The feasibility issue in trajectory tracking by means of regions-of-attraction-based gain scheduling

Linear control theory has been long established and a myriad of techniques are available for designing controllers for linear systems in view of conflicting performance requirements. On the other hand, nonlinear control techniques are often tailored to specific applications and versatile nonlinear control frameworks are still on their infancy. A common approach is to resort to local linearized descriptions at desired set-points over a given desired trajectory and employ linear tools. Furthermore, to enforce stability when switching controllers, the regions-of-attraction approach has gained recent attention. This paper questions whether such method - when applied to a well-posed smooth nonlinear controllable system - always yields a sequence of controllers that successfully tracks a given reference equilibrium trajectory, and an analytic counter-example is provided and thoroughly discussed. Finally, our case study additionally shed light on how gain scheduling fails to track particular trajectories for certain globally controllable systems

Longitudinal study of a tilt-body vehicle: modeling, control and stability analysis

This work studies a longitudinal high incidence flight envelope dynamic model for use in a convertible tilt-body vehicle designed for indoor/outdoor environments. The model assumptions are chosen so that a singularity-free nonlinear differential equation system is obtained. The model is complex enough to predict wind tunnel experiments yet simple enough to be described by analytical expressions (instead of physically difficult to interpret lookup tables). Wind tunnel measurements took place to identify flying model parameters, validate model and support autopilot design by means of scheduled linear quadratic regulator controller. Finally, controller design is validated by means of stability analysis based on regions of attraction computation via Lyapunov theorems and invariant sets during the entire transition between airplane mode and hover mode

Development of the flight model of a tilt-body MAV

This article presents the results of a wind tunnel campaign for a tilt-body UAV, the MAVion. The objective of this campaign is to develop a simplified flight model for use in control systems design and implementation. In order to achieve precise flight control during transition, stationary and cruise modes, the aerodynamic coefficients are identified for a wide flight envelope of angle of attack and sideslip. Additionally, the equilibrium transition is studied and the results validate the MAVion design. Moreover, an analysis of performance on aerodynamics due to addition of winglets in this platform is carried out

Definition of a landing strategy for a model-scale reusable rocket

Model-scale rockets differ from their real-size counterparts in important ways. For one, the lack of significant thrust throttling limits retro propulsion landing capabilities. This paper studies its feasibility by employing model-scale non-throttleable solid-propellant engines. Our landing strategy comprises an aerodynamic passive descent followed by a thrust vector control touchdown, and thus thrust is modulated not by magnitude but by direction. This strategy imposes additional levels of under-actuation and nonlinearities that cannot be easily tackled with linear approaches. We propose a Nonlinear Model Predictive Controller as a solution and test its performance and robustness in simulation in different scenarios

Global Singularity-Free Aerodynamic Model for Algorithmic Flight Control of Tail Sitters

This paper addresses fundamental issues in tail-sitting and transition flight aerodynamics modeling in view of sumof- squares (SOS) algorithmic guidance and control design. A novel approach, called ϕ theory, for modeling aerodynamic forces and moments is introduced herein. It yields polynomial-like differential equations of motion that are well suited to SOS solvers for real-time algorithmic guidance and control law synthesis. The proposed ϕ theory allows for first principles model parameter identification and captures dominant dynamical features over the entire flight envelope. Furthermore, ϕ theory yields numerically stable and consistent models for 360 deg angles of attack and sideslip. Additionally, an algorithm is provided for analytically computing all feasible longitudinal flight operating points. Finally, to establish ϕ-theory validity, predicted trim points and wind-tunnel experiments are compared

Nonlinear curvature basis functions for strain-based geometrically nonlinear beams for very flexible aircraft modeling

This paper proposes a new parametrization of very flexible aircraft structural elements to support geometric control studies. First, a sum of basis functions is used to calculate the torsion and curvature distributions of a beam-like structural element. Secondly, the modal functions are used to determine the attitude on SO(3) and the position of each point on the element, assuming constant curvatures. Finally, a simulator implementation of the method is described, along with numerical simplifying strategies

An Error Model of a Complementary Filter for use in Bayesian Estimation - The CF-EKF Filter

It is well known that stand-alone inertial navigation systems (INS) have their errors diverging with time. Consequently an upper bound on the duration of INS systems precludes their use in low-cost micro unmanned aerial vehicles. The traditional approach for solving this matter is to resort to aiding devices, e.g., global navigation satellite system (GNSS) receivers, sighting devices, etc. Two philosophies have been extensively applied to perform data fusion: extended Kalman filtering (EKF) and complementary filtering (CF). Previous work in the literature showed that the computationally less expensive CF can be robustly applied to attitude estimation using low-cost sensors and achieve performance that is comparable to that of a full EKF. However, performance is degraded by vehicle manoeuvres and no measurement on estimate uncertainties is given. Furthermore, a large number of sensors makes it impracticable for optimal tuning of the CF. The present work lays the foundation for sensor filtering that employs the CF for attitude estimation by means of a magnetometer as an external aid, and an EKF for additional sensors integration. The main feature of this architecture is the possibility of deployment in a distributed multi-platform system and implementation of fault isolation by running the CF stage in a separate low-throughput reliable machine for stand-alone degraded mode operation. A case study is performed on synthetic data from inertial, magnetic and GNSS sensors

An Error Model of a Complementary Filter for use in Bayesian Estimation - The CF-EKF Filter

It is well known that stand-alone inertial navigation systems (INS) have their errors diverging with time. Consequently an upper bound on the duration of INS systems precludes their use in low-cost micro unmanned aerial vehicles. The traditional approach for solving this matter is to resort to aiding devices, e.g., global navigation satellite system (GNSS) receivers, sighting devices, etc. Two philosophies have been extensively applied to perform data fusion: extended Kalman filtering (EKF) and complementary filtering (CF). Previous work in the literature showed that the computationally less expensive CF can be robustly applied to attitude estimation using low-cost sensors and achieve performance that is comparable to that of a full EKF. However, performance is degraded by vehicle manoeuvres and no measurement on estimate uncertainties is given. Furthermore, a large number of sensors makes it impracticable for optimal tuning of the CF. The present work lays the foundation for sensor filtering that employs the CF for attitude estimation by means of a magnetometer as an external aid, and an EKF for additional sensors integration. The main feature of this architecture is the possibility of deployment in a distributed multi-platform system and implementation of fault isolation by running the CF stage in a separate low-throughput reliable machine for stand-alone degraded mode operation. A case study is performed on synthetic data from inertial, magnetic and GNSS sensors

Aided Inertial Estimation of Wing Shape

Advanced large-wing-span aircraft result in more structural flexibility and the potential for instability or poor handling qualities. These shortcomings call for stability augmentation systems that entail active structural control. Consequently, the in-flight estimation of wing shape is beneficial for the control of very flexible aircraft. This paper proposes a new methodology for estimating flexible structural states based on extended Kalman filtering by exploiting ideas employed in aided inertial navigation systems. High-bandwidth-rate gyro angular velocities at different wing stations are integrated to provide a short-term standalone inertial shape estimation solution, and additional low-bandwidth aiding sensors are then employed to bound diverging estimation errors. The proposed filter implementation does not require a flight dynamics model of the aircraft, facilitates the often tedious Kalman filtering tuning process, and allows for accurate estimation under large and nonlinear wing deflections. To illustrate the approach, the technique is verified by means of simulations using sighting devices as aiding sensors, and an observability study is conducted. In contrast to previous work in the literature based on stereo vision, a sensor configuration that provides fully observable state estimation is found using only one camera and multiple rate gyros for Kalman filtering update and prediction phases, respectively

Nonlinear control of a particular tilt-body MAV: The Roll&Fly

This paper details the design of a nonlinear controller for the Roll&Fly mode of a wheeled tiltbody micro air vehicle (MAV), developed at ISAE-SUPAERO, called the MAVion. The Roll&Fly mode consists in flying while rolling on walls or onto the ground to guide or increase the range of the MAV during detection or inspection missions. It therefore implies wall or ground mechanical interactions that calls for nontrivial control laws. Our approach consists in enabling a nonlinear obstacle-free attitude/height controller to adapt itself to wall interactions. The controller regulates the velocity and attitude of the drone by means of an approach based on backstepping and feedback linearization techniques. The attitude controller is parametrized by quaternion algebra to avoid orientation singularities