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.

Nutritional benefits from domatia inhabitants in an ant-plant interaction: interlopers do pay the rent

1. How a symbiosis originates and is maintained are important evolutionary questions. Symbioses in myrmecophytes (plants providing nesting for ants) are believed to be maintained by protection and nutrients provided by specialist plant-ants in exchange for nesting spaces (called domatia) and nourishment offered by ant-plants. However, besides the benefits accrued from housing protective ants, the mechanisms contributing to the fitness advantages of bearing domatia have rarely been examined, especially because the domatia trait is usually constitutively expressed, and many myrmecophytes have obligate mutualisms with single ant species resulting in invariant conditions. 2. In the unspecialized ant-plant Humboldtia brunonis (Fabaceae) that offers extrafloral nectar to ants, only some plants produce domatia in the form of hollow internodes. These domatia have a self-opening slit making them more prone to interlopers and are occupied mostly by non-protective ants and other invertebrates, especially arboreal earthworms. The protection mutualism with ants is restricted in geographical extent, occurring only at a few sites in the southernmost part of this plant's range in the Western Ghats of India. 3. We examined nutrient flux from domatia residents to the plant using stable isotopes. We found that between 9% (earthworms) and 17% (protective or non-protective ants) of nitrogen of plant tissues nearest the domatium came from domatia inhabitants. Therefore, interlopers such as earthworms and non-protective ants contributed positively to the nitrogen budget of localized plant modules of this understorey tree. N-15-enriched feeding experiments with protective ants demonstrated that nutrients flowed from domatia inhabitants to nearby plant modules. Fruit set did not differ between paired hand-pollinated inflorescences on domatia and non-domatia bearing branches. This was possibly due to the nutrient flux from domatia to adjacent branches without domatia within localized modules. 4. This study has demonstrated the nutritive role of non-protective ants and non-ant invertebrates, hitherto referred to as interlopers, in an unspecialized myrmecophyte. Our study suggests that even before the establishment of a specialized ant-plant protection mutualism, nutritional benefits conferred by domatia inhabitants can explain the fitness benefits of bearing domatia, and thus the maintenance of a trait that facilitates the establishment of a specialized ant-plant symbiosis.

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.

Generalized Model Predictive Static Programming and Angle-Constrained Guidance of Air-to-Ground Missiles

A new generalized model predictive static programming technique is presented for rapidly solving a class of finite-horizon nonlinear optimal control problems with hard terminal constraints. Two key features for its high computational efficiency include one-time backward integration of a small-dimensional weighting matrix dynamics, followed bya static optimization formulation that requires only a static Lagrange multiplier to update the control history. It turns out that under Euler integration and rectangular approximation of finite integrals it is equivalent to the existing model predictive static programming technique. In addition to the benchmark double integrator problem, usefulness of the proposed technique is demonstrated by solving a three-dimensional angle-constrained guidance problem for an air-to-ground missile, which demands that the missile must meet constraints on both azimuth and elevation angles at the impact point in addition to achieving near-zero miss distance, while minimizing the lateral acceleration demand throughout its flight path. Simulation studies include maneuvering ground targets along with a first-order autopilot lag. Comparison studies with classical augmented proportional navigation guidance and modern general explicit guidance lead to the conclusion that the proposed guidance is superior to both and has a larger capture region as well.

Capturability Analysis of a 3-D Retro-PN Guidance Law for Higher Speed Nonmaneuvering Targets

This brief presents the capturability analysis of a 3-D Retro-proportional navigation (Retro-PN) guidance law, which uses a negative navigation constant (as against the usual positive one), for intercepting targets having higher speeds than interceptors. This modification makes it possible to achieve collision conditions that were inaccessible to the standard PN law. A modified polar coordinate system, that makes the model more compact, is used in this brief for capturability analysis. In addition to the ratio of the target to interceptor speeds, the directional cosines of the interceptor, and target velocity vectors play a crucial role in the capturability. The existence of nontrivial capture zone of the Retro-PN guidance law and necessary and sufficient conditions, for capturing the target in finite time, are presented. A sufficient condition on the navigation constant is derived to ensure finiteness of the line-of-sight turn rate. The results are more extensive than those available for 2-D engagements, which can be obtained as special cases of this brief. Simulation results are given to support the analytical results.

Formation Flying with Nonlinear Partial Integrated Guidance and Control

Using the dynamic inversion philosophy, a nonlinear partial integrated guidance and control approach is presented in this paper for formation flying. It is based on the evolving philosophy of integrated guidance and control. However, it also retains the advantages of the conventional guidance then control philosophy by retaining the timescale separation between translational and rotational dynamics explicitly. Simulation studies demonstrate that the proposed technique is effective in bringing the vehicles into formation quickly and maintaining the formation.

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.

Three Dimensional Impact Angle Constrained Guidance Law using Sliding Mode Control

In this paper, three dimensional impact angle control guidance laws are proposed for stationary targets. Unlike the usual approach of decoupling the engagement dynamics into two mutually orthogonal 2-dimensional planes, the guidance laws are derived using the coupled dynamics. These guidance laws are designed using principles of conventional as well as nonsingular terminal sliding mode control theory. The guidance law based on nonsingular terminal sliding mode guarantees finite time convergence of interceptor to the desired impact angle. In order to derive the guidance laws, multi-dimension switching surfaces are used. The stability of the system, with selected switching surfaces, is demonstrated using Lyapunov stability theory. Numerical simulation results are presented to validate the proposed guidance law.

An integrated estimation/guidance approach for seeker-less interceptors

This paper addresses the problem of intercepting highly maneuverable threats using seeker-less interceptors that operate in the command guidance mode. These systems are more prone to estimation errors than standard seeker-based systems. In this paper, an integrated estimation/guidance (IEG) algorithm, which combines interactive multiple model (IMM) estimator with differential game guidance law (DGL), is proposed for seeker-less interception. In this interception scenario, the target performs an evasive bang-bang maneuver, while the sensor has noisy measurements and the interceptor is subject to acceleration bound. The IMM serves as a basis for the synthesis of efficient filters for tracking maneuvering targets and reducing estimation errors. The proposed game-based guidance law for two-dimensional interception, later extended to three-dimensional interception scenarios, is used to improve the endgame performance of the command-guided seeker-less interceptor. The IMM scheme and an optimal selection of filters, to cater to various maneuvers that are expected during the endgame, are also described. Furthermore, a chatter removal algorithm is introduced, thus modifying the differential game guidance law (modified DGL). A comparison between modified DGL guidance law and conventional proportional navigation guidance law demonstrates significant improvement in miss distance in a pursuer-evader scenario. Simulation results are also presented for varying flight path angle errors. A numerical study is provided which demonstrates the performance of the combined interactive multiple model with game-based guidance law (IMM/DGL). Simulation study is also carried out for combined IMM and modified DGL (IMM/modified DGL) which exhibits the superior performance and viability of the algorithm reducing the chattering phenomenon. The results are illustrated by an extensive Monte Carlo simulation study in the presence of estimation errors.

Nonlinear Differential Games-Based Impact-Angle-Constrained Guidance Law

The problem of intercepting a maneuvering target at a prespecified impact angle is posed in nonlinear zero-sum differential games framework. A feedback form solution is proposed by extending state-dependent Riccati equation method to nonlinear zero-sum differential games. An analytic solution is obtained for the state-dependent Riccati equation corresponding to the impact-angle-constrained guidance problem. The impact-angle-constrained guidance law is derived using the states line-of-sight rate and projected terminal impact angle error. Local asymptotic stability conditions for the closed-loop system corresponding to these states are studied. Time-to-go estimation is not explicitly required to derive and implement the proposed guidance law. Performance of the proposed guidance law is validated using two-dimensional simulation of the relative nonlinear kinematics as well as a thrust-driven realistic interceptor model.

Nonlinear control of an air-breathing engine including its validation with vehicle guidance

An implementable nonlinear control design approach is presented for a supersonic air-breathing ramjet engine. The primary objective is to ensure that the thrust generated by the engine tracks the commanded thrust without violating the operational constraints. An important constraint is to manage the shock wave location in the intake so that it neither gets detached nor gets too much inside the intake. Both the objectives are achieved by regulating the fuel flow to the combustion chamber and by varying the throat area of the nozzle simultaneously. The design approach accounts for the nonlinear cross-coupling effects and nullifies those. Also, an extended Kalman filter has been used to filter out the sensor and process noises as well as to make the states available for feedback. Furthermore, independent control design has been carried out for the actuators. To test the performance of the engine for a realistic flight trajectory, a representative trajectory is generated through a trajectory optimization process, which is augmented with a newly-developed finite-time state dependent Riccati equation technique for nullifying the perturbations online. Satisfactory overall performance has been obtained during both climb and cruise phases. (C) 2015 Elsevier Masson SAS. All rights reserved.

Impact Time Guidance for Large Heading Errors Using Sliding Mode Control

In this paper, sliding mode control-based impact time guidance laws are proposed. Even for large heading angle errors and negative initial closing speeds, the desired impact time is achieved by enforcing a sliding mode on a switching surface designed by using the concepts of collision course and estimated time-to-go. Unlike existing guidance laws, the proposed guidance strategy achieves impact time successfully even when the estimated interception time is greater than the desired impact time. Simulation results are also presented.