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Eric Feron

Publications and source records attributed to Eric Feron.

At least 37 records · Page 2Linked to original sources
arXiv2020

A Numerical Method to Compute Stability Margins of Switching Linear Systems

Stability margins for linear time-varying (LTV) and switched-linear systems are traditionally computed via quadratic Lyapunov functions, and these functions certify the stability of the system under study. In this work, we show how the more general class of homogeneous polynomial Lyapunov functions is used to compute stability margins with reduced conservatism, and we show how these Lyapunov functions aid in the search for periodic trajectories for marginally stable LTV systems. Our work is premised on the recent observation that the search for a homogeneous polynomial Lyapunov function for some LTV systems is easily encoded as the search for a quadratic Lyapunov function for a related LTV system, and our main contribution is an intuitive algorithm for generating upper and lower bounds on the system's stability margin. We show also how the worst-case switching scheme - which draws an LTV system closest to a periodic orbit - is generated. Three numerical examples are provided to aid the reader and demonstrate the theoretical contributions of the work.

eess.SY↗
arXiv2020

Performance Analysis and Non-Quadratic Lyapunov Functions for Linear Time-Varying Systems

Performance analysis for linear time-invariant (LTI) systems has been closely tied to quadratic Lyapunov functions ever since it was shown that LTI system stability is equivalent to the existence of such a Lyapunov function. Some metrics for LTI systems, however, have resisted treatment via means of quadratic Lyapunov functions. Among these, point-wise-in-time metrics, such as peak norms, are not captured accurately using these techniques, and this shortcoming has prevented the development of tools to analyze system behavior by means other than e.g. time-domain simulations. This work demonstrates how the more general class of homogeneous polynomial Lyapunov functions can be used to approximate point-wise-in-time behavior for LTI systems with greater accuracy, and we extend this to the case of linear time-varying (LTV) systems as well. Our findings rely on the recent observation that the search for homogeneous polynomial Lyapunov functions for LTV systems can be recast as a search for quadratic Lyapunov functions for a related hierarchy of time-varying Lyapunov differential equations; thus, performance guarantees for LTV systems are attainable without heavy computation. Numerous examples are provided to demonstrate the findings of this work.

eess.SY↗
arXiv2020

Additive manufacturing for high precision structural properties via feedback control

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.

eess.SY↗
arXiv2020

Putting the Air Transportation System to sleep: a passenger perspective measured by passenger-generated data

This paper aims at analyzing the effect on the US air transportation system of the travel restriction measures implemented during the COVID-19 pandemic from a passenger perspective. Flight centric data are not already publicly and widely available therefore the traditional metrics used to measure the state of this system are not yet available. Seven metrics based on three different passenger-generated datasets are proposed here. They aim to measure in close to real-time how the travel restriction measures impacted the relation between major stakeholders of the US air transportation system, namely passengers, airports and airlines.

physics.soc-ph↗
arXiv2020

Modeling and Experimental Validation of a Fractal Tetrahedron UAS Assembly

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.

cs.RO↗
arXiv2020

Lyapunov Differential Equation Hierarchy and Polynomial Lyapunov Functions for Switched Linear Systems

This work studies the problem of searching for homogeneous polynomial Lyapunov functions for stable switched linear systems. Specifically, we show an equivalence between polynomial Lyapunov functions for systems of this class and quadratic Lyapunov functions for a related hierarchy of Lyapunov differential equations. This creates an intuitive procedure for checking the stability properties of switched linear systems and a computationally competitive algorithm is presented for generating high-order homogeneous polynomial Lyapunov functions in this manner. Additionally, we provide a comparison between polynomial Lyapunov functions generated with our proposed approach and polynomial Lyapunov functions generated with a more traditional sum-of-squares based approach.

eess.SY↗
arXiv2019

Decentralized On-line Task Reallocation on Parallel Computing Architectures with Safety-Critical Applications

This work presents a decentralized allocation algorithm of safety-critical application on parallel computing architectures, where individual Computational Units can be affected by faults. The described method consists in representing the architecture by an abstract graph where each node represents a Computational Unit. Applications are also represented by the graph of Computational Units they require for execution. The problem is then to decide how to allocate Computational Units to applications to guarantee execution of the safety-critical application. The problem is formulated as an optimization problem, with the form of an Integer Linear Program. A state-of-the-art solver is then used to solve the problem. Decentralizing the allocation process is achieved through redundancy of the allocator executed on the architecture. No centralized element decides on the allocation of the entire architecture, thus improving the reliability of the system. Experimental reproduction of a multi-core architecture is also presented. It is used to demonstrate the capabilities of the proposed allocation process to maintain the operation of a physical system in a decentralized way while individual component fails.

cs.DC↗
arXiv2019

Modeling and Experimental Validation of the Mechanics of a Wheeled Non-Holonomic Robot Capable of Enabling Homeostasis

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.

cs.RO↗
arXiv2019

Monitor-Based Runtime Assurance for Temporal Logic Specifications

This paper introduces the safety controller architecture as a runtime assurance mechanism for system specifications expressed as safety properties in Linear Temporal Logic (LTL). The safety controller has three fundamental components: a performance controller, a backup controller, and an assurance mechanism. The assurance mechanism uses a monitor, constructed as a finite state machine (FSM), to analyze a suggested performance control input and search for system trajectories that are bad prefixes of the system specification. A fault flag from the assurance mechanism denotes a potentially dangerous future system state and triggers a sequence of inputs that is guaranteed to keep the system safe for all time. A case study is presented which details the construction and implementation of a safety controller on a non-deterministic cyber-physical system.

eess.SY↗
arXiv2019

Bounding the State Covariance Matrix for a Randomly Switching Linear System with Noise

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.

math.DS↗
arXiv2018

3D printing of a leaf spring: A demonstration of closed-loop control in additive manufacturing

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.

eess.SY↗
arXiv2018

Towards a New Paradigm of UAV Safety

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.

cs.RO↗
arXiv2017

Maneuver Regulation for Accelerating Bodies in Atmospheric Environments

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.

eess.SY↗
arXiv2017

Foundations of Intelligent Additive Manufacturing

During the last decade, additive manufacturing has become increasingly popular for rapid prototyping, but has remained relatively marginal beyond the scope of prototyping when it comes to applications with tight tolerance specifications, such as in aerospace. Despite a strong desire to supplant many aerospace structures with printed builds, additive manufacturing has largely remained limited to prototyping, tooling, fixtures, and non-critical components. There are numerous fundamental challenges inherent to additive processing to be addressed before this promise is realized. One ubiquitous challenge across all AM motifs is to develop processing-property relationships through precise, in situ monitoring coupled with formal methods and feedback control. We suggest a significant component of this vision is a set of semantic layers within 3D printing files relevant to the desired material specifications. This semantic layer provides the feedback laws of the control system, which then evaluates the component during processing and intelligently evolves the build parameters within boundaries defined by semantic specifications. This evaluation and correction loop requires on-the-fly coupling of finite element analysis and topology optimization. The required parameters for this analysis are all extracted from the semantic layer and can be modified in situ to satisfy the global specifications. Therefore, the representation of what is printed changes during the printing process to compensate for eventual imprecision or drift arising during the manufacturing process.

cs.LO↗
arXiv2017

Motion Rectification for an Homeostasis-Enabling Wheel

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.

cs.RO↗
arXiv2016

Discrete and Continuous ambush games: optimal policies and approximate solutions

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.

cs.RO↗
arXiv2016

A Framework for Collision-Tolerant Optimal Trajectory Planning of Autonomous Vehicles

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.

cs.RO↗