Safe Maneuvering Envelope Estimation based on a Physical Approach

Abstract

This paper discusses a computationally efficient algorithm for estimating the safe maneuvering envelope of damaged aircraft. The algorithm performs a robust reachability analysis through an optimal control formulation while making use of time scale separation and taking into account uncertainties in the aerodynamic derivatives. This approach differs from others since it is physically inspired. This more transparent approach allows interpreting data in each step, and it is assumed that these physical models based upon flight dynamics theory will therefore facilitate certification for future real life applications.

Optimal Control Framework for Estimating Autopilot Safety Margins

“…From (20) and (21) it follows that the optimization variable θ re f in (22) and (23) is affine to both x and…”

“…The other approach that can be found in the literature is the reachability formulation for estimating the safe flight envelope (see also [17,18]). For example, in Oort et al [19] and Lombearts et al [20] the flight envelope was characterized as the intersection between the forward and backward reachable set of the aircraft trim set. In any case, both approaches are computationally intensive and require a fully integrated modeling of aerodynamic, structural and propulsive aspects of the aircraft in order to obtain high fidelity approximations of the maneuvering envelope.…”

Distance-Fields-Over-Grids Method for Aircraft Envelope Determination

“…This set intuitively satisfies the definition of the viability kernel, as simply giving the trim inputs will keep the aircraft within the set. However, in reality, the true viability kernel will be larger, [17].…”

“…(a) away from equilibrium This set is called the viability kernel, which is a concept closely related to reachability analysis as explained in [17,21]. Here, safe flight will be defined as steady, straight and level flight, i.e.…”

“…Then there is the concept of level sets where the boundary of the reachable set is posed as a partial differential equation. This method is already used extensively in the past, [14][15][16] and also very recently, [17]. Recently, another method for the computation of reachable sets, Distance…”