Missile guidance and autopilot have been active fields of research since the second world war. There are lots of literature on the subjects, but the bulk of which are confined to overly simplified models, and therefore the publications of the methods applied to more realistic models are scarce. In this report a nonlinear 6 DOF simulation model of a tail-controlled air-to-air missile is considered. Through several assumptions and simplifications a linearized approximation of the plant is obtained, which then is used in the implementation of 5 guidance laws and 2 autopilots. The guidance laws are all based on a linearized collision geometry, and the autopilots are based on model predictive control (MPC). Both autopilots use linear quadratic MPC (LQMPC), and one is more robust to modelling errors than the conventional LQMPC. The guidance laws and autopilots are then evaluated with respect to performance in terms of miss distance in 4 interception scenarios with a moving target. The results show that the in this model the autopilots perform equally well, and that the guidance laws with more information about the target generally exhibit smaller miss distances, but at the cost of a considerably larger flight time for some scenarios. The conclusions are that the simplifying assumptions in the modelling are legitimate and that the challenges of missile control probably does not lie in the guidance or autopilot, but rather in the target tracking. Therefore it is suggested that future work include measurement noise and process disturbances in the model. / Det har forskats kring styrlagarna och styrautomaterna för robotar sedan an-dra världskrigets. Det finns mycket litteratur på områdena, men merparten av de publicerade resultaten behandlar enbart grovt förenklade modeller, och därför är tillgången på publikationer där metoderna applicerats i en mer realistisk modell begränsat. I denna rapport behandlas en olinjär simuleringsmodell av en jaktrobot som styrs med stjärtfenor och har sex frihetsgrader. Genom en rad antaganden och förenklingar erhålls en linjäriserad modell av missilen, vilket sedan används för implementering av fem styrlagar och två styrautomater. Styr-lagarna är alla baserade på en linjäriserad kollisionsgeometri och styrautomaterna är baserade på modellprediktiv styrning (MPC). Båda styrautomaterna använder linjärkvadratisk MPC, där den ena påstås vara mer robust gentemot modellfel. Styrlagarna och -automaterna utvärderas ur ett prestandaperspektiv med fokus på bomavstånd i fyra realistiska genskjutningsscenarier med ett rörligt mål. Resultaten visar att båda styrautomaterna presterar lika bra, och att de styrlagar med mer information om målets position/hastighet/acceleration generellt presterar bättre, men att de för vissa skjutfall får en väsentligt längre flygtid. Slutsatserna är att förenklingarna och antagandena i linjäriseringen är välgrundade, och att utmaningarna i missilstyrning inte ligger i utformning av styrlag/-automat, utan förmodligen i målsökningen. Därför föreslås det slutligen att framtida arbete bl. a. inkluderar mätbrus och störningar.

This thesis proposes and evaluates a new cooperative guidance law called General Vector Explicit - Impact Time and Angle Control Guidance (GENEX-ITACG). The motivation for GENEX-ITACG came from an explicit trajectory shaping guidance law called General Vector Explicit Guidance (GENEX). GENEX simultaneously achieves design specifications on miss distance and terminal missile approach angle while also providing a design parameter that adjusts the aggressiveness of this approach angle. Encouraged by the applicability of this user parameter, GENEX-ITACG is an extension that allows a salvo of missiles to cooperatively achieve the same objectives of GENEX against a stationary target through the incorporation of a cooperative trajectory shaping guidance law called Impact Time and Angle Control Guidance (ITACG). ITACG allows a salvo of missile to simultaneously hit a stationary target at a prescribed impact angle and impact time. This predetermined impact time is what allows each missile involved in the salvo attack to simultaneously arrived at the target with unique approach angles, which greatly increases the probability of success against well defended targets. GENEX-ITACG further increases this probability of kill by allowing each missile to approach the target with a unique approach angle rate through the use of a user design parameter. The incorporation of ITACG into GENEX is accomplished through the use of linear optimal control by casting the cost function of GENEX into the formulation of ITACG. The feasibility GENEXITACG is demonstrated across three scenarios that demonstrate the ITACG portion of the guidance law, the GENEX portion of the guidance law, and finally the entirety of the guidance law. The results indicate that GENEX-ITACG is able to successfully guide a salvo of missiles to simultaneously hit a stationary target at a predefined terminal impact angle and impact time, while also allowing the user to adjust the aggressiveness of approach.

The main body of this thesis consists of six appended papers. In the  first two, different  cooperative surveillance problems are considered. The second two consider different aspects of the trajectory planning problem, while the last two deal with observer design for mobile robotic and Euler-Lagrange systems respectively.In Papers A and B,  a combinatorial optimization based framework to cooperative surveillance missions using multiple Unmanned Ground Vehicles (UGVs) is proposed. In particular, Paper A  considers the the Minimum Time UGV Surveillance Problem (MTUSP) while Paper B treats the Connectivity Constrained UGV Surveillance Problem (CUSP). The minimum time formulation is the following. Given a set of surveillance UGVs and a polyhedral area, find waypoint-paths for all UGVs such that every point of the area is visible from  a point on a waypoint-path and such that the time for executing the search in parallel is minimized.  The connectivity constrained formulation  extends the MTUSP by additionally requiring the induced information graph to be  kept recurrently connected  at the time instants when the UGVs  perform the surveillance mission.  In these two papers, the NP-hardness of  both these problems are shown and decomposition techniques are proposed that allow us to find an approximative solution efficiently in an algorithmic manner.Paper C addresses the problem of designing a real time, high performance trajectory planner for an aerial vehicle that uses information about terrain and enemy threats, to fly low and avoid radar exposure on the way to a given target. The high-level framework augments Receding Horizon Control (RHC) with a graph based terminal cost that captures the global characteristics of the environment.  An important issue with RHC is to make sure that the greedy, short term optimization does not lead to long term problems, which in our case boils down to two things: not getting into situations where a collision is unavoidable, and making sure that the destination is actually reached. Hence, the main contribution of this paper is to present a trajectory planner with provable safety and task completion properties. Direct methods for trajectory optimization are traditionally based on a priori temporal discretization and collocation methods. In Paper D, the problem of adaptive node distribution is formulated as a constrained optimization problem, which is to be included in the underlying nonlinear mathematical programming problem. The benefits of utilizing the suggested method for  online  trajectory optimization are illustrated by a missile guidance example.In Paper E, the problem of active observer design for an important class of non-uniformly observable systems, namely mobile robotic systems, is considered. The set of feasible configurations and the set of output flow equivalent states are defined. It is shown that the inter-relation between these two sets may serve as the basis for design of active observers. The proposed observer design methodology is illustrated by considering a  unicycle robot model, equipped with a set of range-measuring sensors. Finally, in Paper F, a geometrically intrinsic observer for Euler-Lagrange systems is defined and analyzed. This observer is a generalization of the observer proposed by Aghannan and Rouchon. Their contractivity result is reproduced and complemented  by  a proof  that the region of contraction is infinitely thin. Moreover, assuming a priori bounds on the velocities, convergence of the observer is shown by means of Lyapunov's direct method in the case of configuration manifolds with constant curvature. / QC 20100622 / TAIS, AURES

<p>The main body of this thesis consists of four appended papers. The first two consider different aspects of the trajectory planning problem, while the last two deal with observer design for mobile robotic and Euler-Lagrange systems respectively.</p><p>The first paper addresses the problem of designing a real time, high performance trajectory planner for aerial vehicles. The main contribution is two-fold. Firstly, by augmenting a novel safety maneuver at the end of the planned trajectory, this paper extends previous results by having provable safety properties in a 3D setting. Secondly, assuming initial feasibility, the planning method is shown to have finite time task completion. Moreover, in the second part of the paper, the problem of simultaneous arrival of multiple aerial vehicles is considered. By using a time-scale separation principle, one is able to adopt standard Laplacian control to this consensus problem, which is neither unconstrained, nor first order.</p><p>Direct methods for trajectory optimization are traditionally based on<i> a</i> <i>priori </i>temporal discretization and collocation methods. In the second paper, the problem of adaptive node distribution is formulated as a constrained optimization problem, which is to be included in the underlying nonlinear mathematical programming problem. The benefits of utilizing the suggested method for online trajectory optimization are illustrated by a missile guidance example.</p><p>In the third paper, the problem of active observer design for an important class of non-uniformly observable systems, namely mobile robotics systems, is considered. The set of feasible configurations and the set of output flow equivalent states are defined. It is shown that the inter-relation between these two sets may serve as the basis for design of active observers. The proposed observer design methodology is illustrated by considering a unicycle robot model, equipped with a set of range-measuring sensors.</p><p>Finally, in the fourth paper, a geometrically intrinsic observer for Euler-Lagrange systems is defined and analyzed. This observer is a generalization of the observer recently proposed by Aghannan and Rouchon. Their contractivity result is reproduced and complemented by a proof that the region of contraction is infinitely thin. However, assuming <i>a</i> <i>priori </i>bounds on the velocities, convergence of the observer is shown by means of Lyapunov's direct method in the case of configuration manifolds with constant curvature.</p>

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.

Autonomous aerial vehicles like missiles and unmanned aerial vehicles (UAVs) have attracted various military and civilian applications. The primary guidance objective of any autonomous vehicle is to reach the desired destination point (target or waypoint). However, many practical engagements impose additional constraints like minimum control effort, a desired final velocity direction or a predefined engagement time. This thesis addresses engagement time constrained guidance problems pertaining to missiles and UAVs. The first part of the thesis discusses a nonlinear guidance law for impact time control of missiles against stationary target. The guidance law is designed with a particular choice of missile heading error variation as a function of ran to-target. The proposed heading error variation leads to an exact closed-form expression for the impact time. controlling the impact time, a closed-form relation is derived relating the control parameter to the desired impact time. A new Lyapunov based guidance law with a monotonically decreasing lateral acceleration is proposed in the next part of the thesis. An exact expression for impact time with minimum and maximum achievable impact times is derived. A control parameter is proposed with a closed-form relationship to the desired impact time. Using the concept of predicted interception point, the two guidance laws are extended for impact time control against non-maneuvering and moving targets. The proposed guidance models are extended to three-dimensional engagements by deducing yaw and pitch lateral accelerations satisfying the desired heading error profile. Extensive simulation studies are carried out for single missile and salvo attack scenarios. The last part of the thesis presents a guidance methodology governing the arrival time of a UAV at a waypoint. A specific arrival angle is considered as an additional constraint. The arrival constraints are satisfied by varying the navigation gain of the proportional navigation guidance law. The methodology is applied for simultaneous and sequential arrival of UAVs at a waypoint.

The main body of this thesis consists of four appended papers. The first two consider different aspects of the trajectory planning problem, while the last two deal with observer design for mobile robotic and Euler-Lagrange systems respectively. The first paper addresses the problem of designing a real time, high performance trajectory planner for aerial vehicles. The main contribution is two-fold. Firstly, by augmenting a novel safety maneuver at the end of the planned trajectory, this paper extends previous results by having provable safety properties in a 3D setting. Secondly, assuming initial feasibility, the planning method is shown to have finite time task completion. Moreover, in the second part of the paper, the problem of simultaneous arrival of multiple aerial vehicles is considered. By using a time-scale separation principle, one is able to adopt standard Laplacian control to this consensus problem, which is neither unconstrained, nor first order. Direct methods for trajectory optimization are traditionally based on a priori temporal discretization and collocation methods. In the second paper, the problem of adaptive node distribution is formulated as a constrained optimization problem, which is to be included in the underlying nonlinear mathematical programming problem. The benefits of utilizing the suggested method for online trajectory optimization are illustrated by a missile guidance example. In the third paper, the problem of active observer design for an important class of non-uniformly observable systems, namely mobile robotics systems, is considered. The set of feasible configurations and the set of output flow equivalent states are defined. It is shown that the inter-relation between these two sets may serve as the basis for design of active observers. The proposed observer design methodology is illustrated by considering a unicycle robot model, equipped with a set of range-measuring sensors. Finally, in the fourth paper, a geometrically intrinsic observer for Euler-Lagrange systems is defined and analyzed. This observer is a generalization of the observer recently proposed by Aghannan and Rouchon. Their contractivity result is reproduced and complemented by a proof that the region of contraction is infinitely thin. However, assuming a priori bounds on the velocities, convergence of the observer is shown by means of Lyapunov's direct method in the case of configuration manifolds with constant curvature. / QC 20101108