This CPS Frontiers project addresses highly dynamic Cyber-Physical Systems (CPSs), understood as systems where a computing delay of a few milliseconds or an incorrectly computed response to a disturbance can lead to catastrophic consequences. Such is the case of cars losing traction when cornering at high speed, unmanned air vehicles performing critical maneuvers such as landing, or disaster and rescue response bipedal robots rushing through the rubble to collect information or save human lives. The preceding examples currently share a common element: the design of their control software is made possible by extensive experience, laborious testing and fine tuning of parameters, and yet, the resulting closed-loop system has no formal guarantees of meeting specifications. The vision of the project is to provide a methodology that allows for complex and dynamic CPSs to meet real-world requirements in an efficient and robust way through the formal synthesis of control software. The research is developing a formal framework for correct-by-construction control software synthesis for highly dynamic CPSs with broad applications to automotive safety systems, prostheses, exoskeletons, aerospace systems, manufacturing, and legged robotics. The design methodology developed here will improve the competitiveness of segments of industry that require a tight integration between hardware and highly advanced control software such as: automotive (dynamic stability and control), aerospace (UAVs), medical (prosthetics, orthotics, and exoskeleton design) and robotics (legged locomotion). To enhance the impact of these efforts, the PIs are developing interdisciplinary teaching materials to be made freely available and disseminating their work to a broad audience. This is a continuing grant of Award # 1562236

Due to their increasing use by civil and federal authorities and vast commercial and amateur applications, Unmanned Aerial Systems (UAS) will be introduced into the National Air Space (NAS); the question is only how this can be done safely. Today, NASA and the FAA are designing a new, (NextGen) automated air traffic control system for all aircraft, manned or unmanned. New algorithms and tools will need to be developed to enable computation of the complex questions inherent in designing such a system while proving adherence to rigorous safety standards. Researchers must develop the tools of formal analysis to be able to address the UAS in the NAS problem, reason about UAS integration during the design phase of NextGen, and tie this design to on-board capabilities to provide runtime System Health Management (SHM), ensuring the safety of people and property on the ground. This proposal takes a holistic view and integrates advances in the state of the art from three intertwined perspectives to address safe integration of unmanned systems into the national airspace: from on-board the vehicle, from the environment (NAS), and from the underlying theory enabling their formal analysis. There has been rapid development of new UAS technologies yet few of them are formally mathematically rigorous to the degree needed for FAA safety-critical system certification. This project bridges that gap, integrating new UAS and air traffic control designs with advances in formal analysis. Within the wealth of promising directions for autonomous UAS capabilities, this project fills a unique need, providing a direct synergy between on-board UAS SHM, the NAS environment in which they must operate, and the theoretical foundations common to both of these. This research will help to build a safer NAS with increased capacity for UAS and create broadly impactful capabilities for SHM on-board UAS. Advancements will require theoretical research into more scalable model checking and debugging of safety properties. Safety properties express the sentiment that "something bad does not happen" during any system execution; they represent the vast majority of the requirements for NextGen designs and all requirements researchers can monitor on-board a UAS for system heath management during runtime. This research will tackle new frontiers in embedding health management capabilities on-board UAS. Collaborations with aerospace system designers at the National Aeronautics and Space Administration and tool designers at the Bruno Kessler Foundation will aid real-life utility and technology transfer. Broader impact will be achieved by involving undergraduate students in the design of an open-source, affordable, all-COTS and 3D-printable UAS, which will facilitate flight testing of this project's research advances. An open-UAS design for academia will be useful both for classroom demonstrations and as a research platform. Further impact will be achieved by using this UAS and the research it enables in interactive teaching experiences for K-12, undergraduate, and graduate students and in mentoring outreach specifically targeted at girls achieving in Science, Technology, Engineering and Mathematics (STEM) subjects.

The objective of this work is to generate new fundamental science that enables the operation of cyber-physical systems through complex environments. Predicting how a system will behave in the future requires more computing power if that system is complex. Navigating through environments with many obstacles could require significant computing time, which may delay the issue of decisions that have to be made by the on-board algorithms. Fortunately, systems do not always need the most accurate model to predict their behavior. This project develops new theory for deciding between the best model to use when making a decision in real time. The approach involves switching between different predictive models of the system, depending on the computational burden of the associated controller, and the accuracy that the predictive model provides. These tools will pave the way for more kinds of aircraft to navigate closely and safely with one another through the National Air Space (NAS), including Unmanned Air Systems (UAS). The results from this project will enable more accurate and faster trajectory synthesis for controllers with nonlinear plants, or nonlinear constraints that encode obstacles. The approach utilizes hybrid control to switch between models whose accuracy is normalized by their computational burden of predictive control methods. This synergistic approach enables computationally-aware cyber-physical systems (CPSs), in which model accuracy can be jointly considered with computational requirements. The project advances the knowledge on modeling, analysis, and design of CPSs that utilize predictive methods for trajectory synthesis under constraints in real-time cyber-physical systems. 
 The results will include methods for the design of algorithms that adapt to the computational limitations of autonomous and semi-autonomous systems while satisfying stringent timing and safety requirements. With these methods come new tools to account for computational capabilities in real-time, and new hybrid feedback algorithms and prediction schemes that exploit computational capabilities to arrive at more accurate predictions within the time constraints. The algorithms will be modeled in terms of hybrid dynamical systems, to guarantee dynamical properties of interest. The problem space will draw from models of UAS in the NAS.