Sliding mode control based guidance law with impact time constraints

In this paper, the sliding mode control based guidance laws to intercept stationary targets at a desired impact time are proposed. Then, it is extended to constant velocity targets using the notion of predicted interception. The desired impact time is achieved by selecting the interceptor's lateral acceleration to enforce a sliding mode on a switching surface designed using non-linear engagement dynamics. Numerical simulation results are presented to validate the proposed guidance law for different initial engagement geometries, impact times and salvo attack scenarios

Biased PN based impact angle constrained guidance using a nonlinear engagement model

Impact angle constrained guidance laws are important in many applications such as guidance of torpedoes, anti-ballistic missiles and reentry vehicles. In this paper, we design a guidance law which is capable of achieving a wide range of impact angles. Biased proportional navigation guidance uses a bias term in addition to the basic PN command to satisfy additional constraints. Angle constrained BPNG (ACBPNG) uses small angle approximations to derive the bias term for impact angle requirement. We design a modified ACBPNG (MACBPNG) where the required bias term is derived in a closed form considering non-linear equations of motion. Simulations are carried out for a wide range of impact angle requirements. We also analyze capturability from different initial positions and also the launch angles possible at each initial position. The performance of the proposed law is compared with an existing law.

Sliding mode control based terminal impact angle constrained guidance laws using dual sliding surfaces

In this paper, sliding mode control theory based guidance laws to intercept non-maneuvering targets at a desired impact angle are presented. The desired impact angle, defined in terms of a desired line-of-sight (LOS) angle, is achieved by selecting the missile's lateral acceleration (latax) to enforce sliding mode on a sliding surface based on this LOS angle. As will be shown, this guidance law does not ensure interception for all states of the missile and the target during the engagement. Hence, to satisfy the requirement of interception at the desired impact angle, a second sliding surface is designed and a switching logic, based on the conditions necessary for interception, is presented that allows the latax to switch between enforcing sliding mode on one of these surfaces so that the target can be intercepted at the desired impact angle. The guidance laws are designed using non-linear engagement dynamics.

Non-singular terminal sliding mode guidance and control with terminal angle constraints for non-maneuvering targets

In this paper guidance laws to intercept stationary and constant velocity targets at a desired impact angle, based on sliding mode control theory, are proposed. The desired impact angle, which is defined in terms of a desired line-of-sight (LOS) angle, is achieved in finite time by selecting the missile's lateral acceleration (latax) to enforce non-singular terminal sliding mode on a switching surface designed using this desired LOS angle and based on non-linear engagement dynamics. Numerical simulation results are presented to validate the proposed guidance laws for different initial engagement geometries and impact angles.

Impact angle constraint guidance law using cubic splines for intercepting stationary targets

In this paper the cubic spline guidance law is presented for intercepting a stationary target at a desired impact angle. The guidance law is obtained from cubic spline curve based trajectory using an inverse method. The cubic spline t rajectory curve expresses the altitude as a cubic polynomial of the downrange. The guidance law is modified to achieve interception in the cases where impact angle is greater that or equal to 90◦. The guidance law is implemented in a feedback mode to maintain the desired impact angle and to reduce miss distance in the presence of lateral acceleration saturation and atmospheric distur- bances. The simulation results show that the guidance law fulfills all the requirements.

Zero miss distance guidance using feedforward and periodic control

There have been attempts at obtaining robust guidance laws to ensure zero miss distance (ZMD) for interceptors with parametric uncertainties. All these laws require the plant to be of minimum phase type to enable the overall guidance loop transfer function to satisfy strict positive realness (SPR). The SPR property implies absolute stability of the closed loop system, and has been shown in the literature to lead to ZMD because it avoids saturation of lateral acceleration. In these works higher order interceptors are reduced to lower order equivalent models for which control laws are designed to ensure ZMD. However, it has also been shown that when the original system with right half plane (RHP) zeros is considered, the resulting miss distances, using such strategies, can be quite high. In this paper, an alternative approach using the circle criterion establishes the conditions for absolute stability of the guidance loop and relaxes the conservative nature of some earlier results arising from assumption of in�nite engagement time. Further, a feedforward scheme in conjunction with a lead-lag compensator is used as one control strategy while a generalized sampled hold function is used as a second strategy, to shift the RHP transmission zeros, thereby achieving ZMD. It is observed that merely shifting the RHP zero(s) to the left half plane reduces miss distances signi�cantly even when no additional controllers are used to ensure SPR conditions.

Partially integrated guidance and control of an air-dropped guided munition with explicit trajectory fixing

An innovative partially integrated guidance and control (PIGC) technique is developed for trajectory fixing by considering six degree-of-freedom (Six-DOF) nonlinear engagement dynamics for successful interception of ground targets by guided munitions. This trajectory fixing algorithm gives closed form solution, where two different trajectories are designed in x - h and x - y planes separately using simple quadratic equations. In order to follow designed trajectories commanded pitch and yaw rates are generated in outer loop using dynamic inversion technique. In inner loop these body rates are tracked using faster dynamic inversion loop by generating the necessary control surface deflections. Simulation studies with actuator dynamics have been carried out to account for three dimensional (3D) engagement geometry to demonstrate the usefulness of PIGC technique.

Differential evolution based 3-D guidance law for a realistic interceptor model

This paper presents a novel, soft computing based solution to a complex optimal control or dynamic optimization problem that requires the solution to be available in real-time. The complexities in this problem of optimal guidance of interceptors launched with high initial heading errors include the more involved physics of a three dimensional missile-target engagement, and those posed by the assumption of a realistic dynamic model such as time-varying missile speed, thrust, drag and mass, besides gravity, and upper bound on the lateral acceleration. The classic, pure proportional navigation law is augmented with a polynomial function of the heading error, and the values of the coefficients of the polynomial are determined using differential evolution (DE). The performance of the proposed DE enhanced guidance law is compared against the existing conventional laws in the literature, on the criteria of time and energy optimality, peak lateral acceleration demanded, terminal speed and robustness to unanticipated target maneuvers, to illustrate the superiority of the proposed law. (C) 2013 Elsevier B. V. All rights reserved.

Robust Reentry Guidance of a Reusable Launch Vehicle Using Model Predictive Static Programming

A robust suboptimal reentry guidance scheme is presented for a reusable launch vehicle using the recently developed, computationally efficient model predictive static programming. The formulation uses the nonlinear vehicle dynamics with a spherical and rotating Earth, hard constraints for desired terminal conditions, and an innovative cost function having several components with associated weighting factors that can account for path and control constraints in a soft constraint manner, thereby leading to smooth solutions of the guidance parameters. The proposed guidance essentially shapes the trajectory of the vehicle by computing the necessary angle of attack and bank angle that the vehicle should execute. The path constraints are the structural load constraint, thermal load constraint, bounds on the angle of attack, and bounds on the bank angle. In addition, the terminal constraints include the three-dimensional position and velocity vector components at the end of the reentry. Whereas the angle-of-attack command is generated directly, the bank angle command is generated by first generating the required heading angle history and then using it in a dynamic inversion loop considering the heading angle dynamics. Such a two-loop synthesis of bank angle leads to better management of the vehicle trajectory and avoids mathematical complexity as well. Moreover, all bank angle maneuvers have been confined to the middle of the trajectory and the vehicle ends the reentry segment with near-zero bank angle, which is quite desirable. It has also been demonstrated that the proposed guidance has sufficient robustness for state perturbations as well as parametric uncertainties in the model.

Partial Integrated Guidance and Control of Interceptors for High-Speed Ballistic Targets

A new partial integrated guidance and control design approach is proposed in this paper, which combines the benefits of both integrated guidance and control as well as the conventional guidance and control design philosophies. The proposed technique essentially operates in a two-loop structure. In the outer loop, an optimal guidance problem is formulated considering the nonlinear six degrees-of-freedom equation of motion of the interceptor. From this loop, the required pitch and yaw rates are generated by solving a nonlinear suboptimal guidance formulation in a computationally efficient manner while simultaneously assuring roll stabilization. Next, the inner loop tracks these outer loop body rate commands. This manipulation of the six degrees-of-freedom dynamics in both loops preserves the inherent time scale separation property between the translational and rotational dynamics, while retaining the philosophy of integrated guidance and control design as well. Because of this, the tuning process is quite straightforward and nontedious as well. Extensive six degrees-of-freedom simulations studies have been carried out, considering three-dimensional engagement geometry, to demonstrate the effectiveness of the proposed new design approach engaging high-speed ballistic targets. A variety of comparison studies have also been carried out to demonstrate the effectiveness of the proposed approach.

Generalized State Estimation and Model Predictive Guidance for Spiraling and Ballistic Targets

An extended Kalman filter based generalized state estimation approach is presented in this paper for accurately estimating the states of incoming high-speed targets such as ballistic missiles. A key advantage of this nine-state problem formulation is that it is very much generic and can capture spiraling as well as pure ballistic motion of targets without any change of the target model and the tuning parameters. A new nonlinear model predictive zero-effort-miss based guidance algorithm is also presented in this paper, in which both the zero-effort-miss as well as the time-to-go are predicted more accurately by first propagating the nonlinear target model (with estimated states) and zero-effort interceptor model simultaneously. This information is then used for computing the necessary lateral acceleration. Extensive six-degrees-of-freedom simulation experiments, which include noisy seeker measurements, a nonlinear dynamic inversion based autopilot for the interceptor along with appropriate actuator and sensor models and magnitude and rate saturation limits for the fin deflections, show that near-zero miss distance (i.e., hit-to-kill level performance) can be obtained when these two new techniques are applied together. Comparison studies with an augmented proportional navigation based guidance shows that the proposed model predictive guidance leads to a substantial amount of conservation in the control energy as well.

Nonsingular Terminal Sliding Mode Guidance with Impact Angle Constraints

Guidance laws based on a conventional sliding mode ensures only asymptotic convergence. However, convergence to the desired impact angle within a finite time is important in most practical guidance applications. These finite time convergent guidance laws suffer from singularity leading to control saturation. In this paper, guidance laws to intercept targets at a desired impact angle, from any initial heading angle, without exhibiting any singularity, are presented. The desired impact angle, which is defined in terms of a desired line-of-sight angle, is achieved in finite time by selecting the interceptor's lateral acceleration to enforce nonsingular terminal sliding mode on a switching surface designed using nonlinear engagement dynamics. Numerical simulation results are presented to validate the proposed guidance laws for different initial engagement geometries and impact angles. Although the guidance laws are designed for constant speed interceptors, its robustness against the time-varying speed of interceptors is also evaluated through extensive simulation results.

Intermittent electrical stimuli for guidance of human mesenchymal stem cell lineage commitment towards neural-like cells on electroconductive substrates

In the context of the role of multiple physical factors in dictating stem cell fate, the present paper demonstrates the effectiveness of the intermittently delivered external electric field stimulation towards switching the stem cell fate to specific lineage, when cultured in the absence of biochemical growth factors. In particular, our findings present the ability of human mesenchymal stem cells (hMSCs) to respond to the electric stimuli by adopting extended neural-like morphology on conducting polymeric substrates. Polyaniline (PANI) is selected as the model system to demonstrate this effect, as the electrical conductivity of the polymeric substrates can be systematically tailored over a broad range (10(-9) to 10 S/cm) from highly insulating to conducting by doping with varying concentrations (10(-5) to 1 M) of HCl. On the basis of the culture protocol involving the systematic delivery of intermittent electric field (dc) stimulation, the parametric window of substrate conductivity and electric field strength was established to promote significant morphological extensions, with minimal cellular damage. A time dependent morphological change in hMSCs with significant filopodial elongation was observed after 7 days of electrically stimulated culture. Concomitant with morphological changes, a commensurate increase in the expression of neural lineage commitment markers such as nestin and PI tubulin was recorded from hMSCs grown on highly conducting substrates, as revealed from the mRNA expression analysis using Reverse Transcriptase Polymerase Chain Reaction (RT-PCR) as well as by immune-fluorescence imaging. Therefore, the present work establishes the key role of intermittent and systematic delivery of electric stimuli as guidance cues in promoting neural-like differentiation of hMSCs, when grown on electroconductive substrates. (C) 2014 Elsevier Ltd. All rights reserved.

Capturability of Augmented Pure Proportional Navigation Guidance Against Time-Varying Target Maneuvers

This paper proposes a variation of the pure proportional navigation guidance law, called augmented pure proportional navigation, to account for target maneuvers, in a realistic nonlinear engagement geometry, and presents its capturability analysis. These results are in contrast to most work in the literature on augmented proportional navigation laws that consider a linearized geometry imposed upon the true proportional navigation guidance law. Because pure proportional navigation guidance law is closer to a realistic implementation of proportional navigation than true proportional navigation law, and any engagement process is predominantly nonlinear, the results obtained in this paper are more realistic than any available in the literature. Sufficient conditions on speed ratio, navigation gain, and augmentation parameter for capturability, and boundedness of lateral acceleration, against targets executing piecewise continuous maneuvers with time, are obtained. Further, based on a priori knowledge of the maximum maneuver capability of the target, a significant simplification of the guidance law is proposed in this paper. The proposed guidance law is also shown to require a shorter time of interception than standard pure proportional navigation and augmented proportional navigation. To remove chattering in the interceptor maneuver at the end phase of the engagement, a hybrid guidance law using augmented pure proportional navigation and pure proportional navigation is also proposed. Finally, the guaranteed capture zones of standard and augmented pure proportional navigation guidance laws against maneuvering targets are analyzed and compared in the normalized relative velocity space. It is shown that the guaranteed capture zone expands significantly when augmented pure proportional navigation is used instead of pure proportional navigation. Simulation results are given to support the theoretical findings.