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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 397 records · Page 22

Laser-boosted lightcraft technology demonstrator

The ultimate goal for this NASA/USRA-sponsored 'Apollo Lightcraft Project' is to develop a revolutionary manned launch vehicle technology that can potentially reduce payload transport costs by a factor of 1000 below the space shuttle orbiter. The Rensellaer design team proposes to utilize advanced, highly energetic, beamed-energy sources (laser, microwave) and innovative combined-cycle (airbreathing/rocket) engines to accomplish this goal. This year's effort, the detailed description and performance analysis of an unmanned 1.4-m Lightcraft Technology Demonstrator (LTD) drone, is presented. The novel launch system employs a 100-MW-class ground-based laser to transmit power directly to an advanced combined-cycle engine that propels the 120-kg LTD to orbit, with a mass ratio of two. The single-stage-to-orbit (SSTO) LTD machine then becomes an autonomous sensor satellite that can deliver precise, high-quality information typical of today's large orbital platforms. The dominant motivation behind this study is to provide an example of how laser propulsion and its low launch costs can induce a comparable order-of-magnitude reduction in sensor satellite packaging costs. The issue is simply one of production technology for future, survivable SSTO aerospace vehicles that intimately share both laser propulsion engine and satellite functional hardware. A mass production cost goal of 10(exp 3)/kg for the LTD vehicle is probably realizable.

Antonison, M.↗

Required Technologies for A 10-16 m UV-Visible-IR Telescope on the Moon

A successor to the Hubble Space Telescope, incorporating a 10 to 16 meter mirror, and operating in the UV-Visible-IR is being considered for emplacement on the Moon in the 21st Century. To take advantage of the characteristics of the lunar environment, such a telescope requires appropriate advances in technology. These technologies are in the areas of contamination/interference control, test and evaluation, manufacturing, construction, autonomous operations and maintenance, power and heating/cooling, stable precision structures, optics, parabolic antennas, and communications/control. This telescope for the lunar surface needs to be engineered to operate for long periods with minimal intervention by humans or robots. What is essential for lunar observatory operation is enforcement of a systems engineering approach that makes compatible all lunar operations associated with habitation, resource development, and science.

Johnson, Stewart W.↗

Deployment of Autonomous GPS Stations in Marie Byrd Land, Antarctica

During the 1998-1999 Antarctic field season, we installed three autonomous GPS stations in Marie Byrd Land, West Antarctica to measure glacio-isostatic rebound and rates of spreading across the West Antarctic Rift System. The systems collect data throughout the entire year and therefore must function during the warm, relatively mild summer, and cold, harsh winters. They are powered by gel cell batteries that are charged by wind and solar power. The system includes dual data logging capability. We log data at 5 minute intervals within the receiver and at 30 second intervals to a serial data logger. We do not require 365 days of continuous data for well determined crustal velocities, but rather long periods (greater than 24 hours) of continuous data distributed throughout the year. Therefore, for simplicity, we designed the system to accept occasional data interruptions. The batteries, in addition to supplying power, act as a thermal capacitive heat storage device to help regulate the temperatures within the system. This storage system absorbs the majority of the 10-15 watts of power from the receiver and 5 watts from the data logger which helps to maintain temperature for long periods of time. Power is switched off when the temperature within the system enclosure reaches 50'C and is reconnected at 20 C. If battery voltage drops too low the batteries will freeze. Therefore, we cut the power off when the batteries drop to a low voltage of 12.45V. Power is restored at 13.2V. The temperature and power hysteresis allows for a minimum of several days of data to be collected before system shutdowns. A check of all three stations in late January 1999 indicated that the thermal and power control systems are performing as expected. We plan to implement satellite telemetry to the systems during the 2000-2001 season following a year of development.

Donnellan, Andrea↗

Doppler Lidar Sensor for Precision Navigation in GPS-Deprived Environment

Landing mission concepts that are being developed for exploration of solar system bodies are increasingly ambitious in their implementations and objectives. Most of these missions require accurate position and velocity data during their descent phase in order to ensure safe, soft landing at the pre-designated sites. Data from the vehicle's Inertial Measurement Unit will not be sufficient due to significant drift error after extended travel time in space. Therefore, an onboard sensor is required to provide the necessary data for landing in the GPS-deprived environment of space. For this reason, NASA Langley Research Center has been developing an advanced Doppler lidar sensor capable of providing accurate and reliable data suitable for operation in the highly constrained environment of space. The Doppler lidar transmits three laser beams in different directions toward the ground. The signal from each beam provides the platform velocity and range to the ground along the laser line-of-sight (LOS). The six LOS measurements are then combined in order to determine the three components of the vehicle velocity vector, and to accurately measure altitude and attitude angles relative to the local ground. These measurements are used by an autonomous Guidance, Navigation, and Control system to accurately navigate the vehicle from a few kilometers above the ground to the designated location and to execute a gentle touchdown. A prototype version of our lidar sensor has been completed for a closed-loop demonstration onboard a rocket-powered terrestrial free-flyer vehicle.

Amzajerdian, F.↗

Clinical Decision Support - Concepts of Operation

We are entering a new era in space exploration to return to the moon and explore Mars. These ambitious goals will require significant changes to in-flight and habitat medical care due to constraints on mass, volume, power, crew time and medical evacuation capabilities. These constraints make it absolutely necessary to develop transformative solutions using new technologies. The Exploration Medical Capability (ExMC) Element of the Human Research Program (HRP) pushes the boundary of space medical systems to advance the care of astronauts on future exploration missions beyond low Earth orbit by identifying and testing next-generation medical care and crew health maintenance technologies. The Clinical Decision Support (CDS) project addresses the gap Medical-701 within the Inflight Medical Conditions risk: Enhance medical capabilities within an exploration medical system. For long-duration, deep space missions, computational and data resources will play an important role in maintaining crew health, wellness and performance where the crew will need to be more self-reliant. The aim of the CDS project is to develop and provide recommended requirements for an in-vehicle CDSS that acts as an assistant for delivering optimal health and performance and medical care during exploration missions. The CDSS is envisioned as a software-based tool that will augment a crewmembers’ knowledge, skills and abilities to assist in decision-making and crew health and performance (CHP) management thus increasing CHP systems capabilities. The human interface will be context aware and lessen the cognitive load to assimilate and use information as well as combine large disparate data sets in such a manner that provides the crew with actionable insight to decisions related to crew medical, health and performance management. Crew autonomy will be provided through a CDS that presents knowledge and data in a context aware manner to augment a crew members’ knowledge, skills and abilities during the process of observation, orientation, decisions and action. The CDS project addresses the need for crew members to operate independently during long duration space exploration missions that require medical Levels of Care (LoC) V, the highest level specified by NASA-STD-3001 and described in more detail by the ExMC interpretation of LoC document (NASA/TM-2017-219290), where significant changes to in-flight and habitat medical care necessitate increasing crew autonomy in decision making and task performance. The CDS project will develop and test a series of iterative and increasingly more complex system prototypes. These annual demonstrations of the data system integration with the crew health and performance domain will inform exploration medical system requirements for an on-board Clinical Decision Support System (CDSS) through a series of use cases that guide CDS prototype functionality. CDS concepts are based on ExMC Concept of Operations documents (presented separately) and will highlight architecture extensibility to other more complex analyses and tests using core crew health and performance integrated data management, processing and visualization capabilities. This approach also establishes how externally developed analyses and approaches could be added to expand a clinical decision support system and thus highlight how a comprehensive system can be commercially and/or globally developed. The CDS project will build upon the concept of an integrated data management approach based on the Medical Data Architecture (MDA) project to more fully address challenges associated with in-flight and habitat medical, health and performance care due to constraints on mass, volume, power, crew time and medical evacuation capabilities required for medical LoC V. These requirements will be derived through systems engineering approaches and software prototype developments over the course of the multi-year CDS project to address crew health and performance decision-making and task performance, often autonomously executed by the crew, in a manner that is consistent with the appropriate medical level of care for the mission. This presentation will provide an overview of the vision for the CDS project and highlight the initial accomplishments in project planning, implementation and requirements identification in fiscal year 2020.

clinical decision support↗

Clinical Decision Support - Overview and Update

We are entering a new era in space exploration to return to the moon and explore Mars. These ambitious goals will require significant changes to in-flight and habitat medical care due to constraints on mass, volume, power, crew time and medical evacuation capabilities. These constraints make it absolutely necessary to develop transformative solutions using new technologies. The Exploration Medical Capability (ExMC) Element of the Human Research Program (HRP) pushes the boundary of space medical systems to advance the care of astronauts on future exploration missions beyond low Earth orbit by identifying and testing next-generation medical care and crew health maintenance technologies. The Clinical Decision Support (CDS) project addresses the gap Medical-701 within the Inflight Medical Conditions risk: Enhance medical capabilities within an exploration medical system. For long-duration, deep space missions, computational and data resources will play an important role in maintaining crew health, wellness and performance where the crew will need to be more self-reliant. The aim of the CDS project is to develop and provide recommended requirements for an in-vehicle CDSS that acts as an assistant for delivering optimal health and performance and medical care during exploration missions. The CDSS is envisioned as a software-based tool that will augment a crewmembers’ knowledge, skills and abilities to assist in decision-making and crew health and performance (CHP) management thus increasing CHP systems capabilities. The human interface will be context aware and lessen the cognitive load to assimilate and use information as well as combine large disparate data sets in such a manner that provides the crew with actionable insight to decisions related to crew medical, health and performance management. Crew autonomy will be provided through a CDS that presents knowledge and data in a context aware manner to augment a crew members’ knowledge, skills and abilities during the process of observation, orientation, decisions and action. The CDS project addresses the need for crew members to operate independently during long duration space exploration missions that require medical Levels of Care (LoC) V, the highest level specified by NASA-STD-3001 and described in more detail by the ExMC interpretation of LoC document (NASA/TM-2017-219290), where significant changes to in-flight and habitat medical care necessitate increasing crew autonomy in decision making and task performance. The CDS project will develop and test a series of iterative and increasingly more complex system prototypes. These annual demonstrations of the data system integration with the crew health and performance domain will inform exploration medical system requirements for an on-board Clinical Decision Support System (CDSS) through a series of use cases that guide CDS prototype functionality. CDS concepts are based on ExMC Concept of Operations documents (presented separately) and will highlight architecture extensibility to other more complex analyses and tests using core crew health and performance integrated data management, processing and visualization capabilities. This approach also establishes how externally developed analyses and approaches could be added to expand a clinical decision support system and thus highlight how a comprehensive system can be commercially and/or globally developed. The CDS project will build upon the concept of an integrated data management approach based on the Medical Data Architecture (MDA) project to more fully address challenges associated with in-flight and habitat medical, health and performance care due to constraints on mass, volume, power, crew time and medical evacuation capabilities required for medical LoC V. These requirements will be derived through systems engineering approaches and software prototype developments over the course of the multi-year CDS project to address crew health and performance decision-making and task performance, often autonomously executed by the crew, in a manner that is consistent with the appropriate medical level of care for the mission. This presentation will provide an overview of the vision for the CDS project and highlight the initial accomplishments in project planning, implementation and requirements identification in fiscal year 2020.

clinical decision support system↗

A Self-Tuning Kalman Filter for Autonomous Spacecraft Navigation

Most navigation systems currently operated by NASA are ground-based, and require extensive support to produce accurate results. Recently developed systems that use Kalman Filter and Global Positioning System (GPS) data for orbit determination greatly reduce dependency on ground support, and have potential to provide significant economies for NASA spacecraft navigation. Current techniques of Kalman filtering, however, still rely on manual tuning from analysts, and cannot help in optimizing autonomy without compromising accuracy and performance. This paper presents an approach to produce a high accuracy autonomous navigation system fully integrated with the flight system. The resulting system performs real-time state estimation by using an Extended Kalman Filter (EKF) implemented with high-fidelity state dynamics model, as does the GPS Enhanced Orbit Determination Experiment (GEODE) system developed by the NASA Goddard Space Flight Center. Augmented to the EKF is a sophisticated neural-fuzzy system, which combines the explicit knowledge representation of fuzzy logic with the learning power of neural networks. The fuzzy-neural system performs most of the self-tuning capability and helps the navigation system recover from estimation errors. The core requirement is a method of state estimation that handles uncertainties robustly, capable of identifying estimation problems, flexible enough to make decisions and adjustments to recover from these problems, and compact enough to run on flight hardware. The resulting system can be extended to support geosynchronous spacecraft and high-eccentricity orbits. Mathematical methodology, systems and operations concepts, and implementation of a system prototype are presented in this paper. Results from the use of the prototype to evaluate optimal control algorithms implemented are discussed. Test data and major control issues (e.g., how to define specific roles for fuzzy logic to support the self-learning capability) are also discussed. In addition, architecture of a complete end-to-end candidate flight system that provides navigation with highly autonomous control using data from GPS is presented.

Truong, Son H.↗

The real-time control of planetary rovers through behavior modification

It is not yet clear of what type, and how much, intelligence is needed for a planetary rover to function semi-autonomously on a planetary surface. Current designs assume an advanced AI system that maintains a detailed map of its journeys and the surroundings, and that carefully calculates and tests every move in advance. To achieve these abilities, and because of the limitations of space-qualified electronics, the supporting rover is quite sizable, massing a large fraction of a ton, and requiring technology advances in everything from power to ground operations. An alternative approach is to use a behavior driven control scheme. Recent research has shown that many complex tasks may be achieved by programming a robot with a set of behaviors and activation or deactivating a subset of those behaviors as required by the specific situation in which the robot finds itself. Behavior control requires much less computation than is required by tradition AI planning techniques. The reduced computation requirements allows the entire rover to be scaled down as appropriate (only down-link communications and payload do not scale under these circumstances). The missions that can be handled by the real-time control and operation of a set of small, semi-autonomous, interacting, behavior-controlled planetary rovers are discussed.

Miller, David P.↗

A Framework for Testing Automated Detection, Diagnosis, and Remediation Systems on the Smart Grid

America's electrical grid is currently undergoing a multi-billion dollar modernization effort aimed at producing a highly reliable critical national infrastructure for power - a Smart Grid. While the goals for the Smart Grid include upgrades to accommodate large quantities of clean, but transient, renewable energy and upgrades to provide customers with real-time pricing information, perhaps the most important objective is to create an electrical grid with a greatly increased robustness.

autonomous detection, diagnosis, and remediation (↗

Lattice Confinement Fusion Fast Fission – A Hybrid Power System for Accessing Icy World Oceans

Lattice Confinement Fusion (LCF) is an emerging power technology that can be combined with nuclear fission to produce a hybrid innovative power system. The proposed innovation is a compact, scalable nuclear energy source that does not use highly enriched uranium (HEU), high-assay enriched uranium (HALEU), low enriched uranium (LEU) nor plutonium-238. The nuclear energy source consists of a hybrid fusion-fast-fission method whereby neutrons generated from LCF are used to fission materials such as depleted uranium or thorium. LCF has been demonstrated by both NASA (published in Physical Review C) and by Lawrence Berkeley National Laboratory (published in the Journal of Applied Physics). Although these methods are reminiscent of Low Energy Nuclear Reactions (LENR), both methods operate at much higher energies than any attempt at cold fusion. This new hybrid energy source is sufficient to provide power and heat for melting or boring through icy caps with untethered, autonomous probes. These probes can be used for planetary (i.e., Pluto), lunar (i.e., Enceladus), or asteroid (i.e., Ceres) exploration where icy caps are encountered. Each world may have a liquid water ocean beneath their ice crust. A robotic probe exploring the oceans beneath must either melt or bore through the ice crust first. Such a mission requires a small, but robust and long lived, electrical energy and heat source such as the LCF Fast Fission hybrid power system.

Theresa L. Benyo↗

J-2X Abort System Development

The J-2X is an expendable liquid hydrogen (LH2)/liquid oxygen (LOX) gas generator cycle rocket engine that is currently being designed as the primary upper stage propulsion element for the new NASA Ares vehicle family. The J-2X engine will contain abort logic that functions as an integral component of the Ares vehicle abort system. This system is responsible for detecting and responding to conditions indicative of impending Loss of Mission (LOM), Loss of Vehicle (LOV), and/or catastrophic Loss of Crew (LOC) failure events. As an earth orbit ascent phase engine, the J-2X is a high power density propulsion element with non-negligible risk of fast propagation rate failures that can quickly lead to LOM, LOV, and/or LOC events. Aggressive reliability requirements for manned Ares missions and the risk of fast propagating J-2X failures dictate the need for on-engine abort condition monitoring and autonomous response capability as well as traditional abort agents such as the vehicle computer, flight crew, and ground control not located on the engine. This paper describes the baseline J-2X abort subsystem concept of operations, as well as the development process for this subsystem. A strategy that leverages heritage system experience and responds to an evolving engine design as well as J-2X specific test data to support abort system development is described. The utilization of performance and failure simulation models to support abort system sensor selection, failure detectability and discrimination studies, decision threshold definition, and abort system performance verification and validation is outlined. The basis for abort false positive and false negative performance constraints is described. Development challenges associated with information shortfalls in the design cycle, abort condition coverage and response assessment, engine-vehicle interface definition, and abort system performance verification and validation are also discussed.

Santi, Louis M.↗

Publications of the NASA Controlled Ecological Life Support System (CELSS) Program, 1979-1989

Publications of research sponsored by the NASA Controlled Ecological Life Support System (CELSS) Program from 1979 to 1989 are listed. The CELSS Program encompasses research and technology with the goal of developing an autonomous bioregenerative life support system that continually recycles the solid, liquid, and gaseous materials essential for human life. The bibliography is divided into four major subject areas: food production, nutritional requirements, waste management, and systems management and control.

Wallace, Janice S.↗

NASA Tech Briefs, February 2004

Topics include: Simulation Testing of Embedded Flight Software; Improved Indentation Test for Measuring Nonlinear Elasticity; Ultraviolet-Absorption Spectroscopic Biofilm Monitor; Electronic Tongue for Quantitation of Contaminants in Water; Radar for Measuring Soil Moisture Under Vegetation; Modular Wireless Data-Acquisition and Control System; Microwave System for Detecting Ice on Aircraft; Routing Algorithm Exploits Spatial Relations; Two-Finger EKG Method of Detecting Evasive Responses; Updated System-Availability and Resource-Allocation Program; Routines for Computing Pressure Drops in Venturis; Software for Fault-Tolerant Matrix Multiplication; Reproducible Growth of High-Quality Cubic-SiC Layers; Nonlinear Thermoelastic Model for SMAs and SMA Hybrid Composites; Liquid-Crystal Thermosets, a New Generation of High-Performance Liquid-Crystal Polymers; Formulations for Stronger Solid Oxide Fuel-Cell Electrolytes; Simulation of Hazards and Poses for a Rocker-Bogie Rover; Autonomous Formation Flight; Expandable Purge Chambers Would Protect Cryogenic Fittings; Wavy-Planform Helicopter Blades Make Less Noise; Miniature Robotic Spacecraft for Inspecting Other Spacecraft; Miniature Ring-Shaped Peristaltic Pump; Compact Plasma Accelerator; Improved Electrohydraulic Linear Actuators; A Software Architecture for Semiautonomous Robot Control; Fabrication of Channels for Nanobiotechnological Devices; Improved Thin, Flexible Heat Pipes; Miniature Radioisotope Thermoelectric Power Cubes; Permanent Sequestration of Emitted Gases in the Form of Clathrate Hydrates; Electrochemical, H2O2-Boosted Catalytic Oxidation System; Electrokinetic In Situ Treatment of Metal-Contaminated Soil; Pumping Liquid Oxygen by Use of Pulsed Magnetic Fields; Magnetocaloric Pumping of Liquid Oxygen; Tailoring Ion-Thruster Grid Apertures for Greater Efficiency; and Lidar for Guidance of a Spacecraft or Exploratory Robot.

Source record↗

Miniature Robotic Spacecraft for Inspecting Other Spacecraft

A report discusses the Miniature Autonomous Extravehicular Robotic Camera (Mini AERCam)-- a compact robotic spacecraft intended to be released from a larger spacecraft for exterior visual inspection of the larger spacecraft. The Mini AERCam is a successor to the AERCam Sprint -- a prior miniature robotic inspection spacecraft that was demonstrated in a space-shuttle flight experiment in 1997. The prototype of the Mini AERCam is a demonstration unit having approximately the form and function of a flight system. The Mini AERCam is approximately spherical with a diameter of about 7.5 in. (.19 cm) and a weight of about 10 lb (.4.5 kg), yet it has significant additional capabilities, relative to the 14-in. (36-cm), 35-lb (16-kg) AERCam Sprint. The Mini AERCam includes miniaturized avionics, instrumentation, communications, navigation, imaging, power, and propulsion subsystems, including two digital video cameras and a high-resolution still camera. The Mini AERCam is designed for either remote piloting or supervised autonomous operations, including station keeping and point-to-point maneuvering. The prototype has been tested on an air-bearing table and in a hardware-in-the-loop orbital simulation of the dynamics of maneuvering in proximity to the International Space Station.

Fredrickson, Steven↗

Animal model of neuropathic tachycardia syndrome

Clinically relevant autonomic dysfunction can result from either complete or partial loss of sympathetic outflow to effector organs. Reported animal models of autonomic neuropathy have aimed to achieve complete lesions of sympathetic nerves, but incomplete lesions might be more relevant to certain clinical entities. We hypothesized that loss of sympathetic innervation would result in a predicted decrease in arterial pressure and a compensatory increase in heart rate. Increased heart rate due to loss of sympathetic innervation is seemingly paradoxical, but it provides a mechanistic explanation for clinical autonomic syndromes such as neuropathic postural tachycardia syndrome. Partially dysautonomic animals were generated by selectively lesioning postganglionic sympathetic neurons with 150 mg/kg 6-hydroxydopamine hydrobromide in male Sprague-Dawley rats. Blood pressure and heart rate were monitored using radiotelemetry. Systolic blood pressure decreased within hours postlesion (Delta>20 mm Hg). Within 4 days postlesion, heart rate rose and remained elevated above control levels. The severity of the lesion was determined functionally and pharmacologically by spectral analysis and responsiveness to tyramine. Low-frequency spectral power of systolic blood pressure was reduced postlesion and correlated with the diminished tyramine responsiveness (r=0.9572, P=0.0053). The tachycardia was abolished by treatment with the beta-antagonist propranolol, demonstrating that it was mediated by catecholamines acting on cardiac beta-receptors. Partial lesions of the autonomic nervous system have been hypothesized to underlie many disorders, including neuropathic postural tachycardia syndrome. This animal model may help us better understand the pathophysiology of autonomic dysfunction and lead to development of therapeutic interventions.

NASA Discipline Regulatory Physiology↗

Behavior-based multi-robot collaboration for autonomous construction tasks

The Robot Construction Crew (RCC) is a heterogeneous multi-robot system for autonomous construction of a structure through assembly of Long components. The two robot team demonstrates component placement into an existing structure in a realistic environment. The task requires component acquisition, cooperative transport, and cooperative precision manipulation. A behavior-based architecture provides adaptability. The RCC approach minimizes computation, power, communication, and sensing for applicability to space-related construction efforts, but the techniques are applicable to terrestrial construction tasks.

autonomous construction↗

Online Cable Tester and Rerouter

Hardware and algorithms have been developed to transfer electrical power and data connectivity safely, efficiently, and automatically from an identified damaged/defective wire in a cable to an alternate wire path. The combination of online cable testing capabilities, along with intelligent signal rerouting algorithms, allows the user to overcome the inherent difficulty of maintaining system integrity and configuration control, while autonomously rerouting signals and functions without introducing new failure modes. The incorporation of this capability will increase the reliability of systems by ensuring system availability during operations.

Lewis, Mark↗

Optimal Force Control of Vibro-Impact Systems for Autonomous Drilling Applications

The need to maintain optimal energy efficiency is critical during the drilling operations performed on future and current planetary rover missions (see figure). Specifically, this innovation seeks to solve the following problem. Given a spring-loaded percussive drill driven by a voice-coil motor, one needs to determine the optimal input voltage waveform (periodic function) and the optimal hammering period that minimizes the dissipated energy, while ensuring that the hammer-to-rock impacts are made with sufficient (user-defined) impact velocity (or impact energy). To solve this problem, it was first observed that when voice-coil-actuated percussive drills are driven at high power, it is of paramount importance to ensure that the electrical current of the device remains in phase with the velocity of the hammer. Otherwise, negative work is performed and the drill experiences a loss of performance (i.e., reduced impact energy) and an increase in Joule heating (i.e., reduction in energy efficiency). This observation has motivated many drilling products to incorporate the standard bang-bang control approach for driving their percussive drills. However, the bang-bang control approach is significantly less efficient than the optimal energy-efficient control approach solved herein. To obtain this solution, the standard tools of classical optimal control theory were applied. It is worth noting that these tools inherently require the solution of a two-point boundary value problem (TPBVP), i.e., a system of differential equations where half the equations have unknown boundary conditions. Typically, the TPBVP is impossible to solve analytically for high-dimensional dynamic systems. However, for the case of the spring-loaded vibro-impactor, this approach yields the exact optimal control solution as the sum of four analytic functions whose coefficients are determined using a simple, easy-to-implement algorithm. Once the optimal control waveform is determined, it can be used optimally in the context of both open-loop and closed-loop control modes (using standard realtime control hardware).

Aldrich, Jack B.↗