The objective of this research was to better understand how impact angle influences headform dynamic response and brain tissue deformation. A bare headform was impacted using a pneumatic linear impactor at 5.5 m/s. The impacts were directed on the front and side location at angles of 0, 5, 10 and 15° rightward rotations as well as -5, -10 and -15° (leftward) rotations at the side to examine the characteristics of the head and neckform on the results. Peak resultant linear and rotational accelerations from the headform as well as peak maximum principal strain (MPS) and von Mises stress (VMS) estimated from a brain finite element model were used to measure the effect of impact angle. Significant results were dependent upon the impact angle and location as well as the dependent variable used for comparison (p <0.05). Impact angle produced significant differences in rotational acceleration and MPS at both the front and side; however angle only had an effect on VMS and linear acceleration at the front and side locations, respectively. These findings show that the effect of impact angle is asymmetrical and is specific to the dependent variable. This study suggests that varying impact angle alone may not be as influential on headform dynamic response and brain tissue deformation and that the severity of an impact may be more of a function of how both location and angle create high risk conditions.

The objective of this research was to better understand how impact angle influences headform dynamic response and brain tissue deformation. A bare headform was impacted using a pneumatic linear impactor at 5.5 m/s. The impacts were directed on the front and side location at angles of 0, 5, 10 and 15° rightward rotations as well as -5, -10 and -15° (leftward) rotations at the side to examine the characteristics of the head and neckform on the results. Peak resultant linear and rotational accelerations from the headform as well as peak maximum principal strain (MPS) and von Mises stress (VMS) estimated from a brain finite element model were used to measure the effect of impact angle. Significant results were dependent upon the impact angle and location as well as the dependent variable used for comparison (p <0.05). Impact angle produced significant differences in rotational acceleration and MPS at both the front and side; however angle only had an effect on VMS and linear acceleration at the front and side locations, respectively. These findings show that the effect of impact angle is asymmetrical and is specific to the dependent variable. This study suggests that varying impact angle alone may not be as influential on headform dynamic response and brain tissue deformation and that the severity of an impact may be more of a function of how both location and angle create high risk conditions.

The objective of this research was to better understand how impact angle influences headform dynamic response and brain tissue deformation. A bare headform was impacted using a pneumatic linear impactor at 5.5 m/s. The impacts were directed on the front and side location at angles of 0, 5, 10 and 15° rightward rotations as well as -5, -10 and -15° (leftward) rotations at the side to examine the characteristics of the head and neckform on the results. Peak resultant linear and rotational accelerations from the headform as well as peak maximum principal strain (MPS) and von Mises stress (VMS) estimated from a brain finite element model were used to measure the effect of impact angle. Significant results were dependent upon the impact angle and location as well as the dependent variable used for comparison (p <0.05). Impact angle produced significant differences in rotational acceleration and MPS at both the front and side; however angle only had an effect on VMS and linear acceleration at the front and side locations, respectively. These findings show that the effect of impact angle is asymmetrical and is specific to the dependent variable. This study suggests that varying impact angle alone may not be as influential on headform dynamic response and brain tissue deformation and that the severity of an impact may be more of a function of how both location and angle create high risk conditions.

This thesis deals with development of guidance laws for advanced applications. Two class of guidance problems, namely, impact angle constrained guidance and pulsed guidance for exo-atmospheric engagements, are considered here. Three impact angle constrained guidance schemes are developed using (i) Proportional navigation guidance (PNG), (ii) State Dependent Riccati Equation (SDRE) technique and (iii) geometric concepts, respectively. A collision course based pulsed guidance law is presented for exo-atmospheric interceptors. Proportional Navigation Guidance (PNG) law is the most widely used guidance law because of its ease of implementation and efficiency. However, in its original form, it achieves only a limited set of impact angles. A two stage PNG law is presented for achieving all impact angles against a stationary target. In the first phase of guidance, an orientation PNG command is used. The orientation navigation constant (N ) is a function of the initial engagement geometry and has a lower value (N less than 2). It is proved that following the orientation trajectory, the interceptor can switch to N = 2 and achieve the desired impact angle. Simulations, with a constant speed and with a realistic interceptor model, show successful interception of the target with all desired impact angles. Feedback implementation of the guidance law results in negligible errors in impact angle with uncompensated autopilot delays. The idea of a two-stage PNG law with impact angle constraint is further used to develop a guidance law for intercepting moving targets. Following the orientation trajectory, the interceptor can switch to N = 3 and achieve the desired impact angle. It is proved that the guidance achieves all impact angles in a surface-to-surface engagement scenario with receding and approaching targets, respectively. In a air-to-surface engagement scenario, it is proved that the guidance law achieves all impact angles in a deterministic set. Constant speed and realistic interceptor models are used for simulations. Results show negligible error in impact angle and miss distance for moving targets. The guidance law, in its feedback implementation form, achieves the desired impact angle for interceptors with delay and with a maneuvering target. The impact angle errors are low with negligible errors in miss distance. Next, the impact angle constrained guidance problem against a stationary target is solved as a non-linear regulator problem using the SDRE technique. The interceptor guidance problems are of finite time nature. As the main contribution of this part of the work, we solve a finite time interceptor guidance problem with infinite horizon SDRE formulation by choosing the state weighting matrix as a function of time-to-go. Numerical simulations are carried out both for a constant speed interceptor model and a realistic interceptor model. Simulations for both the models are carried out for various impact angles and firing angles. Robustness of the proposed guidance law with respect to autopilot lag is also verified by simulations. Results obtained show the efficiency of the SDRE approach for impact angle constrained missile guidance. A geometric guidance scheme is proposed for lateral interception of targets in a planar engagement scenario in the absence of line-of-sight rate information. A kill-band is defined for target initial positions capturable by an arc maneuver, followed by a straight line path by the interceptor. Guidance law for capturing targets inside the kill-band is presented and is further modified for targets outside the kill-band. Based on analytical studies on the kill-band, a guidance law is proposed for lateral interception of maneuvering targets. Simulations are carried with for typical low speed engagements. The concept of kill-band provides an inherent robustness to the proposed guidance law with respect to uncompensated system delays and target maneuver. As the final part of the work, an interceptor endgame pulsed guidance law for exoatmospheric engagements is derived by using the notion of collision heading. The proposed guidance law is derived in steps by (i) Obtaining the collision heading based on the collision triangle engagement geometry and then (ii) Computing the width of the pulse fired by the divert thruster to attain the collision heading. It is shown that this strategy is more effective than the existing zero effort miss (ZEM) based guidance laws for intercepting targets with higher heading angles off the nominal head-on collision course. A result on pulse firing sequence is also presented showing that firing pulses in quick succession results in minimum pulse widths and hence minimum control effort for a desired miss distance. Simulations are carried out for various engagement scenarios. Results show better miss-distance and divert thrust performance as compared to the existing ZEM based law.

Various unmanned missions deploy vehicles such as missiles, torpedoes, ground robots, and unmanned aerial vehicles. Guidance strategies for these vehicles aim to intercept a target point and satisfy additional objectives such as specifications on impact angle and interception time. Certain impact angles are crucial for a greater warhead effectiveness, and minimizing the interception time is important for vehicles with limited endurance time and for reducing the probability of detection. This thesis considers the time-optimal impact angle constrained guidance problem for interception of moving targets. In the first part of the thesis, a Dubins paths–based guidance methodology for minimum-time lateral interception of a moving and non-maneuvering target is designed. The existence and the time-optimality of the paths are established for impact angle constrained interception of moving targets. The capture regions are analyzed and a classification of the initial geometries is developed for deducing the time-optimal path type. The corresponding guidance command for optimal interception can be generated from the information of initial engagement geometry and target’s speed. In the next part of the thesis, the concept of equivalent virtual target is introduced to address the problem of impact along a general direction. An algorithm is developed to obtain the optimal interception point for generalized interception scenarios. A proof of convergence is presented for the proposed algorithm. Achieving different impact angles, the interceptor often takes sharp turns. Following such curved trajectories, the interceptor may fail to keep the target inside the seeker field-of-view. In the next part of the thesis, the field-of-view characteristics of the proposed optimal guidance strategies are analyzed. Closed-form expressions are derived for the interceptor’s look-angle to the target. Satisfying field-of-view condition at endpoints of the path segments that constitute the optimal path is proven to guarantee target motion inside the field-of-view throughout the engagement. The stationary target case is also analyzed as a specific scenario. The last part of the thesis presents a method to extend the proposed guidance strategies to maneuvering target scenarios.

To address the concern of classical guidance and control designs (where guidance and control loops are designed separately in an “outer loop – inner loop” structure), integrated guidance and control (IGC) ideas have been proposed in the recent literature. An important limitation of the existing IGC algorithms, however, is that they do not explicitly exploit the inherent time scale separation that exist in aerospace vehicles between rotational and translational motions, and hence, can be ineffective unless the engagement geometry is close to the collision triangle. To address this, a time scale separated partial integrated guidance and control (PIGC) structure has been proposed in this thesis. In this two-loop design, the commanded pitch and yaw rates are directly generated from an outer loop optimal control formulation, which is solved in a computationally efficient manner using the recently-developed model predictive static programming (MPSP) and Model Predictive Spread Control (MPSC) techniques. The necessary roll-rate command is generated from a roll-stabilization loop. The inner loop then tracks the outer loop commands using the nonlinear dynamic inversion philosophy. However, unlike classical guidance and control designs, in both the loops the Six-DOF interceptor model is used directly. This intelligent manipulation preserves the inherent time scale separation property between the translational and rotational dynamics, and hence overcomes the deficiency of current IGC designs, while preserving the benefits of the IGC philosophy. The new approach has been applied in the terminal phase of an endo-atmospheric interceptor for engaging incoming high speed ballistic missile targets. Six–DOF simulation results will be presented accounting for a 3-D engagement geometry to demonstrate the usefulness of this method. It offers two important advantages: (i) it leads to very small (near-zero) miss distance, resulting in a “hit-to-kill” scenario and (ii) it also leads to lesser and smoother body-rate demands, relaxing the demand on actuators as well as enlarging the ‘capture region’ (which relaxes the demand on mid-course guidance). Next, to address the problem of modeling inaccuracy that is inherent in aerospace vehicles (mainly because of the inaccuracy of aerodynamic model generated from wind-tunnel testing), a neuro-adaptive design is augmented to dynamic inversion technique in the inner loop. In this design the unmodelled dynamics is adaptively captured using three neural networks in the roll, pitch and yaw channels. Training of the neural networks is carried out online using the Lyapunov stability theory, which results in stability of the inner-loop error dynamics as well as boundedness of network weights. This adaptive body rate tracking loop augmented with the sub-optimal feedback guidance loop results in substantial enhancement of interception performance in presence of realistic (i.e. fairly large) modeling uncertainties of the interceptor. The results have also been validated with representative seeker noise.

Guidance is defined as the determination of a strategy for following a nominal path in the presence of o-nominal conditions, disturbances and uncertainties, and the strategy employed is called a guidance law. Variants of Proportional Navigation (PN), such as True Proportional Navigation (TPN) and Pure Proportional Navigation (PPN), have been studied extensively in the literature on tactical missile guidance. In the absence of target maneuvers, in a linear interceptor guidance problem, TPN was shown to be optimal. However, the standard PN class of guidance laws per se does not show good performance against maneuvering targets, and was found to be eective in intercepting a maneuvering target only from a restrictive set of initial geometries. Also, since these guidance laws were eectively designed for lower speed targets, they show a degraded performance when applied against higher speed targets. However, in the current defense scenario, two classes of agile targets, which are capable of continuous maneuver, and/or of much higher speed than the interceptor, are a reality. This thesis presents analysis of several variants of PN class of guidance laws against these two classes of agile targets. In the literature, an augmentation of the TPN guidance law, termed as Augmented Proportional Navigation (APN), was shown to be optimal in linearized engagement framework. The present work proposes an augmentation of the PPN guidance law, which is more realistic than TPN for an aerodynamically controlled interceptor, and an-alyzes its capturability in fully nonlinear framework, and develops sauciest conditions on speed ratio, navigation gain and augmentation parameter to ensure that all possible initial engagement geometries are included in the capture zone when applied against a target executing piecewise continuous maneuver. The thesis also obtains the capture zone in the relative velocity space for augmented PPN guidance law. In the literature, a novel guidance law was proposed for the interception of higher speed targets in planar engagement by using a negative navigation gain instead of the standard positive one, and was termed as Retro-PN. It was shown that even though the Retro-PN guided interceptor takes more time than PN guided one in achieving successful interception, Retro-PN performs significantly better than the classical PN law, in terms of capturability, lateral acceleration demand, and closing velocity, when used against higher speed targets. The thesis analyzes Retro-PN guidance law in 3-D engagement geometries to yield the complete capture zone of interceptors guided by Retro-PN guidance philosophy, and derives necessary and sucient conditions for the capture of higher speed non-maneuvering targets with and without a constraint on finiteness of lateral acceleration. Terminal impact angle control is crucial for enhancement of warhead eectiveness. In the literature, this problem has been addressed mostly in the context of targets with lower speeds than the interceptor. The thesis analyzes the performance of a composite PN guidance law, that uses standard PPN and the Retro-PN guidance laws based on initial engagement geometry and requirement of impact angle, against higher speed non-maneuvering targets. Then, to expand the set of achievable impact angles, it proposes a modified composite PN guidance scheme, and analyzes the same. For implementation of many modern guidance laws, a good estimate of time-to-go is essential. This requirement is especially severe in case of impact time constrained en-gagement scenarios. To this end, an ecient and fast time-to-go estimation algorithm for generic 3-D engagement is required. Two time-to-go estimation algorithms are presented and analyzed in this work for the engagement of a PPN or Retro-PN guided interceptor and a higher speed target. The first one is a closed form approximation of time-to-go in terms of range, nominal closing speed and an indicator of heading error, and the second one is a numerical recursive time-to-go estimation algorithm. To improve the odds of intercepting an intelligent target and destroying it, a salvo attack of two or more interceptors could be considered as a viable option. Moreover, this simultaneous salvo attack can also be further improved in eciency by incorporating the shoot-look-shoot approach in making a decision about launching interceptors. This can be considered as the first step towards a layered defense system, which has been described in the literature as a potentially eective strategy against short range or long range ballistic threat. To this end, the present work proposes two PPN and Retro-PN based guidance strategies for achieving simultaneous salvo attack on a higher speed non-maneuvering target. For the implementation of the same the numerical recursive time-to-go estimation technique proposed in this work is utilized

This thesis addresses several aerospace guidance and decision making problems using both no cooperative and cooperative game theoretical solution concepts in the differential games framework. In the first part of the thesis, state dependent Riccati equation (SDRE) method has been extended to a zero-sum nonlinear differential games setting. This framework is used to study problems of intercepting a manoeuvring target, with and without terminal impact angle constraints, in the zero-sum differential games theory perspective. The guidance laws derived according to the proposed method are in closed from and online implementable. In the second part of the thesis, cooperative game theoretic concepts are applied to make a group of unmanned aerial vehicles (UAV) achieve rendezvous, in a given finite time horizon. An algorithm has been proposed that enables the UAVs to realize Nash bargaining solution. In this context, criteria for time consistency of a cooperative solution of nonzero-sum linear quadratic differential games have been studied. The problems where the UAVs try to achieve rendezvous by implementing cooperative game theoretic strategies, based on local information structure only, is also addressed.

In the guidance literature, minimizing miss distance along with optimizing the energy usage had been an objective for several decades. In current day applications, additional terminal performance such as impact angle and impact time are of paramount importance. These terminal constraints increase warhead effectiveness and survivability of the interceptor. This thesis contributes to the design of guidance laws addressing terminal constraints such as impact angle, impact time, and both impact time as well as impact angle, in addition to interception of targets. In the first part of the thesis, the guidance laws which ensure the alignment of the interceptor at a desired impact angle within a finite time is proposed using different variants of sliding mode control(SMC).The impact angle is first redefined in terms of line-of-sight angle and then the impact angle problem is converted to a simpler problem of controlling line-of-sight angle and their rates. The sliding mode capturability and interpretation of the guidance laws are presented. In order to cater to very large heading angle errors, which give rise to negative closing speed initially, modifications to the guidance laws are also suggested. The modifications to the guidance laws for avoiding singularities, which may be encountered during implementation, due to the inherent nature of terminal SMC, are suggested. However, the guidance laws, which alleviates the possibility of such singularities completely, are also designed by using non singular terminal SMC. The two loop guidance and control, for a skid-to-turn cruciform interceptor in the pitch plane, is also proposed with an autopilot designed using the concept of dynamic SMC. The guidance laws addressing impact angle constraint for three dimensional scenarios are also presented. Unlike the usual approach of decoupling the three dimensional engagement in to two mutually orthogonal planar engagements, the guidance laws are derived using coupled engagement dynamics. These guidance laws are designed using conventional and non singular terminal SMC and provide asymptotic and finite time alignment of the intercept or to the desired impact angles, respectively. Next, the SMC based guidance laws which ensure the interception of targets at pre-specified impact times is proposed in this thesis. The guidance law is first designed for stationary targets and then extended to constant velocity targets using the notion of predicted interception point. A switching surface is designed using the concepts of collision course and time-to-go with non-linear engagement dynamics and its role in achieving the objectives is also discussed. In order to account for large heading angle errors and even for negative initial closing speeds, different methods of estimation of time-to-go, resulting in two different guidance laws, are used. Unlike the existing guidance laws, the proposed guidance laws achieve an impact time even less than its initially estimated value. The flexibility in selecting a desired impact time is also exploited using the maximum available acceleration information. A cooperative salvo attack strategy, based on the proposed impact time guidance law, with a desired impact time chosen in real time using a centralized coordination algorithm, is proposed for stationary targets. The coordination manager determines a common impact time based on time-to-goof the interceptors, by minimizing the total switching surface deviations which in turn reduces the control effort. The thesis also proposes a SMC based guidance strategy which addresses impact angle and impact time constraints simultaneously. This guidance scheme is based on switching between impact time and impact angle guidance laws based on certain conditions. Unlike existing impact time guidance laws, the proposed guidance strategy takes into account the curvature of the trajectory due to the impact angle requirement. The interceptor first corrects its course to nullify the impact time error and then aims to achieve interception with desired impact angle. In order to reduce the transitions between the two guidance laws, a novel hysteresis loop is introduced in the switching conditions. Initially stationary targets are considered, and later the same guidance scheme is extended to constant velocity targets using the notion of predicted interception point. Theclaimsofalltheguidancelawsarevalidatedwithextensivesimulationsandtheir performances are compared with existing guidance laws. Although all the guidance laws derived in the thesis are based on the assumption of constant speed interceptors, their performances are evaluated with a time-varying speed interceptor model, subjected to aerodynamic conditions, to validate their efficacy. The implementation of impact time guidance on time-varying speed interceptors is a formidable challenge in the guidance literature. Such implementations have also been presented in the thesis after introducing the notion of average speed and shown to yield satisfactory performance.