On mathematical modelling of insect flight dynamics in the context of micro air vehicles

This paper discusses several aspects of mathematical modelling relevant to the flight dynamics of insect flight in the context of insect-like flapping wing micro air vehicles (MAVs). MAVs are defined as flying vehicles ca six inch in size (hand-held) and are developed to reconnoitre in confined spaces (inside buildings, tunnels etc). This requires power-efficient, highly-manoeuvrable, low-speed flight with stable hover. All of these attributes are present in insect flight and hence the focus of reproducing the functionality of insect flight by engineering means. This can only be achieved if qualitative insight is accompanied by appropriate quantitative analysis, especially in the context of flight dynamics, as flight dynamics underpin the desirable manoeuvrability. We consider two aspects of mathematical modelling for insect flight dynamics. The first one is theoretical (computational), as opposed to empirical, generation of the aerodynamic data required for the six-degrees-of-freedom equations of motion. For these purposes we first explain insect wing kinematics and the salient features of the corresponding flow. In this context, we show that aerodynamic modelling is a feasible option for certain flight regimes, focussing on a successful example of modelling hover. Such modelling progresses from first principles of fluid mechanics, but relies on simplifications justified by the known flow phenomenology and/or geometric and kinematic symmetries. In particular, this is relevant to six types of fundamental manoeuvres, which we define as those steady flight conditions for which only one component of both the translational and rotational body velocities is non-zero (and constant). The second aspect of mathematical modelling for insect flight dynamics addressed here deals with the periodic character of the aerodynamic force and moment production. This leads to consideration of the types of solutions of nonlinear equations forced by nonlinear oscillations. In particular, the existence of non-periodic solutions of equations of motion is of practical interest, since this allows steady recitilinear flight. Progress in both aspects of mathematical modelling for insect flight will require further advances in aerodynamics of insect-like flapping. Improved aerodynamic modelling and computational fluid dynamics (CFD) calculations are required. These theoretical advances must be accompanied by further flow visualisation and measurement to validate both the aerodynamic modelling and CFD predictions

Aeroservoelastic modelling and control of a slender anti-air missile for active damping of longitudinal bending vibrations

Slender anti-air missiles experience longitudinal bending in supersonic flight and yet their autopilots are designed under the rigid-body assumption. Such autopilot design employs notch filters to remove the modal frequencies of the elastic airframe but this approach limits the autopilot bandwidth. In this paper, aeroservoelastic modelling and control of the ASTER 30 missile is proposed to enable autopilot design with extended bandwidth. The aeroservoelastic model combines missile flight dynamics, actuator dynamics and airframe elasticity, the latter focusing on longitudinal bending treated as a continuous Euler–Bernoulli beam problem. The beam is discretised leading to a nodal model and the modal analysis is then performed. The modal model is expressed in the state-space form and its order is reduced to enable optimal sensor placement and active damping control. The aeroservoelastic model of the ASTER 30 missile is further refined for control purposes by optimally choosing actuator inputs together with the number and position of sensors to be mounted on the missile airframe. Once these choices are made, several variants of active vibration damping control are proposed and analysed in order to enable an extended bandwidth for the autopilot by countering the airframe deformation measured by these sensors

Modelling and Verification of Multiple UAV Mission Using SMV

Model checking has been used to verify the correctness of digital circuits, security protocols, communication protocols, as they can be modelled by means of finite state transition model. However, modelling the behaviour of hybrid systems like UAVs in a Kripke model is challenging. This work is aimed at capturing the behaviour of an UAV performing cooperative search mission into a Kripke model, so as to verify it against the temporal properties expressed in Computation Tree Logic (CTL). SMV model checker is used for the purpose of model checking

Effectiveness of autonomous decision making for unmanned combat aerial vehicles in dogfight engagements

The main objective of this work is to perform a study of the utility of unmanned combat aerial vehicles (UCAVs) in dogfighting (DF) engagements, with DF defined as an aerial battle between two fighter aircraft taking place at close range. The key problem is to assess effectiveness of UCAVs in DF combat when using autonomous decision making based on a representative guidance law and a game-theoretic algorithm. The UCAV DF problem is considered here as a two-player (two fighters), zero-sum, sequential-interaction game with limited information (i.e., each fighter only knows the last three positions of its opponent every time a decision needs to be made). A software simulator has been developed to represent a one-versus-one, clear-sky, close-range aerial battle involving three-dimensional trajectories with high-angle-of-attack (AOA) maneuvers for fighters with similar/dissimilar performance capabilities, considered under four initial conditions: offensive, defensive, neutral, and opposing engagements. Different “levels of intelligence” of the enemy are implemented to validate the performance of the UCAV autonomous decision making against diverse opponents. The simulation-based parametric study elucidates the influence of fighters’ performance capabilities and the fighters’ skill on the outcome of the engagement

Airborne mapping of complex obstacles using 2D Splinegon

This paper describes a recently proposed algorithm in mapping the unknown obstacle in a stationary environment where the obstacles are represented as curved in nature. The focus is to achieve a guaranteed performance of sensor based navigation and mapping. The guaranteed performance is quantified by explicit bounds of the position estimate of an autonomous aerial vehicle using an extended Kalman filter and to track the obstacle so as to extract the map of the obstacle. This Dubins path planning algorithm is used to provide a flyable and safe path to the vehicle to fly from one location to another. This description takes into account the fact that the vehicle is made to fly around the obstacle and hence will map the shape of the obstacle using the 2D-Splinegon technique. This splinegon technique, the most efficient and a robust way to estimate the boundary of a curved nature obstacles, can provide mathematically provable performance guarantees that are achievable in practice

Experimental investigation of some aspects of insect-like flapping flight aerodynamics for application to micro air vehicles

Insect-like flapping flight offers a power-efficient and highly manoeuvrable basis for micro air vehicles for indoor applications. Some aspects of the aerodynamics associated with the sweeping phase of insect wing kinematics are examined by making particle image velocimetry measurements on a rotating wing immersed in a tank of seeded water. The work is motivated by the paucity of data with quantified error on insect-like flapping flight, and aims to fill this gap by providing a detailed description of the experimental setup, quantifying the uncertainties in the measurements and explaining the results. The experiments are carried out at two Reynolds numbers-500 and 15,000-accounting for scales pertaining to many insects and future flapping-wing micro air vehicles, respectively. The results from the experiments are used to describe prominent flow features, and Reynolds number-related differences are highlighted. In particular, the behaviour of the leading-edge vortex at these Reynolds numbers is studied and the presence of Kelvin-Helmholtz instability observed at the higher Reynolds number in computational fluid dynamics calculations is also verified

Vulnerability analysis of GPS receiver software

Satellite navigation systems such as the Global Positioning System (GPS)makes it possible for users to find their relative or absolute position. Thanks to its mobility and reliability, the GPS is used in many civil and military applications. However, the GPS does not provide an advanced level of security. Therefore, it could be potentially a target of attacks. With the development of new GPS attacks, the security knowledge has to grow at the same rate, so existing attacks can be detected by updated versions of receiver software or hardware. In this paper, a comparative analysis of GPS receiver resilience to software attacks is performed with the help of GNSS simulator from Spirent. The main objective of this work is to perform a sensitivity analysis of variables involved in calculation of position of the GPS receivers from different price bands that might be targeted by existing or future GPS attack. Variables making the biggest impact on calculated position are determined using the model. Experimentation validation of their influence is performed using selected receivers and corrupted signals generated by GNSS simulator. The testing is based on tuning the selected variables in order to simulate the theoretical error obtained from the sensitivity analysis. The results obtained from testing are discussed in order to analyse the behaviour of the considered GNSS receivers (including the premium class ones)and establish whether they provide a protection from existing or potential GPS attacks

Non-linear unsteady aerodynamic model for insect-like flapping wings in the hover. Part 1: Methodology and analysis

The essence of this two-part paper is the analytical, aerodynamic modelling of insect-like flapping wings in the hover for microair vehicle applications. A key feature of such flapping-wing flows is their unsteadiness and the formation of a leading-edge vortex in addition to the conventional wake shed from the trailing edge. What ensues is a complex interaction between the shed wakes which, in part, determines the forces and moments on the wing. In an attempt to describe such a flow, two-novel coupled, non-linear, wake-integral equations are developed in this first part of the paper, and these form the foundation upon which the rest of the work stands. The circulation-based model thus developed is unsteady and inviscid in nature and essentially two-dimensional. It is converted to a ‘quasi-three-dimensional' model using a blade-element-type method, but with radial chords. The main results from the model are force and moment data for the flapping wing and are derived as part of this article using the method of impulses. These forces and moments have been decomposed into constituent elements. The governing equations developed in the study are exact, but do not have a closed analytic form. Therefore, solutions are found by numerical methods. These are described in the second part of this paper

Modelling and verification of multiple UAV mission Using SMV

Presented at Formal Methods for Aeronautics, November 3, 2009, Eindhoven, NetherlandsModel checking has been used to verify the correctness of digital circuits, security protocols, communication protocols, as they can be modelled by means of finite state transition model. However, modelling the behaviour of hybrid systems like UAVs in a Kripke model is challenging. This work is aimed at capturing the behaviour of an UAV performing cooperative search mission into a Kripke model, so as to verify it against the temporal properties expressed in Computational Tree Logic (CTL). SMV model checker is used for the purpose of model checking