Ashwini Ratnoo

Impact Angle Constrained Interception of Stationary Targets

In Many advanced guidance applications [1–5], it is required to intercept the target from a particular direction, that is, achieve a certain impact angle.

Impact Angle Constrained Guidance Against Nonstationary Nonmaneuvering Targets

G UIDANCE laws with terminal impact angle constraints are widely reported in the literature [1–7]. Proportional navigation guidance (PNG) has been used for deriving impact angle constrained guidance laws for stationary and moving targets. Lu et al. [8] have used PNG in an adaptive guidance law for a hypervelocity impact angle constrained hit at a stationary target. Satisfying impact angle constraint by varying the navigation constant N of the PNG is addressed by Ratnoo and Ghose [9]. In their work [9], a two-stage PNG law is proposed for achieving all impact angles against stationary targets in surface-to-surface engagements. A biased PNG (BPNG) law proposed by Kim et al. [3] has an extra term for annulling the terminal impact angle error together with the conventional line-of-sight rate term for the lateral acceleration command. BPNG law expands the capture region of existing guidance laws against moving targets. However, the performance of BPNG law deteriorates with tail-chase kinds of engagements. The problem of achieving all impact angles against moving targets is addressed here. The idea of a two-stage PNG law, proposed by Ratnoo and Ghose [9], is further investigated and developed for nonstationary nonmaneuvering targets. It should be noted that for different values of N, the PNG law results in a set of impact angles against a moving target. However, studies on classical PNG law [10] reveal that the value of N should be greater than a minimum value for the terminal lateral acceleration demand to be bounded. The achievable set of impact angles is derived for PNG law, with the values of N satisfying the previously mentioned constraint. To achieve the remaining impact angles, an orientation guidance scheme is proposed for the initial phase of the interceptor trajectory. The orientation guidance law is also PNG law, withN being a function of the initial engagement geometry. It is proven that, following the orientation trajectory, the interceptor can switch to N 3 and achieve any desired impact angle in a surface-to-surface engagement scenario.

State-Dependent Riccati-Equation-Based Guidance Law for Impact-Angle-Constrained Trajectories

IN MANY advanced guidance applications, it is required to intercept the target from a particular direction: that is, to achieve a certain impact angle [1–3]. Closed-form solutions for energyoptimal impact-angle-constrained guidance laws have been proposed for a stationary target by Ryoo et al. [4], who used the linear quadratic regulator technique after linearizing the engagement kinematics. The guidance law proposed by them captures all impact angles from any initial launch angle in a planar engagement scenario. Lu et al. [5] solved the problem of guiding a hypersonic gliding vehicle in its terminal phase to a stationary target using adaptive proportional navigation guidance. Ohlmeyer and Phillips [6] extended the idea of explicit guidance (proposed by Cherry [7]) to include a terminal impact angle constraint. However, the simulations by Ohlmeyer and Phillips [6] are carried out only for a vertical impact against a stationary target, and the impact angle errors encountered are sensitive to the launch altitude.

Line-of-Sight Interceptor Guidance for Defending an Aircraft

= missile evasive maneuver normal to defendermissile line of sight amp = missile evasive maneuver component normal to target-missile line of sight at, ad, am = target, defender, and missile lateral accelerations, respectively at max, ad max, am max = target, defender, and missile maximum lateral accelerations, respectively atplos, adplos, amplos = target, defender, and missile accelerations normal to the line of sight, respectively Rd, Rm, Rdm = target-defender, target-missile, and defendermissile closing ranges, respectively tf = defender-missile interception time vt, vd, vm = target, defender, and missile speeds, respectively vtlos, vdlos, vmlos = target, defender, and missile speeds along the line of sight, respectively vtplos, vdplos, vmplos

Guidance Strategies Against Defended Aerial Targets

The three-body engagement scenario is considered where an aerial missile, homing onto a target aircraft, encounters a defender missile launched by the aircraft. A given set of defender-missile guidance laws, namely, proportional navigation and line-of-sight guidance, are considered, and analysis is carried out for proportional navigation and pure pursuit attacking missile strategies. Analytic launch envelopes and lateral accelerations ratios for the four resulting scenarios are derived. Closed-form expressions for attackingmissile initial position and launch angles are derived for a successful evasion from the defender. Numerical simulations are carried out which comply with the analytical findings. The resulting launch envelopes are highly sensitive to the adversary’s guidance strategy, and thus, concerning practical implementation, a game theoretic analysis is carried out. Game solutions are obtained in pure and mixed strategies, resulting in the missile’s evasion probability envelope, that is, based on the four individual launch envelopes.

Path Following Using Trajectory Shaping Guidance

Unmanned vehicle path following by pursuing a virtual target moving along the path is considered. Limitations for pure pursuit guidance are analyzed while following the virtual target on curved paths. Trajectory shaping guidance is proposed as an alternate guidance scheme for a general curvature path. It is proven that under certain tenable assumptions trajectory shaping guidance yields an identical path as that of the virtual target. By linear analysis it is shown that the convergence to the path for trajectory shaping guidance is twice as fast as pure pursuit. Simulations highlight significant improvement in position errors by using trajectory shaping guidance. Comparative simulation studies comply with analytic findings and present better performance as compared with pure pursuit and a nonlinear guidance methodology from the literature. Experimental validation supports the analytic and simulations studies as the guidance laws are implemented on a radio-controlled car in a laboratory environment.

SDRE Based Guidance Law for Impact Angle Constrained Trajectories

In this paper a new guidance law with impact angle constraint is presented for planar engagements. The control problem is formulated as an inflnite horizon non-linear regulator problem. The problem is solved using State Dependent Riccati Equation (SDRE) technique with time varying state weight matrix. The state weight matrix Q is assumed to be a function of time-to-go and controls the states depending on the relative target position. Constant speed missile model is assumed for deriving the guidance law. Numerical simulations for a realistic missile model are carried out with given vehicle and aerodynamic properties. Simulations are carried out for difierent impact angles and initial flring angles. Robustness of the proposed guidance law is verifled by simulations with flrst order autopilot delays.

Kill-Band-Based Lateral Impact Guidance Without Line-of-Sight Rate Information

A geometric guidance scheme is proposed for lateral interception of targets in the absence of line-of-sight rate information.Akill-band isdefinedfortargetpositionscapturable byaninterceptor using arcmaneuver followed by a straight line course. Detailed analytic study of the kill-band and its boundaries is presented. Interceptor speed and heading requirements are derived for expanding the kill band. Based on the kill-band and maneuvers to control its size, guidance laws are proposed for nonmaneuvering and maneuvering targets, respectively. The proposed scheme is based on instantaneous target position and velocity information. The kill-band concept inherently provides robustness to the proposed scheme with respect to uncompensated dynamic lags and target maneuvers. Numerical simulations are carried out to support the analytical findings.

Guidance Laws Against Defended Aerial Targets

The three body engagement scenario is considered where an aerial missile, homing onto a target aircraft, encounters a defender missile launched by the aircraft. A given set of defender missile guidance laws, namely, proportional navigation and line-of-sight guidance are considered and analysis is carried out for proportional navigation and pure pursuit attacking missile strategies. Analytic capture zones and lateral accelerations ratios for the four resulting scenarios are derived. Closed form expression for attacking missile initial position and launch angles are derived for a successful evasion from the defender. Extensive numerical simulations are carried out which comply with the analytical flndings. Nomenclature vt; vd; vm Target, defender, and missile speeds, respectively ∞t; ∞d; ∞m Target, defender, and missile headings, respectively ∞t0; ∞d0; ∞m0 Target, defender, and missile initial headings, respectively _ ∞t; _ ∞d; _ ∞m Target, defender, and missile turning rates, respectively Rd; Rm; Rdm Target-defender, target-missile, and defender-missile closing ranges, respectively Rd0; Rm0; Rdm0 Target-defender, target-missile, and defender-missile initial closing ranges, respectively _ Rd; _ Rm; _ Rdm Target-defender, target-missile, and defender-missile closing range rates, respectively vcdm; vcm Defender-missile and target-missile closing speeds, respectively vcdm0; vcm0 Defender-missile and target-missile initial closing speeds, respectively ‚d; ‚m; ‚dm

Formation-Flying Guidance for Cooperative Radar Deception

teammates and their respective radar positions based on their individual transmitted constraints. All the information obtained in the decentralized individual messages was extracted and group coordination was obtained. The team coordination was shown to be maintained in presence of communication gaps. Numerical solution of the three-dimensional deception as a parameter optimization problem was described by Lee and Bang [6] and sample scenarios were presented. Therein the control input parameterization converts theoptimalcontrolproblemintotheparameteroptimizationproblem with inequality constraints. Xu and Basset [7] used bio inspired camouflagetechniquetosolvetheconstantspeedphantomtargetand maximumtimedeceptioncases.Thetechniquehighlightstheuseofa bio inspired approach to represent the model dynamics by a single degree of freedom vector and thus eases the optimization problem. By definition, each ECAV generates the phantom target along its line-of-sight(LOS)withrespecttotheengagedradar.Inotherwords, the ECAV is always positioned on the line joining the radar and