Showing papers in "Journal of Guidance Control and Dynamics in 2010"

Homing Guidance Law for Cooperative Attack of Multiple Missiles

Abstract: OVER the past few years, there have been significant efforts devoted to the research and development of cooperative unmannedsystems [1–3].The formationflyingofmultipleunmanned aerial vehicles (UAVs) has been studied for radar deception, reconnaissance, surveillance, and surface-to-air-missile jamming in military operations. An example of a cooperative operational scenario of multiple vehicles is that of a small UAV flying over an urban area, dispensingmultiplemicro aerial vehicles to examinepointsof interest fromclosedistances [4].Agroupofwell-organized low-costmultiple vehicles can be far superior to a single high-technology and high-cost UAV in effectiveness. Tactical missile systems as well as UAVs provide more capabilities when they are organized as a coordinated group than when they are operated independently. Modern antiship missiles need to be able to penetrate the formidable defensive systems of battleships such as antiair defense missile systems and close-in weapon system (CIWS). CIWS is a naval shipboard weapon system for detecting and destroying incoming antiship missiles and enemy aircraft at short range. These defensive weapons with powerful fire capability and various strategies seriously intimidate the survivability of the conventional antiship missiles. Hence, antiship missile developers have made great efforts to develop a high-performance missile system with ultimate sea-skimming flight and terminal evasive maneuvering capabilities despite a huge cost. On the other hand, cooperative attack strategies have been studied to enhance survivability of the conventional ones. Here, a cooperative attack means that multiple missiles attack a single target or multiple targets cooperatively or, in a specific case, simultaneously [5,6]. Clearly, it is difficult to defend a group of attackers bursting into sight at the same time, even though each member is the conventional one in performance. So the simultaneous attack ofmultiple missiles is a cost-effective and efficient cooperative attack strategy. A simultaneous attack of a group of missiles against a single common target can be achieved by two ways. The first approach is individual homing, inwhich a common impact time is commanded to all members in advance, and thereafter each missile tries to home on the target on time independently. The second is cooperative homing, inwhich themissiles communicate among themselves to synchronize the arrival times. In other words, the missiles with larger times-to-go try to take shortcuts, whereas others with shorter times-to-go take detours to delay the arrival times. The first concept requires determination of a suitable common impact time before homing, but the second needs online data links throughout the engagement. Despite a number of studies on guidance problems related to timeto-go [7–10], studies on guidance laws to control impact time for a simultaneous attack are rare, except a few recent works by the authors. An impact-time-control guidance law (ITCG) for antiship missiles was developed in [5] and, as an extension of this study, a guidance law to control both impact time and angle (ITACG) was presented in [11]. These individual homing methods are based on optimal control theory, providing analytical closed-loop guidance laws. Herein, the desired impact time is assumed to be prescribed before the homing phase starts. Alternatively, this Note is concerned with a new guidance law based on the second approach, cooperative homing, for a simultaneous attack of multiple missiles. Proportional navigation (PN) is a well-known homing guidance method in which the rate of turn of the interceptor is made proportional with a navigation ratio N to the rate of turn of the line of sight (LOS) between the interceptor and the target. The navigation constant N is a unitless gain chosen in the range from 3 to 5 [12]. Although PNwithN 3 is known to be energy-optimal, an arbitrary N > 3 is also optimal if a time-varying weighting function is included into the cost function of the linear quadratic energy-optimal problem [13,14]. In general, the navigation ratio is held fixed. In some cases, however, it can be considered as a control parameter to achieve a desired terminal heading angle [15].Although PN results in successful intercepts under a wide range of engagement conditions, its control-efficiency is not optimal, in general, especially for the case of maneuvering targets [16]. Augmented proportional navigation, a variant of PN, is useful in cases in which target maneuvers are significant [12]. Biased proportional navigation is also commonly used to compensate for target accelerations and sensor noises or to achieve a desired attitude angle at impact [17]. Even if PN and its variants are alreadywell known andwidely used, they are not directly applicable to many-to-one engagements. This Note proposes a homing guidance law called cooperative proportional navigation (CPN) for many-to-one engagements: CPN has the same structure as conventional PN except that it has a time-varying navigation gain that is adjusted based on the onboard time-to-go and the times-to-go of the other missiles. CPN uses the time-varying navigation gain as a control parameter for reducing the variance of times-on-target of multiple missiles. This Note begins with the formulation of the homing problem of multiple missiles against a single target, subject to constraints on the impact time. Next, preliminary concepts such as the relative time-togo error and the variance of times-to-go of multiple missiles are introduced and a new guidance law is proposed. Then the major property of the law is investigated and the characteristics of the law for the case of twomissiles are examined in detail. Finally, numerical simulation results illustrate the performances of the proposed law.

Robust Flight Control Using Incremental Nonlinear Dynamic Inversion and Angular Acceleration Prediction

Abstract: This paper presents a flight control strategy based on nonlinear dynamic inversion. The approach presented, called incremental nonlinear dynamic inversion, uses properties of general mechanical systems and nonlinear dynamic inversion by feeding back angular accelerations. Theoretically, feedback of angular accelerations eliminates sensitivity to model mismatch, greatly increasing the robust performance of the system compared with conventional nonlinear dynamic inversion. However, angular accelerations are not readily available. Furthermore, it is shown that angular acceleration feedback is sensitive to sensor measurement time delays. Therefore, a linear predictive filter is proposed that predicts the angular accelerations, solving the time delay and angular acceleration availability problem. The predictive filter uses only references and measurements of angular rates. Hence, the proposed control method makes incremental nonlinear dynamic inversion practically available using conventional inertial measurement units.

Minimum-Landing-Error Powered-Descent Guidance for Mars Landing Using Convex Optimization

Abstract: To increase the science return of future missions to Mars and to enable sample return missions, the accuracy with which a lander can be deliverer to the Martian surface must be improved by orders of magnitude. The prior work developed a convex-optimization-based minimum-fuel powered-descent guidance algorithm. In this paper, this convex-optimization-based approach is extended to handle the case when no feasible trajectory to the target exists. In this case, the objective is to generate the minimum-landing-error trajectory, which is the trajectory that minimizes the distance to the prescribed target while using the available fuel optimally. This problem is inherently a nonconvex optimal control problem due to a nonzero lower bound on the magnitude of the feasible thrust vector. It is first proven that an optimal solution of a convex relaxation of the problem is also optimal for the original nonconvex problem, which is referred to as a lossless convexification of the original nonconvex problem. Then it is shown that the minimum-landing-error trajectory generation problem can be posed as a convex optimization problem and solved to global optimality with known bounds on convergence time. This makes the approach amenable to onboard implementation for real-time applications.

Particle Swarm Optimization Applied to Space Trajectories

Abstract: The particle swarm optimization technique is a population-based stochastic method developed in recent years and successfully applied in several fields of research. It represents a very intuitive (and easy to program) methodology for global optimization, inspired by the behavior of bird flocks while searching for food. The particle swarm optimization technique attempts to take advantage of the mechanism of information sharing that affects the overall behavior of a swarm, with the intent of determining the optimal values of the unknown parameters of the problem under consideration. In this research the method is applied to a variety of space trajectory optimization problems, i.e., the determination of periodic orbits in the context of the circular restricted three-body problem, and the optimization of (impulsive and finite thrust) orbital transfers. Despite its simplicity and intuitiveness, the particle swarm algorithm proves to be quite effective in finding the optimal solution to all of the applications considered in the paper, with great numerical accuracy.

Impact Angle Constrained Guidance Against Nonstationary Nonmaneuvering Targets

Abstract: 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.

Wingbeat Shape Modulation for Flapping-Wing Micro-Air-Vehicle Control During Hover

Abstract: A new method of controlling a flapping-wing micro air vehicle by varying the velocity profiles of the wing strokes is presented in this manuscript. An exhaustive theoretical analysis along with simulation results show that this new method, called split-cycle constant-period frequency modulation, is capable of providing independent control over vertical and horizontal body forces as well as rolling and yawing moments using only two physical actuators, whose oscillatory motion is defined by four parameters. An actuated bob-weight is introduced to enable independent control of pitching moment. A general method for deriving sensitivities of cycle-averaged forces and moments to changes in wingbeat kinematic parameters is provided, followed by an analytical treatment for a case where the angle of attack of each wing is passively regulated and the motion of the wing spar in the stroke plane is driven by a split-cycle waveform. These sensitivities are used in the formulation of a cycle-averaged control law that successfully stabilizes and controls two different simulation models of the aircraft. One simulation model is driven by instantaneous aerodynamic forces derived from blade-element theory, while the other is driven by an empirical representation of an unsteady aerodynamic model that was derived from experiments.

Air-Combat Strategy Using Approximate Dynamic Programming

Abstract: Unmanned aircraft systems have the potential to perform many of the dangerous missions currently flown by manned aircraft, yet the complexity of some tasks, such as air combat, have precluded unmanned aircraft systems from successfully carrying out these missions autonomously. This paper presents a formulation of a level-flight fixed-velocity one-on-one air-combat maneuvering problem and an approximate dynamic programming approach for computing an efficient approximation of the optimal policy. In the version of the problem formulation considered, the aircraft learning the optimal policy is given a slight performance advantage. This approximate dynamic programming approach provides a fast response to a rapidly changing tactical situation, long planning horizons, and good performance, without explicit coding of air-combat tactics. The method's success is due to extensive feature development, reward shaping, and trajectory sampling. An accompanying fast and effective rollout-based policy extraction method is used to accomplish online implementation. Simulation results are provided that demonstrate the robustness of the method against an opponent, beginning from both offensive and defensive situations. Flight results are also presented using unmanned aircraft systems flown at the Massachusetts Institute of Technology's real-time indoor autonomous vehicle test environment.

Cooperative Multiple-Model Adaptive Guidance for an Aircraft Defending Missile

Abstract: A cooperative guidance law, for a defender missile protecting an aerial target from an incoming homing missile, is presented. The filter used is a nonlinear adaptation of a multiple model adaptive estimator, in which each model represents a possible guidance law and guidance parameters of the incoming homing missile. Fusion of measurements from both the defender missile and protected aircraft is performed. A matched defender’s missile guidance law is optimized to the identified homing missile guidance law. It utilizes cooperation between the aerial target and the defender missile. The cooperation stems from the fact that the defender knows the future evasive maneuvers to be performed by the protected target and thus can anticipate the maneuvers it will induce on the incoming homing missile. Moreover, the target performs a maneuver that minimizes the control effort requirements from the defender. The estimator and guidance law are combined in a multiple model adaptive control configuration. Simulation results show that combining the estimations with the proposed optimal guidance law, that utilizes cooperation between the defending missile and protected target, yields hit-to-kill closed loop performance with very low control effort. This facilitates the use of relatively small defending missiles to protect aircrafts from homing missiles.

Path Following for Small Unmanned Aerial Vehicles Using L1 Adaptive Augmentation of Commercial Autopilots

Abstract: The paper presents a three-dimensional path-following control algorithm that expands the capabilities of conventional autopilots, which are normally designed to provide only guidance loops for waypoint navigation. Implementation of this algorithm broadens the range of possible applications of small unmanned aerial vehicles. The solution proposed takes explicit advantage of the fact that normally these vehicles are equipped with autopilots stabilizing the vehicles and providing angular-rate tracking capabilities. Therefore, the overall closed-loop system exhibits naturally an inner-outer (dynamics-kinematics) control loop structure. The outer-loop path-following control law developed relies on a nonlinear control strategy derived at the kinematic level, while the inner-loop consisting of the autopilot together with an L1 adaptive augmentation loop is designed to meet strict performance requirements in the presence of unmanned aerial vehicle modeling uncertainty and environmental disturbances. A rigorous proof of stability and performance of the path-following closed-loop system, including the dynamics of the unmanned aerial vehicle with its autopilot, is given. The paper bridges the gap between theory and practice and includes results of extensive flight tests performed in Camp Roberts, California, which demonstrate the benefits of the framework adopted for the control system design.

Airspace Encounter Models for Estimating Collision Risk

Abstract: Airspace encounter models, providing a statistical representation of geometries and aircraft behavior during a close encounter, are required to estimate the safety and robustness of collision avoidance systems. Prior encounter models, developed to certify the Traffic Alert and Collision Avoidance System, have been limited in their ability to capture important characteristics of encounters as revealed by recorded surveillance data, do not capture the current mix of aircraft types or noncooperative aircraft, and do not represent more recent airspace procedures. This paper describes a methodology for encounter model construction based on a Bayesian statistical framework connected to an extensive set of national radar data. In addition, this paper provides examples of using several such high-fidelity models to evaluate the safety of collision avoidance systems for manned and unmanned aircraft.

Lyapunov-Based Exponential Tracking Control of a Hypersonic Aircraft with Aerothermoelastic Effects

Abstract: Hypersonic flightconditionsproducetemperaturevariationsthatcanalterboththestructuraldynamicsand flight dynamics. These aerothermoelastic effects are modeled bya nonlinear, temperature-dependent, parameter-varying state-space representation. The model includes an uncertain parameter-varying state matrix, an uncertain parameter-varying nonsquare (column-deficient) input matrix, and a nonlinear additive bounded disturbance. A Lyapunov-based continuous robust controller is developed that yields exponential tracking of a reference model, despite the presence of bounded nonvanishing disturbances. Simulation results for a hypersonic aircraft are provided to demonstrate the robustness and efficacy of the proposed controller.

Backstepping control design with actuator torque bound for spacecraft attitude maneuver

Abstract: BACKSTEPPING is a popular nonlinear control design technique [1,2]. It hinges on using a part of the system states as virtual controls to control the other states. Generating a family of globally asymptotically stabilizing control laws is the main advantage of this method that can be exploited for addressing robustness issues and solving adaptive problems. The term backstepping refers to the recursive nature of the control design procedure in which a control law and a control Lyapunov function are recursively constructed to guarantee stability. Backstepping has been considered for the spacecraft slew maneuvers [3,4]. The cascaded structure of spacecraft kinematics and dynamics makes the integrator backstepping a preferred approach for the spacecraft attitude maneuver problem, resulting in smooth feedback controls [5]. However, the typical control actuators used for this problem (such as reaction wheels, control moment gyros, or thrusters) have an upper bound on the control torque they can exert onto the system and the simple or conventional backstepping control method may result in excessive control input beyond that saturation bound. The issue has been addressed in the literature using other control methodologies such as nonlinear proportional–integral–derivative control [6], Lyapunovoptimal control [7] and variable structure control [8–11]. In this work, we design a nonlinear backstepping attitude controller using the inverse tangent-based tracking function [4] and a family of augmented Lyapunov functions [12]. Using this control law, we derive an analytical upper bound of the control torque norm. The bound is effectively used to tune the control parameters so that, for the given settling time specification, the upper bound of the control input is minimized. The performance of the proposed controller has shown improvements in minimizing the peak control torque and the settling time. The rest of the Note is organized as follows: First, the kinematics and dynamics of rigid spacecraft are summarized. Second, the details of the design procedure for the proposed controller and the analytical bounds for the control torque components are given. Third, the efficacy of the proposed scheme is demonstrated by the numerical simulations for the cases of attitude stabilization and tracking both. Finally, the conclusions are presented.

Constrained Predictor-Corrector Entry Guidance

Abstract: In this paper we develop a numerical predictor-corrector entry guidance algorithm for vehicles with medium to higher lifting capability. A major dierence between the current algorithm and existing predictor-corrector algorithms is that the current algorithm has the ability to enforce all inequality trajectory constraints commonly seen in entry ight. The enabling mechanism is the so-called quasi-equilibrium glide condition (QEGC). The QEGC allows convenient translation of the path constraints in the velocity-altitude space into the energy-dependent upper and lower bounds for the magnitude of the bank angle. As such, the algorithm is able to enforce the path constraints without suering the usual side eects of increasing complexity and degraded robustness. Another unique feature of the current algorithm is on-line adaptation of a parameter in the lateral guidance logic so that the nal heading alignment oset is tightly regulated. Extensive dispersion simulation results are presented to demonstrate the eectiveness and precision of the algorithm.

Low-Thrust Transfers in the Earth-Moon System, Including Applications to Libration Point Orbits

Abstract: Preliminary designs of low-thrust transfer trajectories are developed in the Earth-moon three-body problem with variable specific impulse engines and fixed engine power. The solution for a complete time history of the thrust magnitude and direction is initially approached as a calculus of variations problem to locally maximize the final spacecraft mass. The problem is then solved directly by sequential quadratic programming, using either single or multiple shooting. The coasting phase along the transfer exploits invariant manifolds and, when possible, considers locations along the entire manifold surface for insertion. Such an approach allows for a nearly propellant-free final coasting phase along an arc selected from a family of known trajectories that contract to the periodic libration point orbit. This investigation includes transfer trajectories from an Earth parking orbit to some sample libration point trajectories, including L 1 halo orbits, L 1 and L 2 vertical orbits, and L 2 butterfly orbits. Given the availability of variable specific impulse engines in the future, this study indicates that fuel-efficient transfer trajectories could be used in future lunar missions, such as south pole communications satellite architectures.

Neurobiologically Inspired Control of Engineered Flapping Flight

Abstract: This paper presents a new control approach and a dynamic model for engineered flapping flight with many interacting degrees of freedom. This paper explores the applications of neurobiologically inspired control systems in the form of central pattern generators to control flapping-flight dynamics. A rigorous mathematical and control theoretic framework to design complex three-dimensional wing motions is presented based on phase synchronization of nonlinear oscillators. In particular, we show that flapping-flying dynamics without a tail or traditional aerodynamic control surfaces can be effectively controlled by a reduced set of central pattern generator parameters that generate phase-synchronized or symmetry-breaking oscillatory motions of two main wings. Furthermore, by using Hopf bifurcation, we show that tailless aircraft alternating between flapping and gliding can be effectively stabilized by smooth wing motions driven by the central pattern generator network. Results of numerical simulation with a full six-degree-of-freedom flight dynamic model validate the effectiveness of the proposed neurobiologically inspired control approach.

Endgame Problem Part 2: Multibody Technique and the Tisserand-Poincare Graph

Abstract: This two-part series studies the anatomy of the endgame problem, the last part of the spacecraft trajectory before the orbit-insertion maneuver into the science orbit. The endgame provides large savings in the capture A v, and therefore it is an important element in the design of ESA and NASA missions to the moons of Jupiter and Saturn. The endgame problem has been approached in different ways with different results: the ν ∞ -leveraging-maneuver approach leads to high-Δ ν, short-time-of-flight transfers, and the multibody technique leads to low-Δν, long-time-of-flight transfers. This paper series investigates the link between the two approaches, giving a new insight to the complex dynamics of the multibody gravity-assist problem. In this paper we focus on the multibody approach using a new graphical tool, the Tisserand-Poincare graph. The Tisserand-Poincare graph shows that ballistic endgames are energetically possible and it explains why they require resonant orbits patched with high-altitude flybys, whereas in the ν ∞ -leveraging-maneuver approach, flybys alone are not effective without impulsive maneuvers in between them. We then use the Tisserand-Poincare graph to design quasi-ballistic transfers. Unlike previous methods, the Tisserand-Poincare graph provides a valuable energy-based target point for the design of the endgame and begin-game and a simple way to patch them. Finally, we present two transfers. The first transfer is between low-altitude orbits at Europa and Ganymede using almost half the Δν of the Hohmann transfer; the second transfer is a 300-day quasi-ballistic transfer between halo orbits of the Jupiter-Ganymede and Jupiter-Europa. With approximately 50 m/s the transfer can be reduced by two months.

Distributed Control of Spacecraft Formations via Cyclic Pursuit: Theory and Experiments

Abstract: In this paper, distributed control policies for spacecraft formations that draw inspiration from the simple idea of cyclic pursuit are studied. First studied are cyclic-pursuit control laws for both single- and double-integrator models in three dimensions. In particular, control laws are developed that only require relative measurements of position and velocity with respect to the two leading neighbors in the ring topology of cyclic pursuit and that allow convergence to a variety of symmetric formations, including evenly spaced circular and elliptic formations and evenly spaced Archimedes spirals. Second, potential applications are discussed, including spacecraft formation for interferometric imaging. Finally, experimental results obtained by implementing the aforementioned control laws on the Synchronized Position Hold Engage Reorient Experimental Satellite testbed onboard the International Space Station are presented and discussed.

Modeling and Simulation of Hose-Paradrogue Aerial Refueling Systems

Abstract: A dynamic modeling and simulation analysis of hose-paradrogue aerial refueling systems is presented. A set of governing equations of motion is derived using a finite-segment approach that describes the dynamics of the hose-paradrogue assembly under a prescribed motion of the tanker. The hose is modeled by a series of ball-and-socket-connected rigid links subject to gravitational and aerodynamic loads that account for the effects of tanker wake, steady wind, and atmospheric turbulence. Numerical simulations show a good correlation of the model's steady-state characteristics with previously reported flight-test data. Also investigated are the dynamic characteristics of the paradrogue assembly resulting from atmospheric turbulence and a typical pitch doublet maneuver of the tanker. Finally, the dynamic motion resulting from an in-flight adjustment of the paradrogue drag associated with strut-angle changes is studied.

Autonomous Navigation in Three-Dimensional Urban Environments Using Wide-Field Integration of Optic Flow

Abstract: In this paper, a control theoretic framework is introduced to analyze an information extraction approach from patterns of optic flow based on analogs to wide-field motion-sensitive interneurons in the insect visuomotor system. An algebraic model of optic flow is developed, based on a parameterization of three-dimensional urban environments. It is shown that estimates of proximity and speed, relative to these environments, can be extracted using weighted summations of the instantaneous patterns of optic flow. Small perturbation techniques are then applied to link weighting patterns to outputs, which are applied as feedback to facilitate stability augmentation and perform local obstacle avoidance and terrain following. Additive noise and environment uncertainties are incorporated into an offline procedure for determination of optimal weighting functions. Stability is proven via local asymptotic analysis and the resulting approach demonstrated in simulation using a micro helicopter in a three-dimensional urbanlike environment.

Polynomial Chaos-Based Analysis of Probabilistic Uncertainty in Hypersonic Flight Dynamics

Abstract: In this paper, we present a novel computational framework for analyzing the evolution of the uncertainty in state trajectories of a hypersonic air vehicle due to the uncertainty in initial conditions and other system parameters. The framework is built on the so-called generalized polynomial chaos expansions. In this framework, stochastic dynamical systems are transformed into equivalent deterministic dynamical systems in higher dimensional space. Here, the evolution of uncertainty due to initial condition, ballistic coefficient, lift over drag ratio, and atmospheric density is analyzed. The problem studied here is related to the Mars entry, descent, and landing problems. We demonstrate that the polynomial chaos framework is able to predict evolution of uncertainty, in hypersonic flight, with the same order of accuracy as the Monte-Carlo methods but with more computational efficiency.

Control of Electromagnetic Satellite Formations in Near-Earth Orbits

Abstract: Electromagnetic formation flying is a novel concept of controlling the relative degrees of freedom of a satellite formation without the expenditure of fuel by using high-temperature superconducting wires to create magnetic electromagnetic formation flying. Because of inherent nonlinearities and couplings, the dynamics and control problem associated with electromagnetic formation flying are difficult, especially for near-Earth operations. This paper presents the application of nonlinear adaptive control laws that enable formation maintenance and reconfiguration. An approach to control allocation as the solution of an optimization problem is also proposed. The accumulation of angular momentum in the presence of Earth's magnetic field is an issue with electromagnetic formation flying and ways of managing it by exploiting the nonlinearity of magnetic dipoles using polarity switching are presented as a solution. Closed-loop nonlinear simulation results are also presented to demonstrate the feasibility and importance of the control scheme described for electromagnetic formation flying for near-Earth operations.

Modeling and Model Reference Adaptive Control of Aircraft with Asymmetric Damage

Abstract: This paper addresses some fundamental issues in adaptive control of aircraft with struc- tural damage It presents a thorough study of linearized aircraft models with damage to obtain new details of system descriptions, such as coupling and partial derivatives of lateral and longitudinal dynamics A detailed study of system invariance under damage conditions is performed for generic aircraft models to obtain key system characterizations for model reference adaptive control (MRAC), such as infinite zero structure and signs of high frequency gain matrices A comprehensive study of multivariable MRAC systems in the presence of damage is performed to obtain critical design specifications for adaptive flight control, such as system and controller parametrizations and adaptive parameter up- date laws Both analytical and simulation results are given to illustrate the design and performance of adaptive control systems for aircraft flight control Adaptive control of aircraft in the presence of damage has been an important topic in the research of flight control design for aircraft safety Damage can cause uncertain parametric and structural variations, which requires new aircraft modeling and control approaches In Reference (1), a study of aircraft dynamics with damage is presented, and a neural network based adaptive control algorithm is introduced for control of aircraft in the presence of structure uncertainties In (2), equations of motion are introduced in detail for aircraft with asymmetric mass loss In (3), we introduced a nonlinear aircraft model with partial wing damage, and illustrated linearization of such a model In (4), real time identification of a damaged aircraft model is studied A two-step identification process is introduced, which consists of an aircraft state estimation phase and an aerodynamic model identification step With such a two-step process, the nonlinear part of the model identification is isolated in the first phase, and the aerodynamic parameter identification procedure is simplified to a linear one A hybrid adaptive control method is proposed in (5) for control of aircraft with damage The control design is based on a neural network parameter estimation blended with a direct adaptive law A stability and convergence analysis is presented for this adaptive control methodology For accommodating unknown changes in the structure and parameters, multivariable MRAC designs offer many advantages In (6), we introduced an MRAC design based on the LDS decomposition of the high frequency gain matrix for the control of aircraft with multiple wing damage The key design conditions are that, both the nominal and post-damage systems should have a uniform known modified interactor matrix, and the leading principal minors of their high frequency gain matrices should be nonzero with their signs unchanged In (7), we studied linearization of nonlinear aircraft models under damage conditions and designed a multivariable MRAC scheme which does not require the knowledge of the signs of the high frequency gain matrix Potential extension to aircraft flight control systems with changing signs of the high frequency gain matrix remains a topic of future research

Predictor-Based Model Reference Adaptive Control

Abstract: This paper is devoted to robust, Predictor-based Model Reference Adaptive Control (PMRAC) design. The proposed adaptive system is compared with the now-classical Model Reference Adaptive Control (MRAC) architecture. Simulation examples are presented. Numerical evidence indicates that the proposed PMRAC tracking architecture has better than MRAC transient characteristics.

Command Generation for Flexible Systems by Input Shaping and Command Smoothing

Abstract: DOI: 10.2514/1.50270Aggressive motions are often discouraged when a system has flexible dynamics. Common practice suggests thatsmooth commands, such as S-curves, should be used to drive the system. However, smooth commands cannot beimplementedonsomeactuators,suchastheon/offthrustersusedonspacecraftoron/offvalvesusedwithhydraulicsand pneumatics. Furthermore, smooth commands can lead to sluggish response. A rigorous comparison of smoothand nonsmooth reference commands is presented in this paper. The evaluation is performed by treating smoothcommandprofilesasinput-shapedfunctions.Inputshapingisamethodofreducingresidualvibrationbyconvolvinga sequence of impulses with a baseline reference command. By interpreting smooth commands as input-shapedfunctions, a common criterion for comparing smooth and nonsmooth commands is developed. The results of thiscomprehensive comparison indicate that input-shaped step functions are usually more efficient for reducingvibration than commonly used smooth commands. A portable tower crane is used to experimentally verify thecomparison between input-shaped and smooth commands.

Electric Sail Mission Analysis for Outer Solar System Exploration

Abstract: Missions towards the boundaries of the Solar System require long transfer times and advanced propulsion systems. An interesting option is offered by electric sails, a new propulsion concept that uses the solar wind dynamic pressure for generating a continuous thrust without the need for reaction mass. The aim of this paper is to investigate the performance of such a propulsion system for obtaining escape conditions from the Solar System and planning a mission to reach the heliosphere boundaries. The problem is studied in an optimal framework, by minimizing the time to reach a given solar distance or a given hyperbolic excess speed. Depending on the value of the sail characteristic acceleration, it is possible that, in an initial mission phase, the sailcraft may approach the Sun to exploit the increased available thrust due to the growing solar wind electron density. The corresponding optimal trajectory is constrained to not pass inside a heliocentric sphere whose admissible radius is established by thermal constraints. Once the escape condition is met, the sail is jettisoned and the payload alone continues its journey without any propulsion system. A medium performance electric sail is shown to have the potentialities to reach the heliosheath, at a distance of 100 AU, in about fifteen years. Finally, the Interstellar Heliopause Probe mission is used as a reference mission to further quantify the electric sail capabilities for an optimal transfer towards the heliopause nose (200 AU).

Online Aerodynamic Model Structure Selection and Parameter Estimation for Fault Tolerant Control

Abstract: This paper describes a new recursive algorithm for the approximation of time varying nonlinear aerodynamic models by means of a joint adaptive selection of the model structure and parameter estimation. This procedure is called Adaptive Recursive Orthogonal Least Squares (AROLS), and is an extension and modification of the classical Recursive Orthogonal Least Squares (ROLS). This algorithm is considered to be particularly useful for indirect fault tolerant flight control, making use of model based adaptive control routines. After the failure, a completely new aerodynamic model can be elaborated recursively with respect to structure as well as parameter values. The performance of the identification algorithm is demonstrated on some simulation data sets.

Maximum Torque and Momentum Envelopes for Reaction Wheel Arrays

Abstract: Spacecraft reaction wheel maneuvers are limited by the maximum torque and/or angular momentum that the wheels can provide. For an n-wheel configuration, the torque or momentum envelope can be obtained by projecting the n-dimensional hypercube, representing the domain boundary of individual wheel torques or momenta, into three dimensional space via the 3xn matrix of wheel axes. In this paper, the properties of the projected hypercube are discussed, and algorithms are proposed for determining this maximal torque or momentum envelope for general wheel configurations. Practical strategies for distributing a prescribed torque or momentum among the n wheels are presented, with special emphasis on configurations of four, five, and six wheels.

Fault Tolerant Reconfigurable Satellite Formations Using Adaptive Variable Structure Techniques

Abstract: This paper proposes two adaptive nonlinear control algorithms based on a variable-structure control design for multiple spacecraft formation flying. The nonlinear dynamics describing the motion of the follower spacecraft relative to the leader spacecraft are considered for the case in which the leader spacecraft is in an elliptical reference orbit, and the stability of such a formation in the presence of external perturbations is investigated. This paper presents fault-tolerant control schemes to account for accidental or degradation faults in spacecraft sensors and thrusters. The nonlinear analytical model describing the system is used to develop two adaptive fault-tolerant control laws (continuous sliding mode control and nonsingular terminal sliding mode control) that guarantee global asymptotic convergence of the position tracking error in the presence of unknown follower spacecraft mass and external disturbances. Several numerical examples are presented to demonstrate the efficacy of the proposed controllers to maintain the relative motion by correcting for initial offsets and external perturbation effects that tend to disperse the formation. Simulation results confirm that the suggested methodologies yield submillimeter formation, keeping precision and effectiveness in ensuring formation maneuvering. In addition, an abrupt blockage of the relative position sensors, thruster failure for a period of time, and thruster degradation (amidst formation keeping and reconfiguration maneuvers) are simulated to demonstrate the fault recovery capability of the controllers. The numerical results clearly establish the robustness of the proposed reconfigurable adaptive control scheme for precise formation keeping in the event of sensor and thruster faults.

Hybrid Steering Logic for Single-Gimbal Control Moment Gyroscopes

Abstract: The development of a hybrid steering logic that maintains attitude tracking precision while avoiding hyperbolic internal singularities or escaping elliptic singularities inherent to single-gimbal control moment gyroscopes is discussed. The hybrid steering logic enables null motion and limits torque error when approaching a hyperbolic internal singularity, or it adds torque error and limits null motion when approaching an elliptic internal or external singularity. The hybrid-steering-logic algorithm accomplishes these tasks through the definitions of novel singularity metrics that transition continuously from local-gradient to pseudoinverse methods when moving from hyperbolic to elliptic singularities. Analysis and simulations are presented to demonstrate the performance of the hybrid steering logic as compared with the two legacy methods. The development and results are applied to a four-single-gimbal-control-moment-gyroscope pyramid arrangement with a skew angle of θ = 54.74 deg.

Synthetic-Waypoint Guidance Algorithm for Following a Desired Flight Trajectory

Abstract: T HE development of aircraft guidance, navigation, and control systems has been a long-standing research area. Numerous methods relating to the enhancement of aircraft performance under various mission parameters have been developed in response to a need for more reliable and robust guidance systems. Current guidance systems applied to commercial, civilian, and unmanned aircraft rely on the knowledge of a flight path, specified bywaypoints located in inertial space. Most missions are considered successful when the vehicle reaches the designatedwaypoint at which new commands are issued to the vehicle to proceed to the next waypoint. Two common types of conventional aircraft guidance are the direct-to-waypoint (DTW) and track-to-waypoint (TTW) methods in relation to pathfollowing between designated waypoints. The DTWmethod simply issues heading commands to the vehicle based on the angular difference between thewaypoint and vehicle.When thevehicle reaches the waypoint, the control system issues a new command to guide the aircraft to the next waypoint. The TTW method aims to follow the track betweenwaypoints. In this guidancemethod the control system aims to minimize the lateral offset between the prescribed flight path and the aircraft’s position, issuing heading commands that return the vehicle to the nominal flight path. The track method therefore places the additional constraint on a flight path that the vehicle must follow in order to reach the waypoint, rather than simply reaching the waypoint. However, both methods are far from optimal. This is evident in how the aircraft transitions between flight paths after reaching awaypoint. During theseflight-path transitions, the aircraft will often overshoot the desiredflight path to correct its track, particularlywhen the flight-path transition angle is acute. Various control strategies have been investigated to alleviate or minimize flight-path deviations. Such strategies include applyingmodern control methods such as receding-horizon control [1,2] and model predictive control [3] to anticipate flight-path changes and take control action before reaching a goal while maintaining adequate vehicle flight performance. Missile guidance and control systems operate on similar principles to commercial, civilian, and unmanned aircraft guidance and control algorithms. The primary mission for missile systems is to intercept a moving target using information about the relative position and velocity between the pursuer and target. One of thefirstmethods used in missile guidance was pursuit guidance (PG) [4–7]. The method operates by forcing the angular displacement error between a pursuer and its target to zero. Control commands scaled by a proportional factor of the current error are then issued to direct the pursuer along the line of sight (LOS) between the pursuer and target. PG solutions, however, do not consider the path taken or the levels of system performance required by the pursuer in reaching the target, resulting in a far-from-optimal solution. To address this problem of suboptimality, additional parameters have been introduced to enhance missile performance. One method includes taking into account the motion of the commanded line of sight between the pursuer and target [4,7–10], issuing lateral acceleration commands based on tracking error and tracking error rate to the target. This approach has been shown to improve overall interceptor performance compared with conventional PG [4,7]. Another suchmethod aims tomodify the level of control the guidance algorithm possesses over the vehicle by adjusting the level of proportional gain. This is achieved by gain scheduling [11] to select gain values based on current interceptor states. In addition to modifying internal missile guidance and control parameters such as variable gains and LOS rate estimation, mission performance can be enhanced by manipulating the trajectory taken by the pursuer to the targets. A good example of such a method is discussed in [12], in which a missile aims to exploit the aerodynamic benefits of high-altitude flight by tracking a virtual target at some initially high altitude that is not necessarily along the trajectory to the true target. This Note discusses the development of a guidance law fusing the virtual-target concepts with those of pursuit guidance for implementation into an aircraft guidance system. This Note develops a path-following aircraft guidance algorithm that pursues synthetic waypoints using only a small set of guidance parameters, extending the virtual-target concept to complete aircraft guidance. The path is defined by the track between a minimal set of waypoints at specified locations, removing the need for a smooth path to be defined or the need for complicated path-switching logic or trajectory planning when awaypoint is reached. The synthetic waypoint travels along the path between waypoints, with the trailing aircraft traveling a smooth path generated through its own dynamics in following the synthetic waypoint. The guidance law is tested by varying guidance parameters, thus assessing vehicle sensitivity to and overall system performance of parameter variations. The following sections discuss the basic concepts of missile and aircraft guidance and provide a detailed description of the structure of the synthetic-waypoint guidance algorithm. A discussion on the implementation of the algorithm into the underlying aircraft control system will also be presented, followed by an analysis of the performance of the guidance algorithm in nonlinear simulation. Received 30 June 2009; revision received 3 November 2009; accepted for publication 9November 2009.Copyright©2009 by theAmerican Institute of Aeronautics and Astronautics, Inc. All rights reserved. Copies of this paper may be made for personal or internal use, on condition that the copier pay the $10.00 per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923; include the code 0731-5090/10 and $10.00 in correspondence with the CCC. ∗Graduate Research Student, School of Aerospace, Mechanical and Mechatronic Engineering; e.medagoda@aeromech.usyd.edu.au. Senior Lecturer, School of Aerospace, Mechanical and Mechatronic Engineering; pwg@aeromech.usyd.edu.au. JOURNAL OF GUIDANCE, CONTROL, AND DYNAMICS Vol. 33, No. 2, March–April 2010