Eric Feron

Erwan Salaün, Maxime Gariel, Adan Vela et al.

With the forecast increase in air traffic demand over the next decades, it is imperative to develop tools to provide traffic flow managers with the information required to support decision making. In particular, decision-support tools for traffic flow management should aid in limiting controller workload and complexity, while supporting increases in air traffic throughput. While many decision-support tools exist for short-term traffic planning, few have addressed the strategic needs for medium- and long-term planning for time horizons greater than 30 minutes. This paper seeks to address this gap through the introduction of 3D aircraft proximity maps that evaluate the future probability of presence of at least one or two aircraft at any given point of the airspace. Three types of proximity maps are presented: presence maps that indicate the local density of traffic; conflict maps that determine locations and probabilities of potential conflicts; and outliers maps that evaluate the probability of conflict due to aircraft not belonging to dominant traffic patterns. These maps provide traffic flow managers with information relating to the complexity and difficulty of managing an airspace. The intended purpose of the maps is to anticipate how aircraft flows will interact, and how outliers impact the dominant traffic flow for a given time period. This formulation is able to predict which "critical" regions may be subject to conflicts between aircraft, thereby requiring careful monitoring. These probabilities are computed using a generative aircraft flow model. Time-varying flow characteristics, such as geometrical configuration, speed, and probability density function of aircraft spatial distribution within the flow, are determined from archived Enhanced Traffic Management System data, using a tailored clustering algorithm. Aircraft not belonging to flows are identified as outliers.

Mardavij Roozbehani, Alexandre Megretski, Eric Feron

The paper proposes a control-theoretic framework for verification of numerical software systems, and puts forward software verification as an important application of control and systems theory. The idea is to transfer Lyapunov functions and the associated computational techniques from control systems analysis and convex optimization to verification of various software safety and performance specifications. These include but are not limited to absence of overflow, absence of division-by-zero, termination in finite time, presence of dead-code, and certain user-specified assertions. Central to this framework are Lyapunov invariants. These are properly constructed functions of the program variables, and satisfy certain properties-resembling those of Lyapunov functions-along the execution trace. The search for the invariants can be formulated as a convex optimization problem. If the associated optimization problem is feasible, the result is a certificate for the specification.

Mardavij Roozbehani, Alexandre Megretski, Eric Feron

The paper proposes a control-theoretic framework for verification of numerical software systems, and puts forward software verification as an important application of control and systems theory. The idea is to transfer Lyapunov functions and the associated computational techniques from control systems analysis and convex optimization to verification of various software safety and performance specifications. These include but are not limited to absence of overflow, absence of division-by-zero, termination in finite time, presence of dead-code, and certain user-specified assertions. Central to this framework are Lyapunov invariants. These are properly constructed functions of the program variables, and satisfy certain properties-resembling those of Lyapunov functions-along the execution trace. The search for the invariants can be formulated as a convex optimization problem. If the associated optimization problem is feasible, the result is a certificate for the specification.

Kevin Garanger, Thanakorn Khamvilai, Eric Feron

This paper presents the integration of a feedback control loop during the printing of a plastic object using additive manufacturing. The printed object is a leaf spring made of several parts of different infill density values, which are the control variables in this problem. In order to achieve a desired objective stiffness, measurements are taken after each part is completed and the infill density is adjusted accordingly in a closed-loop framework. The absolute error in the stiffness at the end of printing is reduced from 11.63% to 1.34% by using a closed-loop instead of an open-loop control. This experiments serves as a proof of concept to show the relevance of using feedback control in additive manufacturing. By considering the printing process and the measurements as stochastic processes, we show how stochastic optimal control and Kalman filtering can be used to improve the quality of objects manufactured with rudimentary printers.

Timothy Wang, Romain Jobredeaux, Marc Pantel et al.

The efficiency of modern optimization methods, coupled with increasing computational resources, has led to the possibility of real-time optimization algorithms acting in safety critical roles. There is a considerable body of mathematical proofs on on-line optimization programs which can be leveraged to assist in the development and verification of their implementation. In this paper, we demonstrate how theoretical proofs of real-time optimization algorithms can be used to describe functional properties at the level of the code, thereby making it accessible for the formal methods community. The running example used in this paper is a generic semi-definite programming (SDP) solver. Semi-definite programs can encode a wide variety of optimization problems and can be solved in polynomial time at a given accuracy. We describe a top-to-down approach that transforms a high-level analysis of the algorithm into useful code annotations. We formulate some general remarks about how such a task can be incorporated into a convex programming autocoder. We then take a first step towards the automatic verification of the optimization program by identifying key issues to be adressed in future work.

Vlad Popescu, John-Paul B. Clarke, Karen M. Feigh et al.

A method to quantify the probabilistic controller taskload inherent to maintaining aircraft adherence to 4-D trajectories within flow corridors is presented. An Ornstein-Uhlenbeck model of the aircraft motion and a Poisson model of the flow scheduling are introduced along with reasonable numerical values of the model parameters. Analytic expressions are derived for the taskload probability density functions for basic functional elements of the flow structure. Monte Carlo simulations are performed for these basic functional elements and the controller taskload probabilities are exhibited.

Kévin Garanger, Thanakorn Khamvilai, Eric Feron

This paper discusses the possibility of making an object that precisely meets global structural requirements using additive manufacturing and feedback control. An experimental validation is presented by printing a cantilever beam with a prescribed stiffness requirement. The printing process is formalized as a model-based finite-horizon discrete control problem, where the control variables are the widths of the successive layers. Sensing is performed by making {\em in situ} intermediate stiffness measurements on the partially built part. The hypothesis that feedback control is effective in enabling the 3D-printed beam to meet precise stiffness requirements is validated experimentally.

Yongeun Yoon, Corbin Klett, Eric Feron

The propagation of a state vector is governed by a set of time-invariant state transition matrices that switch arbitrarily between two values. The evolution of the state is also perturbed by white Gaussian noise with a variance that switches randomly with the state transition relation. The behavior of this system can be characterized by the covariance matrix of the state vector, which is time varying. However, we can bound the set of covariances by comparing the switching system to an augmented system derived with Kronecker algebra. We formulate a matrix optimization problem to compute an ellipsoid that bounds the covariance dynamics, which in turn bounds the state covariance of the set of switching systems subject to white noise. In developing this approach, an invariant ellipsoid for a linear switching affine system is computed along the way.

Pierrick Burgain, Eric Feron

Airport departure operations constitute an important source of airline delays and passenger frustration. Excessive surface traffic is the cause of increased controller and pilot workload; It is also the source of increased emissions; It worsens traffic safety and often does not yield improved runway throughput. Acknowledging this fact, this paper explores some of the feedback mechanisms by which airport traffic can be optimized in real time according to its current degree of congestion. In particular, it examines the environmnetal benefits that improved surveillance technologies can bring in the context of gate- or spot-release aircraft strategies. It is shown that improvements can lead yield 4% to 6% emission reductions for busy airports like New-York La Guardia or Seattle Tacoma. These benefits come on top of the benefits already obtained by adopting threshold strategies currently under evaluation.

Yi-Hsuan Chen, Salman Ghori, Ania Adil et al.

Autonomous navigation in complex, non-convex environments remains challenging when robot dynamics, control limits, and exact robot geometry must all be taken into account. In this paper, we propose a hierarchical planning and control framework that bridges long-horizon guidance and geometry-aware safety guarantees for a polytopic robot navigating among polytopic obstacles. At the high level, Mixed-Integer Linear Programming (MILP) is embedded within a Model Predictive Control (MPC) framework to generate a nominal trajectory around polytopic obstacles while modeling the robot as a point mass for computational tractability. At the low level, we employ a control barrier function (CBF) based on the exact signed distance in the Minkowski-difference space as a safety filter to explicitly enforce the geometric constraints of the robot shape, and further extend its formulation to a high-order CBF (HOCBF). We demonstrate the proposed framework in U-shaped and maze-like environments under single- and double-integrator dynamics. The results show that the proposed architecture mitigates the topology-induced local-minimum behavior of purely reactive CBF-based navigation while enabling safe, real-time, geometry-aware navigation.

Mohannad Alhakami, Dylan R. Ashley, Joel Dunham et al.

Advanced machine learning algorithms require platforms that are extremely robust and equipped with rich sensory feedback to handle extensive trial-and-error learning without relying on strong inductive biases. Traditional robotic designs, while well-suited for their specific use cases, are often fragile when used with these algorithms. To address this gap -- and inspired by the vision of enabling curiosity-driven baby robots -- we present a novel robotic limb designed from scratch. Our design has a hybrid soft-hard structure, high redundancy with rich non-contact sensors (exclusively cameras), and easily replaceable failure points. Proof-of-concept experiments using two contemporary reinforcement learning algorithms on a physical prototype demonstrate that our design is able to succeed in a simple target-finding task even under simulated sensor failures, all with minimal human oversight during extended learning periods. We believe this design represents a concrete step toward more tailored robotic designs for achieving general-purpose, generally intelligent robots.

Kévin Garanger, Jeremy Epps, Eric Feron

This paper presents the foundation of a modular robotic system comprised of several novel modules in the shape of a tetrahedron. Four single-propeller submodules are assembled to create the Tetracopter, a tetrahedron-shaped quad-rotorcraft used as the elementary module of a modular flying system. This modular flying system is built by assembling the different elementary modules in a fractal shape. The fractal tetrahedron structure of the modular flying assembly grants the vehicle more rigidity than a conventional two-dimensional modular robotic flight system while maintaining the relative efficiency of a two-dimensional modular robotic flight system. A prototype of the Tetracopter has been modeled, fabricated, and successfully flight-tested by the Decision and Control Laboratory at the Georgia Institute of Technology. The results of this research set the foundation for the development of Tetrahedron rotorcraft that can maintain controllable flight and assemble in flight to create a Fractal Tetrahedron Assembly.

Jeremy Epps, Eric Feron, Mark Mote

The field of bio-inspired robotics seeks to create mechanical systems that mimic the designs and concepts used by biological systems. One of the more challenging biological concepts to imitate in mechanical systems is the ability to create an internal environment that can foster homeostasis through the use of a membrane similar to skin. A robot with this ability would be able to regulate internal parameters, repair itself using the internal sub-environment, and defend its internal parts from the surrounding environment. This paper presents the internal structure of a non-holonomic wheeled system that enables homeostasis via a fully connected interior, protected from the outside environment by a flexible membrane. The three objectives of this paper are to: 1) Explore the idea of nature creating higher-order life forms with wheeled limbs given the correct intermediate steps. 2) Characterize a robot that uses a homeostasis enabling wheel. 3) Determine the feasibility of using a homeostasis enabling wheel as a mode of locomotion.

J. Pablo Afman, Eric Feron, Mitchell Walker

We propose to develop a full-accuracy flight test environment for the Mars helicopter and related Mars-atmospheric vehicles. The experiment would use reduced-g atmospheric flights with an aircraft that houses a properly sized vacuum chamber.

Juan-Pablo Afman, Laurent Ciarletta, Eric Feron et al.

With the rising popularity of UAVs in the civilian world, we are currently witnessing and paradim shift in terms of operational safety of flying vehicles. Safe and ubiquitous human-system interaction shall remain the core requirement but those prescribed in general aviation are not adapted for UAVs. Yet we believe it is possible to leverage the specific aspects of unmanned aviation to meet acceptable safety requirements. We start this paper with by discussing the new operational context of civilian UAVs and investigate the meaning of safety in light of this new context. Next, we explore the different approaches to ensuring system safety from an avionics point of view. Subsets of operational requirements such as geofencing or mechanical systems for termination or impact limitation can easily be implemented. These are presented with the goal of limiting the collateral damages of a system failure. We then present some experimental results regarding two of the major problems with UAVs. With actual impacts, we demonstrate how dangerous uncontrolled crashes can be. Furthermore, with the large number of runaway drone experiences during civilian operations, the risk is even higher as they can travel a long way before crashing. We provide data on such a case where the software controller is working, keeping the UAV in the air, but the operator is unable to actually control the system. It should be terminated! Finally, after having analyzed the context and some actual solutions, based on a minimal set of requirement and our own experience, we are proposing a simple mechanical based safety system. It unequivocally terminates the flight in the most efficient way by instantly removing parts of the propellers leaving a minimal lifting surface. It takes advantage of what controllability may remain but with a deterministic ending: a definite landing.

Juan-Pablo Afman, Mark Mote, Eric Feron

A wheel that is capable of producing thrust and maintaining vehicle internal integrity is presented. The wheel can be seen as an organic extension to the central unit (eg the vehicle) it is attached to, that is, the system and the wheel can be completely surrounded by the same tegument while enabling continuous wheel rotation without tearing the tegument. Furthermore, a skeleton linking the central unit of the system to the wheel's center can be made through the use of joints and linear links, while allowing the apparatus to rotate continuously in the same direction with bounded twisting and no tegument tear. For that reason, artificial muscles can also be used to actuate the entire system. The underlying enabling mechanism is the rectification of a small number of oscillatory inputs. Another contribution of the proposed setup is to offer a plausible, yet untested, evolutionary path from today's living animals towards animals capable of wheeled locomotion.

Juan-Pablo Afman, Eric Feron, John Hauser

In order to address the need for an affordable reduced gravity test platform, this work focuses on the analysis and implementation of atmospheric acceleration tracking with an autonomous aerial vehicle. As proof of concept, the vehicle is designed with the objective of flying accurate reduced-gravity parabolas. Suggestions from both academia and industry were taken into account, as well as requirements imposed by a regulatory agency. The novelty of this work is the Proportional Integral Ramp Quadratic PIRQ controller, which is employed to counteract the aerodynamic forces impeding the vehicles constant acceleration during the maneuver. The stability of the free-fall maneuver under this controller is studied in detail via the formation of the transverse dynamics and the application of the circle criterion. The implementation of such a controller is then outlined, and the PIRQ controller is validated through a flight test, where the vehicle successfully tracks Martian gravity 0.378 G's with a standard deviation of 0.0426.

Emmanuel Boidot, Aude Marzuoli, Eric Feron

We consider an autonomous navigation problem, whereby a traveler aims at traversing an environment in which an adversary tries to set an ambush. A two players zero sum game is introduced. Players' strategies are computed as random path distributions, a realization of which is the path chosen by the traveler. A parallel is drawn between the discrete problem, where the traveler moves on a network, and the continuous problem, where the traveler moves in the plane. Analytical optimal policies are derived. Using assumptions from the Minimal Cut - Maximal Flow literature, the optimal value of the game is shown to be related to the maximum flow on the environment in both the discrete and the continuous cases, when the reward function for the ambusher is uniform. A linear program is introduced that allows for the computation of optimal policies, compatible with non-uniform reward functions. In order to relax the assumptions for the computation of the players' optimal strategies of the continuous game, a network is created, inspired by recently introduced sampling based motion planning techniques, and the linear program is adapted for continuous constraints.

Juan-Pablo Afman, John Franklin, Mark L. Mote et al.

This paper describes the process and challenges behind the design and development of a micro-gravity enabling aerial robot. The vehicle, designed to provide at minimum 4 seconds of micro-gravity at an accuracy of .001 g's, is designed with suggestions and constraints from both academia and industry as well a regulatory agency. The feasibility of the flight mission is validated using a simulation environment, where models obtained from system identification of existing hardware are implemented to increase the fidelity of the simulation. The current development of a physical test bed is described. The vehicle employs both control and autonomy logic, which is developed in the Simulink environment and executed in a Pixhawk flight control board.

Mark L. Mote, Juan-Pablo Afman, Eric Feron

Collision-tolerant trajectory planning is the consideration that collisions, if they are planned appropriately, enable more effective path planning for robots capable of handling them. A mixed integer programming (MIP) optimization formulation demonstrates the computational practicality of optimizing trajectories that comprise planned collisions. A damage quantification function is proposed, and the influence of damage functions constraints on the trajectory are studied in simulation. Using a simple example, an increase in performance is achieved under this schema as compared to collision-free optimal trajectories.

Daniel Pickem, Paul Glotfelter, Li Wang et al.

This paper describes the Robotarium -- a remotely accessible, multi-robot research facility. The impetus behind the Robotarium is that multi-robot testbeds constitute an integral and essential part of the multi-robot research cycle, yet they are expensive, complex, and time-consuming to develop, operate, and maintain. These resource constraints, in turn, limit access for large groups of researchers and students, which is what the Robotarium is remedying by providing users with remote access to a state-of-the-art multi-robot test facility. This paper details the design and operation of the Robotarium and discusses the considerations one must take when making complex hardware remotely accessible. In particular, safety must be built into the system already at the design phase without overly constraining what coordinated control programs users can upload and execute, which calls for minimally invasive safety routines with provable performance guarantees.

Daniel Pickem, Li Wang, Paul Glotfelter et al.

This paper describes the development of the Robotarium -- a remotely accessible, multi-robot research facility. The impetus behind the Robotarium is that multi-robot testbeds constitute an integral and essential part of the multi-agent research cycle, yet they are expensive, complex, and time-consuming to develop, operate, and maintain. These resource constraints, in turn, limit access for large groups of researchers and students, which is what the Robotarium is remedying by providing users with remote access to a state-of-the-art multi-robot test facility. This paper details the design and operation of the Robotarium as well as connects these to the particular considerations one must take when making complex hardware remotely accessible. In particular, safety must be built in already at the design phase without overly constraining which coordinated control programs the users can upload and execute, which calls for minimally invasive safety routines with provable performance guarantees.

Emmanuel Boidot, Aude Marzuoli, Eric Feron

Operating vehicles in adversarial environments between a recurring origin-destination pair requires new planning techniques. A two players zero-sum game is introduced. The goal of the first player is to minimize the expected casualties undergone by a convoy. The goal of the second player is to maximize this damage. The outcome of the game is obtained via a linear program that solves the corresponding minmax optimization problem over this outcome. Different environment models are defined in order to compute routing strategies over unstructured environments. To compare these methods for increasingly accurate representations of the environment, a grid-based model is chosen to represent the environment and the existence of a sufficient network size is highlighted. A global framework for the generation of realistic routing strategies between any two points is described. This framework requires a good assessment of the potential casualties at any location, therefore the most important parameters are identified. Finally the framework is tested on real world environments.

Aude Marzuoli, Emmanuel Boidot, Eric Feron et al.

Transportation networks constitute a critical infrastructure enabling the transfers of passengers and goods, with a significant impact on the economy at different scales. Transportation modes, whether air, road or rail, are coupled and interdependent. The frequent occurrence of perturbations on one or several modes disrupts passengers' entire journeys, directly and through ripple effects. The present paper provides a case report of the Asiana Crash in San Francisco International Airport on July 6th 2013 and its repercussions on the multimodal transportation network. It studies the resulting propagation of disturbances on the transportation infrastructure in the United States. The perturbation takes different forms and varies in scale and time frame : cancellations and delays snowball in the airspace, highway traffic near the airport is impacted by congestion in previously never congested locations, and transit passenger demand exhibit unusual traffic peaks in between airports in the Bay Area. This paper, through a case study, aims at stressing the importance of further data-driven research on interdependent infrastructure networks for increased resilience. The end goal is to form the basis for optimization models behind providing more reliable passenger door-to-door journeys.

Alireza Esna Ashari, Eric Feron

The aim is to create reliable and verifiable fault detection software to detect abrupt changes in safety-critical dynamic systems. Fault detection methods are implemented as software on digital computers that monitor and control the system. We implement three observer-based fault detection methods on a 3 degrees of freedom (3DOF) laboratory helicopter, in the form of software. We examine the performance of those methods to detect different faults during flight in a closed-loop setup. All selected methods show acceptable detection performance. However, it is not possible to repeat the test for every possible conditions, inputs and fault scenarios. In this paper, we translate fault detection properties and mathematical proofs into a formal language, previously used in software validation and verification. We include the translated properties in software in the form of non-executable annotations that can be read by machine. Consequently, some high level functional properties of the code can be verified by automatic software verification tools. This certifies fault detection software for a set of bounded data and increases the reliability in practice.

Timothy Wang, Romain Jobredeaux, Heber Herencia et al.

This article describes a fully automated, credible autocoding chain for control systems. The framework generates code, along with guarantees of high level functional properties which can be independently verified. It relies on domain specific knowledge and fomal methods of analysis to address a context of heightened safety requirements for critical embedded systems and ever-increasing costs of verification and validation. The platform strives to bridge the semantic gap between domain expert and code verification expert. First, a graphical dataflow language is extended with annotation symbols enabling the control engineer to express high level properties of its control law within the framework of a familiar language. An existing autocoder is enhanced to both generate the code implementing the initial design, but also to carry high level properties down to annotations at the level of the code. Finally, using customized code analysis tools, certificates are generated which guarantee the correctness of the annotations with respect to the code, and can be verified using existing static analysis tools. Only a subset of properties and controllers are handled at this point.

Sang Hyun Kim, Eric Feron, John-Paul Clarke et al.

Passengers' experience is becoming a key metric to evaluate the air transportation system's performance. Efficient and robust tools to handle airport operations are needed along with a better understanding of passengers' interests and concerns. Among various airport operations, this paper studies airport gate scheduling for improved passengers' experience. Three objectives accounting for passengers, aircraft, and operation are presented. Trade-offs between these objectives are analyzed, and a balancing objective function is proposed. The results show that the balanced objective can improve the efficiency of traffic flow in passenger terminals and on ramps, as well as the robustness of gate operations.

Emmanuel Boidot, Eric Feron

Operating vehicles in adversarial environments require non-conventional planning techniques. A two-player, zero-sum non-cooperative game is introduced, which is solved via a linear program. An extension is proposed to construct networks displaying good representations of the environment characteristics, while offering acceptable results for the technique used. Sensitivity of the solution to the LP solver algorithm is identified. The performances of the planner are finally assessed by comparison with those of conventional planners. Results are used to formulate secondary objectives to the problem.