Launch Envelope Optimization of Virtual Sliding Target Guidance Scheme

This paper presents an optimization of the performance of a recently proposed virtual sliding target (VST) guidance scheme in terms of maximization of its launch envelope for three-dimensional (3-D) engagements. The objective is to obtain the launch envelope of the missile using the VST guidance scheme for different lateral launch angles with respect to the line of sight (LOS) and demonstrate its superiority over kinematics-based guidance laws like proportional navigation (PN). The VST scheme uses PN as its basic guidance scheme and exploits the relation between the atmospheric properties, missile aerodynamic characteristics, and the optimal trajectory of the missile. The missile trajectory is shaped by controlling the instantaneous position and the speed of a virtual target which the missile pursues during the midcourse phase. In the proposed method it is shown that an appropriate value of initial position for the virtual target in 3-D, combined with optimized virtual target parameters, can significantly improve the launch envelope performance. The paper presents the formulation of the optimization problem, obtains the approximate models used to make the optimization problem more tractable, and finally presents the optimized performance of the missile in terms of launch envelope and shows significant improvement over kinematic-based guidance laws. The paper also proposes modification to the basic VST scheme. Some simulations using the full-fledged six degrees-of-freedom (6-DOF) models are also presented to validate the models and technique used.     

Pure proportional navigation against time-varying target manoeuvres

Capturability of the pure proportional navigation (PPN) guidance law against a target executing bounded piecewise continuous time-varying manoeuvres is investigated. A qualitative analysis is carried out to obtain a set of sufficient conditions for capture defined on the engagement parameters and initial conditions. These conditions are significantly less restrictive than the ones obtained previously by others using the Lyapunov method. It is shown that the actual capture region for time-varying target manoeuvres, obtained by using the conditions derived, is much larger than that obtained from the Lyapunov technique. We also show that though a bounded tine varying target manoeuvre does change the constant target manoeuvre capture region to some extent, it does not reduce it drastically. Further, we show that the worst case capture region is obtained when the target executes a constant manoeuvre equal to the bound on the manoeuvre level. Some bounds on the missile lateral acceleration are also obtained for certain regions in the engagement plane. These results are generalizations and extensions of existing results on the capturability of the PPN guidance law against targets executing constant or time-varying target manoeuvres     

Radar-assisted collision avoidance/guidance strategy for planarflight

We propose a radar-assisted collision avoidance/guidance strategy (RACAGS) for flight vehicles on low altitude missions. The task of obstacle avoidance and guidance are integrated in a single collision avoidance/guidance strategy. The avionic aids and computational requirements are modest as the strategy mainly depends on range-map and inertial system information. The strategy is first implemented in a planar scenario and then extended to three-dimensional and nominal trajectory following flight scenarios. Several simulation studies are presented for illustration     

On the generalization of true proportional navigation

A simple framework to define generalized true proportional navigation (GTPN) guidance laws is presented. It is shown that this framework subsumes many of the generalizations presented in the earlier literature. The capture regions of a number of GTPN guidance laws are obtained through a rigorous qualitative analysis. The method of analysis is simpler and lends itself directly to an easy geometrical interpretation. A considerable amount of misinterpretation in the previous results, arising out of certain basic misconceptions, are corrected here. It is shown that a logical application of the guidance philosophy, through a minor modification of GTPN to take into account the direction of rotation of the line-of-sight (LOS), contributes substantially to the expansion of the capture region in the relative velocity space. In particular, it is shown that the capture region also extends to the negative closing velocity region, thus making the modified GTPN almost comparable, so far as the domain of capturability of guidance laws is concerned, to the pure proportional navigation (PPN) guidance law. A number of new results on the exact bounds on the capture region are derived and illustrated through examples     

Search using multiple UAVs with flight time constraints

We consider a large scale system consisting of multiple unmanned aerial vehicles (UAVs) performing a search and surveillance task, based on the uncertainty map of an unknown region. The search algorithm is based on the k-shortest path algorithm that maximizes the effectiveness of the search in term of searching through the maximum uncertainty region, given a constraint on the endurance time of the UAV and on the location of the base station from which the UAVs operate. These constraints set apart this class of problems from the usual search and surveillance problems. We compare the performance of this algorithm with a random search and a greedy strategy search, We also implement the algorithm for the case of multiple UAVs searching an unknown region. The cases of delayed and partial information are also considered. Simulation results that demonstrate the efficacy of the technique are also presented.     

Empirical virtual sliding target guidance law design: an aerodynamic approach

We present a novel empirical virtual sliding target (VST) guidance law for the midcourse phase of a long range surface-to-air missile that uses the simplicity of the conventional proportional navigation (PN) guidance law while exploiting the aerodynamic characteristics of a missile's flight through the atmosphere to enable the missile to achieve superior performance than that achieved by conventional PN guidance laws. The missile trajectory emulates the trajectory of an optimal control based guidance law formulated on a realistic aerodynamic model of the missile-target engagement. The trajectory of the missile is controlled by controlling the speed of a virtual target that slides towards a predicted intercept point during the midcourse phase. Several sliding schemes, both linear and nonlinear, are proposed and the effect of the variation of the sliding parameters, which control the sliding speed of the virtual target, on the missile performance, are examined through extensive simulations that take into account the atmospheric characteristics as well as limitations on the missile in terms of the energy available and lateral acceleration limits. Launch envelopes for these sliding schemes for approaching and receding targets are also obtained. These results amply demonstrate the superiority of the proposed guidance law over the conventional PN law.     

True proportional navigation with maneuvering target

We analytically obtain the capture regions for the true proportional navigation (TPN) missile guidance law against an intelligently maneuvering target. Two versions of TPN are considered. The first is the original TPN which assumes the commanded lateral acceleration to be directly proportional to the line-of-sight (LOS) rate only, the proportionality factor being an arbitrary constant or dependent only on the initial closing velocity. The other, known as RTPN (realistic TPN), assumes the commanded lateral acceleration to be directly proportional to the LOS rate and also the current closing velocity. The target is assumed to maneuver in such a way as to increase the LOS rate and thus directly oppose the proportional navigation (PN) philosophy of annulling the LOS rate. A necessary and sufficient condition for capture is derived for the original TPN, and using it, the exact capture region is obtained. A sufficient condition for capture is derived for RTPN and is used to obtain its capture region partially. Some necessary conditions for capture are also derived for RTPN and are used to obtain an upper bound on its complete capture region. Using these conditions some important results on the existence of capture regions and a comparative study of capturability of TPN laws are also presented     

Distributed computation in linear networks: closed-form solutions

A linear network of communicating processors is analyzed. The processors in the network may or may not be equipped with front-end processors. The processing load originates either at the boundary or at the interior of the network. Closed-form solutions and computational techniques are presented for the above situations, to obtain time optimal distribution of processing loads on the processors. Some important results are proved analytically using the closed-form expressions     

Measurement and stability of the pointing of the BepiColombo Laser Altimeter under thermal load

The BepiColombo Laser Altimeter (BELA) has been selected to fly on ESA?s BepiColombo mission to Mercury. The instrument will be the first European laser altimeter designed for interplanetary flight. This paper describes the setup used to characterize the angular movements of BELA under the simulated environmental conditions that the instrument will encounter when orbiting Mercury. The system comprises a laser transmitter and a receiving telescope, which can move with respect to each other under thermal load. Tests performed using the Engineering Qualification Model show that the setup is accurate enough to characterize angular movements of the instrument components to an accuracy of ≈10 μrad. The qualification instrument is thermally stable to operate during all mission phases around Mercury proving that the transmitter and receiver sections will remain within the alignment requirements during its mission.