Sum-of-squares Flight Control Synthesis for Deep-stall Recovery

Under review for publication in the Journal of Guidance, Control, and Dynamics.In lieu of extensive Monte-Carlo simulations for flight control verification, sum-of-squares programming techniques provide an algebraic approach to the problem of nonlinear control synthesis and analysis. However, their reliance on polynomial models has hitherto limited the applicability to aeronautical control problems. Taking advantage of recently proposed piecewise polynomial models, this paper revisits sum-of-squares techniques for recovery of an aircraft from deep-stall conditions using a realistic yet tractable aerodynamic model. Local stability analysis of classical controllers is presented as well as synthesis of polynomial feedback laws with the objective of enlarging their nonlinear region of attraction. A newly developed synthesis algorithm for backwards-reachability facilitates the design of recovery control laws, ensuring stable recovery by design. The paper's results motivate future research in aeronautical sum-of-squares applications

Local stability analysis for large polynomial spline systems

International audiencePolynomial switching systems such as multivariate splines provide accurate fitting while retaining an algebraic representation and offering arbitrary degrees of smoothness; yet, application of sum-of-squares techniques for local stability analysis is computationally demanding for a large number of subdomains. This communiqué presents an algorithm for region of attraction estimation that is confined to those subdomains actually covered by the estimate, thereby significantly reducing computation time. Correctness of the results is subsequently proven and the run time is approximated in terms of the number of total and covered subdomains. Application to longitudinal aircraft motion concludes the study

Piecewise Polynomial Model of the Aerodynamic Coefficients of the Generic Transport Model and its Equations of Motion

Comment on Version 2: An appendix has been added to detail a polynomial spline model of the aircraft longitudinal motion.Comment on Version 3: The polynomials for low and high angles of attack and with respect to side-slip and surface deflections have been corrected.The purpose of this document is to illustrate the piecewise polynomial model which has been derived from wind-tunnel measurement data of the Generic Transport Model (GTM) using the pwpfit toolbox. For implementation details and use in MATLAB, please refer to the source code at https://github.com/pwpfit/GTMpw.Comment on Version 2: An appendix has been added to detail a polynomial spline model of the aircraft longitudinal motion.Comment on Version 3: The polynomials for low and high angles of attack and with respect to side-slip and surface deflections have been corrected

Reference Governor Design in the Presence of Uncertain Polynomial Constraints

Reference governors are add-on schemes that are used to modify trajectories to prevent controlled dynamical systems from violating constraints and so are playing an increasingly important role in aerospace, robotic, and other engineering applications. Here we present a novel reference governor design for systems whose polynomial constraints depend on unknown bounded parameters. This is a significant departure from earlier treatments of reference governors, where the constraints were linear or known, because here we transfer the uncertainties into the constraints instead of having them in the closed loop dynamics, which greatly simplifies the task of determining future evolution of the constraints. Unlike our earlier treatment of reference governors with polynomial constraints, which transformed the constraints into linear ones that depend on an augmented state of the system, here we transform the constraints into linear ones that depend on both the system's state and uncertain parameters. Convexity allows us to compute the maximal output admissible set for an uncertain pre-stabilized linear system. We show that it is sufficient to only consider the extreme values of the uncertain parameters when computing and propagating the polynomial constraints. We illustrate our method using an uncertain longitudinal dynamics for civilian aircraft, which is controlled using a disturbance compensation method and needs to satisfy input and state constraints, and where our reference governor method ensures that safety constraints are always satisfied

Optic Flow-Based Nonlinear Control and Sub-optimal Guidance for Lunar Landing

International audience— A sub-optimal guidance and nonlinear control scheme based on Optic Flow (OF) cues ensuring soft lunar land-ing using two minimalistic bio-inspired visual motion sensors is presented here. Unlike most previous approaches, which rely on state estimation techniques and multiple sensor fusion methods, the guidance and control strategy presented here is based on the sole knowledge of a minimum sensor suite (including OF sensors and an IMU). Two different tasks are addressed in this paper: the first one focuses on the computation of an optimal trajectory and the associated control sequences, and the second one focuses on the design and theoretical stability analysis of the closed loop using only OF and IMU measurements as feedback information. Simulations performed on a lunar landing scenario confirm the excellent performances and the robustness to initial uncertainties of the present guidance and control strategy

Collision Avoidance of multiple MAVs using a multiple Outputs to Input Saturation Technique

This paper proposes a novel collision avoidance scheme for MAVs. This scheme is based on the use of a recent technique which is based on the transformation of state constraints into timevarying control input saturations. Here, this technique is extended so as to ensure collision avoidance of a formation of up to three MAVs. Experimental results involving three A.R drones show the efficiency of the approach

Stabilization and Robustness Analysis for a Chain of Saturating Integrators Arising in the Visual Landing of Aircraft

International audienceWe study a chain of saturating integrators with imprecise output measurements. Using a recent backstepping approach that leads to pointwise delays in the control and a dynamic extension, we provide an input-to-state stability result using a bounded control of arbitrarily small amplitude. We apply the result to a problem in the visual landing of aircraft

Sub-optimal Lunar Landing GNC using Non-gimbaled Bio-inspired Optic Flow Sensors

International audienceAutonomous planetary landing is a critical phase in every exploratory space mission. Autopilots have to be safe, reliable, energy-saving, and as light as possible. The 2-D Guidance Navigation and Control (GNC) strategy presented here makes use of biologically inspired landing processes. Based solely on the relative visual motion known as the Optic Flow (OF) assessed with minimalistic 6-pixel 1-D OF sensors and Inertial Measurement Unit measurements, an optimal reference trajectory in terms of the mass was defined for the approach phase. Linear and nonlinear control laws were then implemented in order to track the optimal trajectory. To deal with the demanding weight constraints, a new method of OF estimation was applied, based on a non-gimbaled OF sensor configuration and a linear least squares algorithm. The promising results obtained with Software-In-the-Loop simulations showed that the present full GNC solution combined with our OF bio-inspired sensors is compatible with soft, fuel-efficient lunar spacecraft landing and might also be used as a backup solution in case of conventional sensor failure