Data-driven models or artificial intelligence (AI) have been conceptually investigated by various parties and shown immense potential, especially when provided with a vast volume of real-world data. These data include traffic information, weather contours, operational reports, terrain information, flight procedures, and aviation regulations. Data-driven models learn from historical experiences and observations and provide expeditious recommendations and decision support for various operation tasks, directly contributing to the digital transformation in aviation. This dissertation reports several research studies covering different aspects of air traffic management and ATC service utilizing data-driven modeling, which are validated using real-world big data (flight tracks, flight events, convective weather, workload probes). These studies encompass a range of topics, including trajectory recommendations, weather studies, landing operations, and aviation human factors. Specifically, the topics explored are (i) trajectory recommendations under weather conditions, which examine the impact of convective weather on last on-file flight plans and provide calibrated trajectories based on convective weather; (ii) multi-aircraft trajectory predictions, which study the intention of multiple mid-air aircraft in the near-terminal airspace and provide trajectory predictions; (iii) flight scheduling operations, which involve probabilistic machine learning-enhanced optimization algorithms for robust and efficient aircraft landing sequencing; (iv) aviation human factors, which predict air traffic controller workload level from flight traffic data with conformalized graph neural network. The uncertainties associated with these studies are given special attention and addressed through Bayesian/probabilistic machine learning. Finally, discussions on high-level AI-enabled ATM research directions are provided, hoping to extend the proposed studies in the future. This dissertation demonstrates that data-driven modeling has great potential for aviation digital twins, revolutionizing the aviation decision-making process and enhancing the safety and efficiency of ATM. Moreover, these research directions are not merely add-ons to existing aviation practices but also contribute to the future of transportation, particularly in the development of autonomous systems.
ContributorsPang, Yutian (Author) / Liu, Yongming (Thesis advisor) / Yan, Hao (Committee member) / Zhuang, Houlong (Committee member) / Marvi, Hamid (Committee member) / Ren, Yi (Committee member) / Arizona State University (Publisher)
Created2023
Description
The introduction of assistive/autonomous features in cyber-physical systems, e.g., self-driving vehicles, have paved the way to a relatively new field of system analysis for safety-critical applications, along with the topic of controlling systems with performance and safety guarantees. The different works in this thesis explore and design methodologies that focus on the analysis of nonlinear dynamical systems via set-membership approximations, as well as the development of controllers and estimators that can give worst-case performance guarantees, especially when the sensor data containing information on system outputs is prone to data drops and delays. For analyzing the distinguishability of nonlinear systems, building upon the idea of set membership over-approximation of the nonlinear systems, a novel optimization-based method for multi-model affine abstraction (i.e., simultaneous set-membership over-approximation of multiple models) is designed. This work solves for the existence of set-membership over-approximations of a pair of different nonlinear models such that the different systems can be distinguished/discriminated within a guaranteed detection time under worst-case uncertainties and approximation errors. Specifically, by combining mesh-based affine abstraction methods with T-distinguishability analysis in the literature yields a bilevel bilinear optimization problem, whereby leveraging robust optimization techniques and a suitable change of variables result in a sufficient linear program that can obtain a tractable solution with T-distinguishability guarantees. Moreover, the thesis studied the designs of controllers and estimators with performance guarantees, and specifically, path-dependent feedback controllers and bounded-error estimators for time-varying affine systems are proposed that are subject to delayed observations or missing data. To model the delayed/missing data, two approaches are explored; a fixed-length language and an automaton-based model. Furthermore, controllers/estimators that satisfy the equalized recovery property (a weaker form of invariance with time-varying finite bounds) are synthesized whose feedback gains can be adapted based on the observed path, i.e., the history of observed data patterns up to the latest available time step. Finally, a robust kinodynamic motion planning algorithm is also developed with collision avoidance and probabilistic completeness guarantees. In particular, methods based on fixed and flexible invariant tubes are designed such that the planned motion/trajectories can reject bounded disturbances using noisy observations.
ContributorsHassaan, Syed Muhammad (Author) / Yong, Sze Zheng (Thesis advisor) / Rivera, Daniel (Committee member) / Marvi, Hamidreza (Committee member) / Lee, Hyunglae (Committee member) / Berman, Spring (Committee member) / Arizona State University (Publisher)
Created2023