Rafal Zbikowski

Contaminant Cloud Boundary Monitoring Using Network of UAV Sensors

In this paper, we describe research work currently being undertaken to detect, model, and track the shape of a contaminant cloud boundary using air borne sensor swarms. A model of the contaminant cloud boundary is first developed using a splinegon, defined by a set of vertices linked by segments of constant curvature. This model is then used in an estimator to predict the evolution of the contaminant cloud. This approach is efficient in that only the vertices and segment curvatures are required to define the cloud boundary, rather than using a distribution function to represent the dispersion density.

Direct Intercept Guidance using Differential Geometry Concepts

This paper examines the application of differential geometry to the engagement of both nonmanoeuvring and manoeuvring targets. The kinematics of the engagement for both manoeuvring and nonmanoeuvring target are developed and expressed in differential geometric terms. Two-dimensional geometry is then used to determine the intercept conditions for a straight line target and a constant manoeuvre target. The intercept conditions for both targets are developed for the case when the interceptor missile guides onto a straight line interception. These two cases are shown to have a common set of core conditions such that it enables a unified guidance law to be developed. The guidance law is shown to be globally stable using Lyapunov theory, so that guidance capture is assured for any initial condition. The analysis and guidance law design does not rely on local linearisation and can be shown to produce guidance trajectories that mirror proportional navigation for the straight line interception of a nonmanoeuvring target for which proportional navigation was originally developed. The paper finishes with simulation in two dimensions, illustrating the convergence and solution properties of the approach.

A solution to simultaneous arrival of multiple UAVs using Pythagorean hodograph curves

This paper presents a solution to the problem of simultaneous arrival of a swarm of UAVs by safe and continuously flyable paths. Continuously flyable-paths are generated by satisfying the curvature constraint throughout the path-length. The flyable paths ensure the safety of the UAVs by changing the shape of the flyable-paths by adjusting curvature of the paths. The main idea used in this paper is that a specific type of path is used in the first place for path planning and the shape of the path is varied to meet the multiple constraints. Pythagorean hodograph curves are used for the path planning algorithm. The principle of differential geometry that a planar curve is completely determined by its curvature is used for changing the shape of the path. The multiple constraints are: (i) curvature constraints (ii) minimum-separation-distance and (iii) non-intersection of paths at equal length

3D Path Planning for Multiple UAVs Using Pythagorean Hodograph Curves

This paper presents path planning of multiple UAVs for simultaneous arrival on target. The path planning is divided into phases: firstly design of flyable paths and secondly producing flyable and safe paths achieve the mission. Spatial PH curves are used to produce the paths. The flyable paths are produced by satisfying the maximum curvature and torsion bounds of the UAVs. Latter the flyable paths are tuned to meet the safety conditions and in turn achieve the mission by producing the paths equal in lengths. The curvature bounds and safety conditions and producing paths of equal lengths are all achieved by increasing the curvatures of the paths.

Differential Geometric Guidance Based on the Involute of the Target's Trajectory

This paper presents a novel approach to missile guidance using the differential geometry of curves and not relying on the line of sight information. The target’s trajectory is treated as a smooth curve of known curvature and the new algorithm is based on the involute of the target’s curve. The missile’s trajectory uses the concept of virtual target to generate the correct involute trace. It is shown that the missile is either on the trace immediately or may be able to reach it through an alignment procedure. In general, following the trace requires a three-dimensional maneuver in which the missile flies above the target’s tangent plane. The projection of the three-dimensional trajectory onto the tangent plane coincides with the involute trace, but is traversed in the time-to-go, thus resulting in the intercept. Two air-to-air scenarios of point masses are considered for a maneuvering target of the F-16 fighter class: 1) a two-dimensional engagement with target executing a constant g turn; 2) a three-dimensional engagement with target executing a barrel-roll maneuver. Perfect target information is assumed in simulations. In the first case, intercepts occur both for the involute law and proportional-navigation (PN) guidance; PN based intercepts occur quicker, but the involute-based trajectories are more difficult to evade and always result in a side impact. In the second case, PN fails to intercept the target, while the involute law is successful.

Path Planning of Multiple UAVs Using Dubins Sets

This paper describes Coordinated Path Planning of Multiple UAVs for simultaneous arrival with safe ∞ight-paths. The simultaneous arrival of all UAVs is guaranteed by paths of equal lengths. Two conditions: 1. minimum separation distance and 2. non-intersection of paths at equal length are used/proposed to ensure the safe ∞ight-path of UAVs. These conditions are to avoid inter-UAVs collision. The dubins CLC paths are used for the path planning. The shortest path of each UAV is found out from the available set of CLC paths. The longest of shortest paths is taken as the reference path. The length of remaining paths are adjusted to be equal to that of the reference path. The length of paths are increased to that of the reference path by increasing the turning radius of arcs. Bisection method is used to flnd the optimal turning radii of paths. The path planning guarantees design of paths of equal length with shortest paths. This is having advantages in reducing fuel consumption and increasing the durability of UAVs. Numerical simulations shows the results of the proposal.

Contaminant cloud boundary monitoring using UAV sensor swarms

In this paper we describe research work currently being undertaken to detect, model and track the shape of a contaminant cloud boundary using air borne sensor swarms. The model of the cloud boundary is then used to predict the future evolution of the cloud shape so that an airborne sensor swarm of UAVs can perform manoeuvres that will enable the exact shape and track of the cloud to be determined accurately and in a timely fashion. The contaminant cloud models currently used are usually based on numerical techniques. However in this research work the kinematics of the evolving cloud to approximate the shape of the cloud using splinegons is explored. This approach is e‐cient in that only the vertices and segment curvatures are required to deflne the cloud boundary, rather than a distribution function.

Kripke modelling approaches of a multiple robots system with minimalist communication: A formal approach of choice

Real-time, critical systems such as avionics software and hardware chips, owe their reliability to formal modelling approaches from their design phase. Following this philosophy, an intuitive yet mathematically rigorous approach of Kripke modelling is used for representing a co-operative, decentralised mobile robot group. The robot group operates with minimalist communication and no a priori knowledge of the operating environment for achieving interception and coordinated time-over-target. This scenario is a prototype of a simple task envisaged for a group of unmanned aerial vehicles (UAVs). As such, the resulting behaviour of the UAVs must be designed and analysed, so that guaranteed performance is ensured if only to achieve flight certification. Hence, there is a need for a mathematically rigorous approach, or a formal modelling technique. Several such techniques are briefly reviewed and it is argued that Kripke modelling is the best suited one. Kripke models consist of, firstly, a set of possible worlds (system configurations), secondly, an accessibility relation in the set (transitions between the worlds) and thirdly, a labelling function (which logical statements are true in each world). This approach represents continuous dynamics and discrete decision making of the robots in a unified way. Desirable properties of co-operation can be precisely expressed using temporal logic statements defining safety, liveness etc. Whether a group of robots, whose behaviour is formalised with Kripke models, possesses such properties is then verified using automated model checking tools. Rationale for this approach along with simulation and verification results are presented in the paper.

Robust performance study for lateral autopilot of a quasi-linear parameter-varying missile

A sideslip velocity autopilot is designed for a model of a tactical missile, and the robust performance of the system is investigated. A systematic tool to attain some robust performance is developed. The tail-controlled missile in the cruciform fin configuration is modelled as a second-order quasi-linear parameter-varying system. This nonlinear model presents explicit dependency of the aerodynamic derivatives on a state (sideslip velocity) and external parameters (longitudinal velocity and roll angle). The autopilot design is based on input-output pseudo-linearisation which brings the closed-loop system independent of the choice of equilibria. Thus, if the operating points are in the vicinity of the equilibria, then only one nominal linear model will describe closed-loop dynamics. However, parametric uncertainties lead to a multi-affine uncertain system even in the transformed space. Using multi-linear approximation of the uncertainties, coefficients of a pole placement controller can be estimated for some achievable robust performance. The performance is understood as a D-stability criteria and linear matrix inequalities are solved to design the controller in a Lyapunov approach. Finally, the robust performance analysis of the overall closed-loop system is presented.

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.