Predicting impact scenarios of a rimless wheel: a geometrical approach

The version of record os available online at: http://dx.doi.org/10.1007/s11071-022-07807-7The 2D motion ofarigid rimless wheel on an inclined plane has been widely studied as a first simple case of passive walker. Usually, it is modelled as a hybrid dynamical system alternating continuous smooth phases and discrete impact ones. As in other bipedal walkers, the related research is often devoted to the analysis of cyclic motions and assumes that the spoke-ground collision is a single-point one. This work focuses exclusively on the impact problem and explores the possibility of different transitions within the impact interval (single-point to double-point collisions, dynamic jamb, stick-slide transitions and sliding reversal) as a function of the spokes angular aperture, the wheel inertia, the wheel-ground friction coefficient, and the initial conditions. This analysis is done through an innovative geometrical approach based on the Percussion Centre.Peer ReviewedPostprint (published version

Reducing Computational Cost in the Invariant Unscented Kalman Filtering For Attitude Estimation

This article proposes a new formulation to derive the invariant unscented Kalman filter (IUKF) algorithm for attitude estimation problem, where both state and sigma-point are considered as a transformation group parametrization of the filter. The detailed IUKF equations are presented in this article. The filter equations relie on the same ideas as the usual Unscented Kalman Filter (UKF), but it uses a geometrically adapted correction term based on an invariant output error. The specific interest of the proposed formulation is that only the invariant state estimation errors between the predicted state and each sigma point must be known to determine the predicted outputs errors. As we have already computed the set of invariant state errors during the prediction step, the computation cost to find the covariance matrix of the invariant state estimation in the update step is greatly reduced

Robust impedance active control of flight control devices

This paper focuses on the control of the mechanical impedance of an aircraft yoke. The control architecture involves an inner position servo-loop and an outer loop feedbacking the torque/force measurement to the position reference input through the required admitance model. Two different approaches are presented for the inner position servo-loop design: a classical Proportional-Derivative control and a structured Hinfinity control. These two approaches are compared from the performance/robustness trade off point of view. The performance and robustness indexes are respectively the maximal variation on the required admittance model and the maximal pilot own impedance supported by the closed loop system before to become unstable. These indexes are computed using real mu-analysis. Both approaches are implemented on an experimental test-bed. Analysis and exprimental results with a pilot in the loop confirm that the structured H_infinity$ controller is the best solution

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

The Invariant Unscented Kalman Filter

International audienceThis article proposes a novel approach for nonlinear state estimation. It combines both invariant observers theory and unscented filtering principles whitout requiring any compatibility condition such as proposed in the -IUKF algorithm. The resulting algorithm, named IUKF (Invariant Unscented Kalman Filter), relies on a geometrical-based constructive method for designing filters dedicated to nonlinear state estimation problems while preserving the physical invariances and systems symmetries. Within an invariant framework, this algorithm suggests a systematic approach to determine all the symmetry- preserving terms without requiring any linearization and highlighting remarkable invariant properties. As a result, the estimated covariance matrices of the IUKF converge to quasi-constant values due to the symmetry-preserving property provided by the invariant framework. This result enables the development of less conservative robust control strategies. The designed IUKF method has been successfully applied to some relevant practical problems such as the estimation of attitude for aerial vehicles using low-cost sensors reference systems. Typical experimental results using a Parrot quadrotor are provided in this pape