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Articles 1 - 30 of 64
Full-Text Articles in Aerospace Engineering
Design And Simulation Of An Ai-Powered Autonomous Quadrotor Framework For Search And Rescue Operations, James J. Shope
Design And Simulation Of An Ai-Powered Autonomous Quadrotor Framework For Search And Rescue Operations, James J. Shope
Graduate Theses, Dissertations, and Problem Reports (ETD)
Unmanned aerial vehicles (UAVs), particularly quadrotor platforms, have proven to be indispensable tools for search and rescue (SAR) teams due to their maneuverability, rapid deployment, and affordable operation. The current SAR use cases of quadrotors span from aerial surveillance to mission planning and strategic deliveries. However, most SAR applications remain passive or semi-autonomous, such that they rely on human-operated control or data assessment. Advancements in autonomous control strategies bring about a future where a single SAR operator can program and deploy several UAVs. This thesis details the development and simulation of a fully autonomous, AI-powered quadrotor framework capable of detecting …
Influence Of Actuated Air Brakes On The Apogee Of Sub-Orbital Rockets, Michael L. Farha
Influence Of Actuated Air Brakes On The Apogee Of Sub-Orbital Rockets, Michael L. Farha
Graduate Theses, Dissertations, and Problem Reports (ETD)
Collegiate engineering competitions have played a foundational role in the educational outcomes of university students for as long as they have existed. Among these competitions is the Spaceport America Cup, which challenges students to design, build, and launch high-power rockets with the incentive to fly as close as possible to a pre-established target apogee. Many teams competing in this competition have chosen to approach the challenge by incorporating deployable air brakes into their rocket designs. This approach comes with many uncertainties, both in controls and aerodynamics. For teams just starting out, aerodynamic performance is often one of the most challenging …
Reactive Model-Free Control For Underactuated Vehicles Operating In Resource-Constrained Environments, Austin Lane Sponaugle
Reactive Model-Free Control For Underactuated Vehicles Operating In Resource-Constrained Environments, Austin Lane Sponaugle
Graduate Theses, Dissertations, and Problem Reports (ETD)
Buoyancy-driven, underactuated vehicles offer a compelling solution for long-duration autonomous operations in constrained environments. By leveraging buoyancy to generate lift, these vehicles can remain aloft for extended periods with minimal power requirements, making them well-suited for applications in atmospheric monitoring, planetary exploration, and communications. However, their limited actuation authority, strong coupling with environmental forces, and operating domains introduce significant control challenges, including nonlinearity, sensitivity to external disturbances, and limited observability.
This work investigates the design and implementation of lightweight, reactive model-free control strategies that enable robust autonomy in such constrained settings. A digital Extremum Seeking Controller (ESC) is first implemented …
Deep Target Recognition: Semi-Supervised Annotation, Sensor Fusion And Super-Resolution, Shoaib Meraj Sami
Deep Target Recognition: Semi-Supervised Annotation, Sensor Fusion And Super-Resolution, Shoaib Meraj Sami
Graduate Theses, Dissertations, and Problem Reports (ETD)
Despite the recent expansion of machine learning algorithms to cover a wide range of disciplines, several areas of automatic target recognition (ATR) remain underexplored. This dissertation presents tools developed to improve performance in three significant aspects of ATR: semi-supervised annotation, sensor fusion, and image super-resolution. The aim of the semi-supervised methods is to automatically annotate targets in scenarios where labeled data are scarce in the target domain but available in the source domain. Secondly, to address the limitations of individual image sensors and enhance robustness under different environmental conditions and man-made constraints, a sensor fusion algorithm was developed to improve …
End-To-End Neural Network Based Optimal Control For Asymmetric Quadrotor Uas, Ross O'Hara
End-To-End Neural Network Based Optimal Control For Asymmetric Quadrotor Uas, Ross O'Hara
Graduate Theses, Dissertations, and Problem Reports (ETD)
This thesis presents the development and evaluation of a neural network-based optimal controller for asymmetrically loaded quadrotor unmanned aerial systems (UAS). Traditional control strategies such as PID are typically designed under symmetry assumptions and often degrade in performance when faced with significant loading asymmetries. To address this, a six-degree-of-freedom quadrotor model incorporating rotor dynamics and center-of-mass offsets was developed. A trajectory optimization framework using MATLAB’s fmincon solver generated over 50,000 energy-optimal trajectories across symmetric and asymmetric conditions. These were used to train a range of feedforward neural network architectures in a full-factorial study.
The best-performing controller was identified, having five …
Novel Design And Fabrication Of A High-Speed Transient Heat Flux Sensor For Application To Rotating Detonation Engines, Zachary Todd Tallman
Novel Design And Fabrication Of A High-Speed Transient Heat Flux Sensor For Application To Rotating Detonation Engines, Zachary Todd Tallman
Graduate Theses, Dissertations, and Problem Reports (ETD)
Rotating detonation engine (RDE) combustion systems have been a topic of interest in the pressure gain combustion community for their benefits over traditional gas turbine engine combustors. However, cooling requirements for these engines are significantly higher and less predictable than those of non-detonating engines. To understand and quantify the high-speed heat transfer dynamics within an RDE, a novel high-frequency heat flux sensor is presented. This study aims to design a robust, single-sided sensor that can withstand the high temperature and harsh environment of an RDE for extended durations. Screen printing is used to deposit a layered, platinum-yttria-stabilized zirconia (YSZ) film …
Implementation Of A Neural Network Execution Framework For Generalized And Cross-Platform Deep Learning Deployment And Inference On Spacecraft Systems, Rafael Polanco Segovia
Implementation Of A Neural Network Execution Framework For Generalized And Cross-Platform Deep Learning Deployment And Inference On Spacecraft Systems, Rafael Polanco Segovia
Graduate Theses, Dissertations, and Problem Reports (ETD)
Recent advances in hardware and software technology have made it possible to implement more resource-demanding deep learning algorithms in constrained hardware environments. This creates opportunities to use deep learning for aerospace applications on increasingly smaller aerospace vehicles. This work presents the implementation of a Neural Network Execution Framework (NNEF), which aims to provide a cross-platform and reusable framework to deploy and execute trained neural networks for deep learning aerospace applications. The NNEF executes any neural network inference process regardless of the original deep learning framework in which it was created, for supported flight software platforms, and space-like computer boards. Users …
Physics-Informed Neural Network Based Aerodynamic Modeling Framework, Nathaniel E. Michek
Physics-Informed Neural Network Based Aerodynamic Modeling Framework, Nathaniel E. Michek
Graduate Theses, Dissertations, and Problem Reports (ETD)
Significant advances have been made in developing aerodynamic models over the years. While these advances span many modeling techniques and data collection methods, certain aerodynamic regimes still pose significant challenges. These regimes commonly occur when an aerodynamic body is under extreme flight conditions. Many of these conditions occur simultaneously in the rare and poorly understood case of a tumbling aerodynamic body. The flight of a tumbling aerodynamic body goes through the entire range of aerodynamic angles, alpha and beta, causing significant non-linearities and time-dependent effects associated with flow separation. During tumbling, the aerodynamic body simultaneously rotates about all three axes …
Evaluation Of Small Unmanned Tailsitter Hybrid Air Vehicles Via Full Flight Simulation, Andrew Spencer Winters
Evaluation Of Small Unmanned Tailsitter Hybrid Air Vehicles Via Full Flight Simulation, Andrew Spencer Winters
Graduate Theses, Dissertations, and Problem Reports (ETD)
Small Unmanned Aerial Vehicles have exploded in popularity in the past 15 years among researchers and for industrial uses such as agriculture, search and rescue, and infrastructure inspection. Fixed wing and multirotor designs present two major paths that can be taken with these technologies. Fixed wing platforms have superior aerodynamic efficiency but require large areas for takeoff/landing and cannot hold a constant position in space, limiting their use. Multirotor configurations offer a more versatile platform that can maneuver in 3 dimensions independently but lack the endurance of fixed wing vehicles. This thesis analyses a quadrotor biplane and a variable wingspan …
Parameter Estimation Of A 100 Seater Simulated Passenger Aircraft, Michael James Winston
Parameter Estimation Of A 100 Seater Simulated Passenger Aircraft, Michael James Winston
Graduate Theses, Dissertations, and Problem Reports (ETD)
Virtual flight test aircraft provide good opportunities to test new parameter estimation methods. However, good estimates for the parameters in VIRTTAC Castor, a virtual test aircraft, are unavailable. This thesis uses two well-established time domain methods, the Output Error Method and the Filter Error Method, to estimate the parameters of VIRTTAC Castor. Three standard maneuvers were used: Elevator 3-2-1-1, Rudder Doublet, and Aileron Multi-Step. The parameters were estimated across three different flight conditions: weight, altitude and air speed, which resulted in 27 tests for each maneuver. All parameters, and standard deviations estimated are included in the appendix as a table.
On Uncertainty For Ill-Posed Robot Decision Problems, Jared Joseph Beard
On Uncertainty For Ill-Posed Robot Decision Problems, Jared Joseph Beard
Graduate Theses, Dissertations, and Problem Reports (ETD)
As robots adopt more real world responsibilities, they will be expected to solve more complicated problems. In some cases limited prior knowledge will result in unmodelled environmental conditions; in others, multiple users may have competing perspectives on how to frame a decision problem. Many existing frameworks, namely Markov decision processes (MDP) presuppose users have identified a specific problem with models sufficient to solve or learn a problem. If we wish to extend MDPs to novel problems or those heavily dependent on user feedback, autonomous decision makers must be able to identify limitations in how a given problem is framed and …
Dynamic Load Identification Using Optimal Sensor Placement And Dynamic Condensation Methods, Iole Pecora
Dynamic Load Identification Using Optimal Sensor Placement And Dynamic Condensation Methods, Iole Pecora
Graduate Theses, Dissertations, and Problem Reports (ETD)
Knowledge of excitation loads that structures experience during their service life is pivotal in different engineering fields, not only from a structural design optimization point of view but also as prevention of possible damages to the structures themselves. However, in case of dynamic events such as tornadoes, structures subjected to impulsive load due to their vicinity of explosions, the excitation load cannot be directly determined through direct measurements. In these scenarios, the inverse problem is used, and it is called load identification. This type of problem tries to determine the excitation load knowing the system response through a series of …
Embedded State Estimation For Optimization Of Cislunar Space Domain Awareness Constellation Design, Thomas Henry Clareson
Embedded State Estimation For Optimization Of Cislunar Space Domain Awareness Constellation Design, Thomas Henry Clareson
Graduate Theses, Dissertations, and Problem Reports (ETD)
The traffic in cislunar space is expected to increase over the coming years, leading to a higher likelihood of conjunction events among active satellites, orbital debris, and non-cooperative satellites. This increase necessitates enhanced space domain awareness (SDA) capabilities that include state estimation for targets of interest. Both Earth surface-based and space-based observation platforms in geosynchronous orbit or below face challenges such as range, exclusion, and occlusion that hinder observation. Motivated by the need to place space-based observers in the cislunar space regime to overcome these challenges, this paper proposes a cislunar SDA constellation design and analysis framework that integrates state …
Cellular Level Changes Induced In Cancer Cells Due To Microgravity, Sai Deepika Reddy Yaram
Cellular Level Changes Induced In Cancer Cells Due To Microgravity, Sai Deepika Reddy Yaram
Graduate Theses, Dissertations, and Problem Reports (ETD)
The increase in human activity in space has revealed several kinds of physiological challenges brought on by the absence of Earth's gravitational pull. NASA observed that during spaceflight, astronauts experience a 1-1.5% monthly loss in the mineral density of weight-bearing bones, with rehabilitation efforts on Earth often proving ineffective. This issue extends to muscles, the neuro vestibular system, the cardiovascular system, and vision. Cancer has emerged as a significant cause of mortality among astronauts, with studies up to 2017 showing that 41.3% of natural cause deaths among U.S. astronauts were due to cancer, primarily due to space radiation exposure. Cancer …
Venus Balloon Localization: A Map-Aided Navigation Approach Supported By A Single-Satellite, Heath Scott Cottrill
Venus Balloon Localization: A Map-Aided Navigation Approach Supported By A Single-Satellite, Heath Scott Cottrill
Graduate Theses, Dissertations, and Problem Reports (ETD)
Although Venus and Earth began as twins, possessing comparable size, mass, and composition, past exploration missions have revealed that Venus is now hellishly hot, devoid of oceans, and enveloped in a carbon dioxide-filled atmosphere. To understand when and why this evolutionary divergence occurred, further exploration is required. Today, there is a growing interest in the use of aerial platforms to circumvent the harsh conditions at the surface, which limit the lifetime of landed instruments. In this concept, a single balloon, propelled by the ambient wind field, would operate in the atmosphere at an altitude between 50 and 70 km, where …
Machine Learning-Assisted Multiscale Simulation And Design Optimization Of Composite Jackets Under Low-Velocity Impacts, Masoud Mohammadi
Machine Learning-Assisted Multiscale Simulation And Design Optimization Of Composite Jackets Under Low-Velocity Impacts, Masoud Mohammadi
Graduate Theses, Dissertations, and Problem Reports (ETD)
This research presents the development of a data-driven machine learning-assisted approach to simulate and optimize the design of composite materials subjected to low-velocity impacts. It focuses on a specific type of hybrid composite comprised of fiberglass and Kevlar fabrics stitched with Kevlar threads. The study begins by creating a multiscale finite element simulation for the composite under a low-velocity impact, which operates across three scales: microscale, mesoscale, and macroscale. This simulation accepts various inputs, such as different layer configurations and orientations, and provides impact outputs including maximum load and energy absorption capacity and displacement at failure.
Python and MATLAB scripts …
Integrated Immunity-Based Methodology For Uav Monitoring And Control, Ryan G. Mclaughlin
Integrated Immunity-Based Methodology For Uav Monitoring And Control, Ryan G. Mclaughlin
Graduate Theses, Dissertations, and Problem Reports (ETD)
A general integrated and comprehensive health management framework based on the artificial immune system (AIS) paradigm is formulated and an automated system is developed and tested through simulation for the detection, identification, evaluation, and accommodation (DIEA) of abnormal conditions (ACs) on an unmanned aerial vehicle (UAV). The proposed methodology involves the establishment of a body of data to represent the function of the vehicle under nominal conditions, called the self, and differentiating this operation from that of the vehicle under an abnormal condition, referred to as the non-self. Data collected from simulations of the selected UAV autonomously flying a set …
Design And Manufacture Of An Aerodynamic Body That Meets Scaling Law Requirements And Survives Severe G-Load Environment For Free-Flight Testing, Anthony R. Gonzalez
Design And Manufacture Of An Aerodynamic Body That Meets Scaling Law Requirements And Survives Severe G-Load Environment For Free-Flight Testing, Anthony R. Gonzalez
Graduate Theses, Dissertations, and Problem Reports (ETD)
Design and Manufacture of an Aerodynamic Body that Meets Scaling Law Requirements and Survives Severe G-load Environment for Free-Flight Testing
Anthony Gonzalez
Developing scale models to test functionality and ascertain aerodynamic properties is critical before manufacturing full-size products. Through dimensional analysis and similitude, engineers create scale models to test any parameter of interest. This research aims to design a scale model of an aerodynamic body for repeated free-flight testing. The Froude number is the dominant scale model law used to determine the geometric, mass, and inertia scaling laws. A critical requirement for this research is that the model should be …
Missile Modeling And Simulation Of Nominal And Abnormal Scenarios Resulting From External Damage, James Manuel Floyd Iii
Missile Modeling And Simulation Of Nominal And Abnormal Scenarios Resulting From External Damage, James Manuel Floyd Iii
Graduate Theses, Dissertations, and Problem Reports (ETD)
This thesis presents the development of a six-degree-of-freedom flight simulation environment for missiles and the application thereof to investigate the flight performance of missiles when exposed to external damage. The simulation environment was designed to provide a realistic representation of missile flight dynamics including aerodynamic effects, flight control systems, and self-guidance. The simulation environment was designed to be modular, expandable, and include realistic models of external damage to the missile body obtained by adversarial counteraction.
The primary objective of this research was to examine missile flight performance when subjected to unspecified external damage, including changes in trajectory, stability, and controllability, …
Spin Recovery Analysis On A Simulation Model Of The Nasa F-18 High Alpha Research Vehicle (Harv) Using Thrust Vectoring, Brock M. Dolly
Spin Recovery Analysis On A Simulation Model Of The Nasa F-18 High Alpha Research Vehicle (Harv) Using Thrust Vectoring, Brock M. Dolly
Graduate Theses, Dissertations, and Problem Reports (ETD)
In the early years of aviation, spins were poorly understood and frequently fatal. With just over a century of research and experiments dedicated to spins, today’s aviation world has a very firm grasp on spin aerodynamics. Most fighter aircraft have airframes and control surfaces specifically designed to ensure the ability of departure from the possible spin modes the aircraft can enter. An alternative and/or additional approach is given by thrust vectoring. Implementing thrust vectoring into spin recovery can potentially save an aircraft and/or the life of the pilot in situation where control-surface-only spin recovery is not able to recover the …
Design And Validation Of An Aerodynamic System For A Formula Sae® Vehicle Using Vehicle Dynamic Simulation And Experimentation, Evan S. Cole
Design And Validation Of An Aerodynamic System For A Formula Sae® Vehicle Using Vehicle Dynamic Simulation And Experimentation, Evan S. Cole
Graduate Theses, Dissertations, and Problem Reports (ETD)
This thesis presents the design, simulation, and experimental validation for the aerodynamic system for a Formula SAE® vehicle. The Society of Automotive Engineers ® (SAE) hosts a collegiate competition annually called Formula SAE® where students design, fabricate, and test a small “formula style” vehicle. The vehicle performs in relatively slow maneuvers, around different courses and tests to evaluate the vehicle’s overall performance. Over the years, collegiate teams have put significant research into the design and manufacturing of the aerodynamics of these vehicles. In order to justify this undertaking for future teams at West Virginia University’s Formula SAE® program, a comprehensive …
Motion Planning In Artificial And Natural Vector Fields, Bernardo Martinez Rocamora Junior
Motion Planning In Artificial And Natural Vector Fields, Bernardo Martinez Rocamora Junior
Graduate Theses, Dissertations, and Problem Reports (ETD)
This dissertation advances the field of autonomous vehicle motion planning in various challenging environments, ranging from flows and planetary atmospheres to cluttered real-world scenarios. By addressing the challenge of navigating environmental flows, this work introduces the Flow-Aware Fast Marching Tree algorithm (FlowFMT*). This algorithm optimizes motion planning for unmanned vehicles, such as UAVs and AUVs, navigating in tridimensional static flows. By considering reachability constraints caused by vehicle and flow dynamics, flow-aware neighborhood sets are found and used to reduce the number of calls to the cost function. The method computes feasible and optimal trajectories from start to goal in challenging …
Optimal Deployment Of Air Vehicle As Communication Relay For Multiple Ground Vehicles, Juan David Pabon Arias
Optimal Deployment Of Air Vehicle As Communication Relay For Multiple Ground Vehicles, Juan David Pabon Arias
Graduate Theses, Dissertations, and Problem Reports (ETD)
Heterogeneous teams of both air and ground mobile vehicles can combine the advantages of mobility, sensing capability, and operation time when performing complex tasks. However, when ground vehicles operate in cluttered environments with randomized obstacles, they may experience line of sight (LoS) obstructions and loss of communication due to those obstacles. To mitigate this issue, an airborne relay can be positioned in the vicinity of the ground vehicles to aid communication by establishing two-hop communication links between the vehicles.
This thesis develops an analytical framework to calculate the probability of spanning a two-hop communication between a pair of ground vehicles …
Robust State Estimation Methods For Robotics Applications, Shounak Das
Robust State Estimation Methods For Robotics Applications, Shounak Das
Graduate Theses, Dissertations, and Problem Reports (ETD)
State estimation is an integral component of any autonomous robotic system. Finding the correct position, velocity, and orientation of an agent in its environment enables it to do other tasks like mapping and interacting with the environment, and collaborating with other agents. State estimation is achieved by using data obtained from multiple sensors and fusing them in a probabilistic framework. These include inertial data from Inertial Measurement Unit (IMU), images from camera, range data from lidars, and positioning data from Global Navigation Satellite Systems (GNSS) receivers. The main challenge faced in sensor-based state estimation is the presence of noisy, erroneous, …
Optimal Path Planning For Aerial Robots Using Genetic Algorithm, Anna Puigvert I Juan
Optimal Path Planning For Aerial Robots Using Genetic Algorithm, Anna Puigvert I Juan
Graduate Theses, Dissertations, and Problem Reports (ETD)
This thesis presents a path optimization solution for a robot in two different constrained 3-dimensional (3D) environments. The robot is required to travel from its current position to a goal position following minimum cost paths (optimal paths). The first environment has 3D obstacles that interfere with the robot’s path. The path cost for this environment accounts for the minimum distance traveled by the robot from the start to the goal position while avoiding obstacles. The second environment is the atmosphere of Venus, specifically a flyable region of this atmosphere with characteristics similar to Earth’s. This environment has strong westward winds …
Probabilistic Short Term Solar Driver Forecasting With Neural Network Ensembles, Joshua Daniell
Probabilistic Short Term Solar Driver Forecasting With Neural Network Ensembles, Joshua Daniell
Graduate Theses, Dissertations, and Problem Reports (ETD)
Commonly utilized space weather indices and proxies drive predictive models for thermosphere density, directly impacting objects in low-Earth orbit (LEO) by influencing atmospheric drag forces. A set of solar proxies and indices (drivers), F10.7, S10.7, M10.7, and Y10.7, are created from a mixture of ground based radio observations and satellite instrument data. These solar drivers represent heating in various levels of the thermosphere and are used as inputs by the JB2008 empirical thermosphere density model. The United States Air Force (USAF) operational High Accuracy Satellite Drag Model (HASDM) relies on JB2008, and …
Aerodynamic Analysis Of Damage State Missiles Using Overset Meshing Techniques For Application To Computational Fluid Dynamics Simulation, Jonathan A. D'Alessio
Aerodynamic Analysis Of Damage State Missiles Using Overset Meshing Techniques For Application To Computational Fluid Dynamics Simulation, Jonathan A. D'Alessio
Graduate Theses, Dissertations, and Problem Reports (ETD)
Significant research over the years has aimed to redefine the flight capabilities of aircraft after sustaining structural damage to critical components. Flight survivability and controllability are key areas of concern when designing fault-tolerant flight control systems to handle a wide range of potential scenarios. However, there is a lack of research on the impact of physically damaged missile systems. Missile counter-defense and intercept capabilities have become more advanced as the United States has focused heavily on these areas over the years. Damaged missiles due to a kinetic intercept capability present an opportunity for analysis of the post-damage implications on flight …
Aerodynamic Performance Of A Biologically Inspired Hybrid Plasma-Mechanical Flow Control And Sensing Device, Joseph Dygert
Aerodynamic Performance Of A Biologically Inspired Hybrid Plasma-Mechanical Flow Control And Sensing Device, Joseph Dygert
Graduate Theses, Dissertations, and Problem Reports (ETD)
The continued high global demand for passenger and freight air traffic along with increased use of unmanned aerial vehicles operating in broader Reynolds number regimes has resulted in researchers examining alternative technologies, which would result in safer, more reliable, and superior performing aircraft. Aerodynamic flow control may be one of the most promising approaches to solving this problem, having already proven its ability to enable higher flow efficiency while simultaneously improving overall control of flow behavior such as laminar-to-turbulent transition. Recent research in aerodynamic flow control has seen a pronounced growth in the areas of biomimicry and plasma flow control …
Precise Landing Of Vtol Uavs Using A Tether, Jeremy W. Rathjen
Precise Landing Of Vtol Uavs Using A Tether, Jeremy W. Rathjen
Graduate Theses, Dissertations, and Problem Reports (ETD)
Unmanned Aerial Vehicles (UAVs), also known as drones, are often considered the solution to complex robotics problems. The significant freedom to explore an environment is a major reason why UAVs are a popular choice for automated solutions. UAVs, however, have a very limited flight time due to the low capacity and weight ratio of current batteries. One way to extend the vehicles' flight time is to use a tether to provide power from external batteries, generators on the ground, or another vehicle. Attaching a tether to a vehicle may constrain its navigation but it may also create some opportunities for …
Probabilistic Space Weather Modeling And Forecasting For The Challenge Of Orbital Drag In Space Traffic Management, Richard J. Licata Iii
Probabilistic Space Weather Modeling And Forecasting For The Challenge Of Orbital Drag In Space Traffic Management, Richard J. Licata Iii
Graduate Theses, Dissertations, and Problem Reports (ETD)
In the modern space age, private companies are crowding the already-congested low Earth orbit (LEO) regime with small satellite mega constellations. With over 25,000 objects larger than 10 cm already in LEO, this rapid expansion is forcing us towards the enterprise on Space Traffic Management (STM). STM is an operational effort that focuses on conjunction assessment and collision avoidance between objects. While the equations of motion for objects in orbit are well-known, there are many uncertain parameters that result in the uncertainty of an object's future position. The force that the atmosphere exerts on satellite - known as drag - …