Maneuverability Set Estimation and Trajectory Feasibility Evaluation for eVTOL Aircraft

THE commonly accepted definition of maneuverability is the capability of an aircraft to alter its flight path through the application of acceleration [1]. Besides acceleration, other maneuverability metrics, including load factor and turn rate, are also used in literature [2,3]. Maneuverability analysis is vital to the design of modern aircraft with complex configurations. The concept of electric vertical take-off and landing (eVTOL) aircraft for urban air mobility (UAM) has gained increasing attention. Note that eVTOL aircraft may experience some maneuverability issues, for example, negative lift due to low angles of attack during take-off [4], reduced propeller thrust due to aerodynamic interactions [5], and limited electrical power. Nevertheless, the aircraft must have sufficient maneuverability to operate safely, even in the event of thrust loss. Despite several studies examining eVTOL performance [6,7], flight control [8,9], and trajectory optimization [10,11], less attention has been paid to its maneuverability. In Ref. [12], the authors assessed the low-speed maneuverability of an eVTOL based on the minimal time required to reach a predetermined position and speed from rest. In this Note, the concept of maneuverability set is introduced and applied to investigate the maneuverability of a ``lift + cruise'' eVTOL aircraft. The maneuverability set is defined as a collection of maneuverability metrics that an aircraft can achieve under specific dynamic constraints. Essentially, it is determined by the forces and moments exerted on the vehicle. Although no prior studies have explored the maneuverability set, some studies have described the forces and moments that can be achieved by the aircraft. For example, attainable moment sets (AMSs) are widely used in control allocation [13--15]. In most of these studies, the map between control inputs and moments is linear and time-invariant, and the set of admissible inputs is convex; therefore, the AMS is also convex. Only a few studies have addressed nonlinear dynamics. For instance, in Ref. [16], the authors calculated AMSs for an aircraft model whose yaw moment is a quadratic function of control inputs. In Refs. [17,18], the authors explored AMSs of nonlinear flight systems to support aircraft configuration design but assumed AMSs to be convex. In Ref. [19], the space of attainable global forces for automobiles is estimated using a brute-force method. After making the input variables discrete, it explores the space of attainable forces by computing the forces for all input combinations. This approach can estimate nonconvex sets, but the computational burden spikes as the input dimension increases. On the other hand, we expect to learn ifa flight system can sustain a certain level of maneuverability despite constant or variable disturbances. In this context, we refer to the maneuverability set under constant disturbance as the nominal set. Further, we refer to the intersection of all nominal sets under conceivable disturbances as the robust set. The latter represents the ``worst-case'' maneuverability under variable disturbances. In Ref. [20], the author examined the robust AMS of a linear system with bounded control effectiveness uncertainties. However, few studies have investigated the maneuverability of nonlinear flight systems under disturbances, especially for eVTOL systems. This Note proposes two methods for estimating the maneuverability set ofnonlinear flight dynamics systems. The first method is grid-based and inspired by the distance-field-on-grid (DFOG) method, which was proposed to approximate reachable sets of dynamic systems [21--23]. We extend the DFOG method to estimate the robust maneuverability set under variable disturbances. The second method involves determining the boundary points of the maneuverability set. It can deal with both constant and variable disturbances. Two applications of maneuverability sets to an eVTOL aircraft are also presented. First, we chose horizontal and vertical accelerations as metrics to estimate the maneuverability set of the aircraft during take-off. The maneuverability sets quantify the aircraft's acceleration capacity at different flight phases, as well as the impacts of disturbances and thrust loss. The second application leverages maneuverability sets to evaluate the feasibility of a predefined take-off trajectory. A trajectory is only feasible if every point fulfills the dynamic constraints and input limits [24]. The rest of this Note is organized as follows. Section II introduces the nominal and robust maneuverability sets of a nonlinear flight dynamics system. Two methods for estimating maneuverability sets are described in Secs. III and IV, respectively. Section Vanalyzes the maneuverability of the eVTOL aircraft during take-off, and Sec. VI evaluates the feasibility of the take-off trajectory. Finally, Sec. VII concludes the Note.     «

THE commonly accepted definition of maneuverability is the capability of an aircraft to alter its flight path through the application of acceleration [1]. Besides acceleration, other maneuverability metrics, including load factor and turn rate, are also used in literature [2,3]. Maneuverability analysis is vital to the design of modern aircraft with complex configurations. The concept of electric vertical take-off and landing (eVTOL) aircraft for urban air mobility (UAM) has gained increasing at...     »