Showing papers in "Journal of Guidance Control and Dynamics in 2011"

Wind Field Estimation for Small Unmanned Aerial Vehicles

Abstract: This paper describes a method for estimating wind field (wind velocity, rate of change of wind velocity, and wind gradient) for small and mini unmanned aerial vehicles. The approach uses sensors that are already part of a standard autopilot sensor suite (Global Positioning System, inertial measurement unit, airspeed, and magnetometer). The primary motivation is enabling energy harvesting; a secondary motivation is development of a low-cost atmospheric measurement and sampling system. The paper presents an error analysis and discusses the primary contributions to error in the estimated wind field. Results of Monte Carlo simulations compare predicted errors in wind estimates with actual errors and show the effect of using estimated winds for energy harvesting from gusts.

Optimal Cooperative Pursuit and Evasion Strategies Against a Homing Missile

Abstract: Optimal-control-based cooperative evasion and pursuit strategies are derived for an aircraft and its defending missile. The aircraft-defending missile team cooperates in actively protecting the aircraft from a homing missile. The cooperative strategies are derived assuming that the incoming homing missile is using a known linear guidance law. Linearized kinematics, arbitrary-order linear adversaries' dynamics, and perfect information are also assumed. Specific limiting cases are analyzed in which the attacking missile uses proportional navigation, augmented proportional navigation, or optimal guidance. The optimal one-on-one, noncooperative, aircraft evasion strategies from a missile using such guidance laws are also derived. For adversaries with first-order dynamics it is shown that depending on the initial conditions, and in contrast to the optimal one-on-one evasion strategy, the optimal cooperative target maneuver is either constant or arbitrary. These types of maneuvers are also the optimal ones for the defender missile. Simulation results confirm the usefulness and advantages of cooperation. Specifically, it is shown how the target can lure in the attacker, allowing its defender to intercept the attacking missile even in scenarios in which the defender's maneuverability is at a disadvantage compared with the attacking missile.

Cooperative Differential Games Strategies for Active Aircraft Protection from a Homing Missile

Abstract: Cooperative pursuit―evasion strategies are derived for a team composed of two agents. The specific problem of interest is that of protecting a target aircraft from a homing missile. The target aircraft performs evasive maneuvers and launches a defending missile to intercept the homing missile. The problem is analyzed using a linear quadratic differential game formulation for arbitrary-order linear players' dynamics in the continuous and discrete domains. Perfect information is assumed. The analytic continuous and numeric discrete solutions are presented for zero-lag adversaries' dynamics. The solution of the game provides 1) the optimal cooperative evasion strategy for the target aircraft, 2) the optimal cooperative pursuit strategy for the defending missile, and 3) the optimal strategy of the homing missile for pursuing the target aircraft and for evading the defender missile. The obtained guidance laws are dependent on the zero-effort miss distances of two pursuer―evader pairs: homing missile with target aircraft and defender missile with homing missile. Conditions for the existence of a saddle-point solution are derived and the navigation gains are analyzed for various limiting cases. Nonlinear two-dimensional simulation results are used to validate the theoretical analysis. The advantages of cooperation are shown. Compared with a conventional one-on-one guidance law, cooperation significantly reduces the maneuverability requirements from the defending missile.

Ion Beam Shepherd for Contactless Space Debris Removal

Abstract: T HE steady increase of the space debris population is threatening the future of space utilization for both commercial and scientific purposes. Since the Sputnik 1 launch in 1957 thousands of satellites have been delivered to orbit with a current launch rate of about 60 new satellites per year. A considerable fraction of the launchedmass, almost 6000 tons at the time of writing, has remained in orbit producing more than 15,000 trackable objects. In the current situation this number is growing not only because of newly launched satellites but also due to on-orbit explosions and accidental collisions among resident space objects. According to a study by Liou and Johnson [1], even assuming no new satellites were launched, the increase rate of trackable objects generated by accidental collisions would exceed the decrease rate due to atmospheric drag decay starting from about the year 2055. This trend is mostly due to large and massive objects placed in crowded orbits, that is, at altitudes between 800 and 1000 km and near-polar inclination. It is widely agreed that, in order to reduce this threat, not only newly launched spacecraft and upper stages will need to be deorbited but also a fraction of the existing ones, calling for active debris removal operations. If these operations do not start soon, a “snowball effects” can take place in which collision-generated objects will generate new collisions leading to an escalation of the number of debris in orbit [1]. Thework byLiou and Johnson [1] is significant not only because it analyses the beneficial effects of a planned debris removal campaign but also because it suggests what debris should be targeted first. The preference is put on objects that are more likely to experience collision and to leave a large amount of potential debrismass in orbit: the conclusion is that active debris removal, in order to be effective, should deal with large space debris in crowded orbits up to about 1600 km altitude. By looking at the current U.S. Space Surveillance Network catalogue one finds that there are more than 1000 objects withmass larger than 1 ton in the low-Earth-orbit (LEO) environment (i.e., having perigee larger than 2000 km) with a total mass of more than one third of the total catalogued mass in Earth orbit. The great majority of these objects are in quasi-circular highly inclined orbits. Whatever active removal strategy is chosen, it will clearly need to be able to deorbit an average 2 ton space object in a reasonable amount of time andwith a reasonable cost in terms of hardware and fuel. This is especially true if one considers debris removal campaigns inwhich a few large objects are removed every year and continuously for a few decades [1]. Several active debris removal concepts have been proposed ranging from laser systems [2,3] to electrodynamic tethers [4–6]. Solar sails, which are known to be impractical in LEO, have also been proposed for reorbiting dead satellite in geostationary Earth orbit [7]. Once a quick and effective removal method has been devised there still remains an important technological challenge to overcome: the transmission of momentum from the removal system to the space debris in order to carry out the deorbiting (or reorbiting) maneuver. The most obvious way to do that is to dock the removal system with the target before the deorbiting starts. This operation can, however, be technologically complex and very risky. Space debris are noncooperative objects generally characterized by a problematic attitude motion (tumbling motion, flat-spin rotation, large amplitude oscillations, etc.) which are not easy to dock. Another possible solution is to perform a capture operation with some kind of appendage (e.g., a net or a harpoon) released from the spacecraft. In this case the major difficulty is perhaps connected with the deployment and targeting of the capturing device, which, in addition, would be difficult to reuse for multiple removal operations. Debris removal concepts based on pulsed-laser ablation systems do offer a key advantage in this regard as they can be operated far from the orbiting target, possibly even from the ground. Unfortunately though, the small impulse obtained from material ablation cannot be effective against targets of size exceeding about 20 cm [3]. Recently, our team has begun the study of a new space propulsion concept [8] in which a highly collimated, high-velocity ion beam is produced on board an ion beam shepherd (IBS) spacecraft flying in proximity of a target and directed against the target tomodify its orbit and/or attitudewith no need for docking. Themomentum transmitted by the ion beam (ions have been accelerated up to 30 km=s andmore on board spacecraft in past missions) is orders of magnitude higher than the one obtained, for equal power cost, using material ablation. Figure 1 describes the idea in one of itsmost simple implementations. Note that the idea of accelerating a spacecraft with a flux of incident ions was also recently explored by Brown et al. [9] who propose a lunar-based ion beam generator to remotely propel spacecraft in the Earth–moon system. In addition, a similar ion-beam irradiation system has been proposed very recently as a mean to reorbit space debris in GEO [10]. Potentially, the IBS concept can be used for contactless maneuvering of space debris irrespective of their attitude motion. This Note will assess the feasibility of the concept, its expected performance and its main technological challenges. First the main physics of the ion beammomentumpropagation are addressed taking into account the technological level of state of the art ion thrusters. Next, the deorbiting capability for an optimized system applied to orbital debris in circular orbit in LEO is evaluated. Additional issues to be addressed in future studies are outlined and conclusions are drawn.

Theory and Flight-Test Validation of a Concurrent-Learning Adaptive Controller

Abstract: Theory and results of flight-test validation are presented for a novel adaptive law that concurrently uses current as well as recorded data for improving the performance of model reference adaptive control architectures. This novel adaptive law is termed concurrent learuing. This adaptive law restricts the weight updates based on stored data to the null-space of the weight updates based on current data for ensuring that learning on stored data does not affect responsiveness to current data. This adaptive law alleviates the rank-1 condition on weight updates in adaptive control, thereby improving weight convergence properties and improving tracking performance. Lyapunov-like analysis is used to show that the new adaptive law guarantees uniform ultimate boundedness of all system signals in the framework of model reference adaptive control. Flight-test results confirm expected improvements in performance.

Intercept-Angle Guidance

Abstract: interest is aerial interception between a missile and a maneuvering target. The guidance concept is applicable in all aerial interception geometries: namely, head-on, tail-chase, and the novel head-pursuit. Analytical conditions for existence of these different engagement geometries are derived. The guidance concept is implemented using the sliding-modeapproach. Thecommonassumption of flight alonganinitial collisiontriangle isnottaken,andthusthe guidance law is applicable for both midcourse and endgame guidance. The application in the different engagement geometries is studied via simulation. It is shown that the head-on scenario allows the smallest range of intercept angles.Italsoplacesthemostseveremaneuverabilityrequirementsontheinterceptor.Thus,insomecases,tail-chase or head-pursuit engagements should be considered instead. The choice between the two is dependent on the adversary’s speed ratio; for tail-chase, the interceptor must have a speed advantage over its target, while for headpursuit, it must have a speed disadvantage.

Sparse Gauss-Hermite Quadrature Filter with Application to Spacecraft Attitude Estimation

Abstract: A novel sparse Gauss―Hermite quadrature filter is proposed using a sparse-grid method for multidimensional numerical integration in the Bayesian estimation framework. The conventional Gauss―Hermite quadrature filter is computationally expensive for multidimensional problems, because the number of Gauss―Hermite quadrature points increases exponentially with the dimension. The number of sparse-grid points of the computationally efficient sparse Gauss―Hermite quadrature filter, however, increases only polynomially with the dimension. In addition, it is proven in this paper that the unscented Kalman filter using the suggested optimal parameter is a subset of the sparse Gauss―Hermite quadrature filter. The sparse Gauss-Hermite quadrature filter is therefore more flexible to use than the unscented Kalman filter in terms of the number of points and accuracy level, and it is more efficient than the conventional Gauss―Hermite quadrature filter. The application to the spacecraft attitude estimation problem demonstrates better performance of the sparse Gauss―Hermite quadrature filter in comparison with the extended Kalman filter, the cubature Kalman filter, and the unscented Kalman filter.

Survey of Highly Non-Keplerian Orbits with Low-Thrust Propulsion

Abstract: Celestial mechanics has traditionally been concerned with orbital motion under the action of a conservative gravitational potential. In particular, the inverse square gravitational force due to the potential of a uniform, spherical mass leads to a family of conic section orbits, as determined by Isaac Newton, who showed that Kepler‟s laws were derivable from his theory of gravitation. While orbital motion under the action of a conservative gravitational potential leads to an array of problems with often complex and interesting solutions, the addition of non-conservative forces offers new avenues of investigation. In particular, non-conservative forces lead to a rich diversity of problems associated with the existence, stability and control of families of highly non-Keplerian orbits generated by a gravitational potential and a non-conservative force. Highly non-Keplerian orbits can potentially have a broad range of practical applications across a number of different disciplines. This review aims to summarize the combined wealth of literature concerned with the dynamics, stability and control of highly non-Keplerian orbits for various low thrust propulsion devices, and to demonstrate some of these potential applications.

Dynamics and Control of a Biomimetic Vehicle Using Biased Wingbeat Forcing Functions

Abstract: A wingbeat forcing function and control method are presented that allow six-degree-of-freedom control of a flapping-wing micro air vehicle using only two actuators, each of which independently actuate a wing. Split-cycle constant-period frequency modulation with wing bias is used to produce nonzero cycle-averaged drag. The wing bias provides pitching-moment control and, when coupled with split-cycle constant-period frequency modulation, requires only independently actuated wings to enable six-degree-of-freedom flight. Wing bias shifts the cycle-averaged center-of-pressure locations of the wings, thus providing the ability to pitch the vehicle. Implementation of the wing bias is discussed, and modifications to the wingbeat forcing function are made to maintain wing position continuity. Instantaneous and cycle-averaged forces and moments are computed, cycle-averaged control derivatives are calculated, and a controller is developed. The controller is designed using a simplified aerodynamic model derived with blade-element theory and cycle averaging. The controller is tested using a simulation that includes blade-element-based estimates of the instantaneous aerodynamic forces and moments that are generated by the combined motion of the rigid-body fuselage and the flapping wings. Simulations using this higher-fidelity model indicate that the cycle-averaged blade-element-based controller is capable of achieving controlled flight.

Decentralized Robust Adaptive Control for Attitude Synchronization Under Directed Communication Topology

Abstract: T HE need to maintain accurate relative orientation between spacecraft is critical in many satellite formation missions. For instance, in interferometry application, the relative orientation between spacecraft in a formation is required to be maintained precisely during formation maneuvers. In interspacecraft laser communication operation, the participating spacecraft are also required to maintain accurate relative attitude throughout the communication process. This control problem, commonly referred to as attitude synchronization in the literature, has attracted much research attention. Various solutions have been proposed and these can be broadly classified according to the advocated techniques: leader– follower [1–4], virtual structure [5,6], behavior-based [7–11], and graph-theoretical approach [12–15]. In particular, the graph-theoretical approach has been actively studied for cooperative control of multi-agent system using limited local interaction [16,17] and was adopted for attitude synchronization problem in [12–15]. In the above-cited decentralized attitude synchronization results, except [14,15], it is assumed that the interspacecraft communication links are undirected (i.e. bidirectional). However, in practice, the interspacecraft communication topology may be restricted to be directed, such as in unidirectional satellite laser communication system. The control problem of attitude synchronization under directed communication topology is more challenging as compared with the case with undirected communication topology. This issue was studied in [14] but the proposed control law requires derivative of the angular velocity, which may introduce additional noise into the system. Furthermore, the attitude-tracking performance analysis in [14] is applicable only to the casewhere the directed graph can be simplified to a graph with only one node. This constraint on communication topology is relaxed in [15], which uses modified Rodriguez parameters and Euler– Lagrange system to describe the satellite attitude dynamics. However,modifiedRodriguez parameters contain singularity and are thus not suitable for the development of globally stabilizing control algorithms. This Note proposes a decentralized adaptive sliding-mode control lawwhich regulates attitude and angular velocity errors of individual spacecraft with respect to reference commands and minimizes relative attitude and angular velocity errors between spacecraft. Thus, the proposed control law ensures that each spacecraft attains desired time-varying attitude and angular velocity while maintaining attitude synchronization with other spacecraft in the formation even in the presence of model uncertainties and external disturbances. Moreover, the design is applicable to general communication topology and is not restricted to ring topology or undirected communication topology. In the following section, unit quaternion representation will be introduced into the satellite attitude control problem and algebraic graph theory will be applied to describe general directed communication topology.

Line-of-Sight Interceptor Guidance for Defending an Aircraft

Abstract: = missile evasive maneuver normal to defendermissile line of sight amp = missile evasive maneuver component normal to target-missile line of sight at, ad, am = target, defender, and missile lateral accelerations, respectively at max, ad max, am max = target, defender, and missile maximum lateral accelerations, respectively atplos, adplos, amplos = target, defender, and missile accelerations normal to the line of sight, respectively Rd, Rm, Rdm = target-defender, target-missile, and defendermissile closing ranges, respectively tf = defender-missile interception time vt, vd, vm = target, defender, and missile speeds, respectively vtlos, vdlos, vmlos = target, defender, and missile speeds along the line of sight, respectively vtplos, vdplos, vmplos

Lyapunov Differential Equation Approach to Elliptical Orbital Rendezvous with Constrained Controls

Abstract: and energy. A parametric Lyapunov differential equation approach is proposed in this paper to solve this constrained regulation problem. After establishing the fact that the Tschauner-Hempel equations are both null controllable with controls of bounded magnitude and energy, this paper proves that the proposed linear periodic controllersemigloballystabilizesthesystem.Equivalently,forany fixedinitialconditions,themagnitudeandenergy of the control can be made as small as desired by tuning some free parameters in the feedback laws. In comparison with the existing quadratic-regulation-based approach, which requires solutions to nonlinear Riccati differential equations,thenewapproachrequiresonlythesolutionoflinearperiodicLyapunovdifferentialequations,whichare investigated inthepaperbyusingtheperiodicgenerator approach.Numericalsimulationsofthe nonlinearmodelof the spacecraft rendezvous instead of a linearized one show that both the magnitude and energy of the control can be reduced to an arbitrarily small level by reducing the values of some parameters in the controller and that the rendezvous mission can be accomplished satisfactorily.

Gaussian Sum Filters for Space Surveillance: Theory and Simulations

Abstract: While standard Kalman-based filters, Gaussian assumptions, and covariance-weighted metrics are very effective in data-rich tracking environments, their use in the data-sparse environment of space surveillance ismore limited. To properly characterize non-Gaussian density functions arising in the problem of long-term propagation of state uncertainties, a Gaussian sum filter adapted to the two-body problem in space surveillance is proposed and demonstrated to achieve uncertainty consistency. The proposed filter is made efficient by using only a onedimensional Gaussian sum in equinoctial orbital elements, thereby avoiding the expensive representation of a full six-dimensional mixture and hence the “curse of dimensionality.” Additionally, an alternate set of equinoctial elements is proposed and is shown to provide enhanced uncertainty consistently over the traditional element set. Simulation studies illustrate the improvements in theGaussian sumapproach over the traditional unscentedKalman filter and the impact of correct uncertainty representation in the problems of data association (correlation) and anomaly (maneuver) detection.

Optimal Rendezvous Trajectories of a Controlled Spacecraft and a Tumbling Object

Abstract: This paper formulates and solves the problem of minimum-time and minimum-energy optimal trajectories of rendezvous of a powered chaser and a passive tumbling target, in a circular orbit. Both translational and rotational dynamics are considered. In particular, ending conditions are imposed of matching the positions and velocities of two points of interest onboard the vehicles. A collision-avoidance condition is imposed as well. The optimal control problems are analytically formulated through the use of the Pontryagin minimum principle. The problems are then solved numerically, by using a direct collocation method based on the Gauss pseudospectral approach. Finally, the obtained solutions are verified through the minimum principle, solved by a shooting method. The simulation results show that the pseudospectral solver provides solutions very close to the optimal ones, except in the case of presence of singular arcs when it may not provide a feasible solution. The computational time needed by the pseudospectral solver is a small fraction of the one needed by the indirect approach, but it is still considerably too large to allow for its use in real-time onboard guidance.

Improved Shaping Approach to the Preliminary Design of Low-Thrust Trajectories

Abstract: This paper presents a general framework for the development of shape-based approaches to low-thrust trajectory design. A novel shaping method, based on a three-dimensional description of the trajectory in spherical coordinates, is developed within this general framework. Both the exponential sinusoid and the inverse polynomial shaping are demonstrated to be particular two-dimensional cases of the spherical one. The pseudoequinoctial shaping is revisited within the new framework, and the nonosculating nature of the pseudoequinoctial elements is analyzed. A two step approach is introduced to solve the time of flight constraint, related to the design of low-thrust arcs with boundary constraints for both spherical and pseudoequinoctial shaping. The solution derived from the shaping approach is improved with a feedback linear-quadratic controller and compared against a direct collocation method based on finite elements in time. The new shaping approach and the combination of shaping and linear-quadratic controller are tested on three case studies: a mission to Mars, a mission to asteroid 1989ML, a mission to comet Tempel-1, and a mission to Neptune.

Dispersion Analysis in Hypersonic Flight During Planetary Entry Using Stochastic Liouville Equation

Abstract: A framework is provided for the propagation of uncertainty in planetary entry, descent, and landing. The traditional Monte―Carlo based dispersion analysis is overly resource-expensive for such high-dimensional nonlinear systems and does not provide any methodical way to analyze the effect of uncertainty for mission design. It is shown that propagating the density function through Liouville equation is computationally attractive and suitable for further statistical analysis. Comparative simulation results are provided to bring forth the efficacies of the proposed method. Examples are given from the entry, descent, and landing domain to illustrate how one can retrieve statistical information of interest from an analyst's perspective.

Fault-Tolerant Attitude Control for Flexible Spacecraft Without Angular Velocity Magnitude Measurement

Abstract: S INCE some catastrophic faults or failures may be induced due to the aging or damage of actuators and sensors during the mission of a spacecraft, those faults would lead to performance degradation of the spacecraft attitude control system or even result in the specified aerospacemission failure. Therefore, fault tolerance of the spacecraft attitude control system is one of the key issues that needs to be addressed. With a view to tackle such a challenge, fault-tolerant control (FTC) has received considerable attention in order to enhance the spacecraft reliability and to guarantee the attitude control performance [1–5]. In [5], an adaptive FTC is developed for the flexible spacecraft attitude tracking system where the persistent bounded disturbances, unknown inertia parameter, and even two types of reaction wheel faults are successfully accommodated. Indeed, the aforementioned approaches offer many attractive conceptual features, but at the same time they are derived based on the availability of direct and exact measurements of both the angular velocity and the attitude orientation. It is important to note, however, that when it comes to practical implementation, the angular velocity measurements are not always available because of either cost limitations or implementation constraints. Motivated from such a practical consideration, it is therefore highly desirable to develop partial state feedback attitude control strategies with spacecraft angular velocity measurements eliminated. The issue has been addressed in the literature by using observer-based control [6,7], Lyapunov-based control [8,9], and variable structure control [10] under normal operation of spacecraft. In this work, we provide solutions to two different problems of the flexible spacecraft attitude control system. The first problem consists of developing a control law to perform a attitude stabilization maneuver without angular velocity magnitude. In contrast with the velocity-free control schemes available in the literature, the presented approach can guarantee the attitude control performance be greatly robust to external disturbances and unknown inertia parameters. The second problem solved is the casewhere both loss of control effectiveness and additive fault occur in actuators simultaneously, but the attitude still requires stabilization with high resolution. To the best knowledge of the authors, this study is the first attempt to deal with fault-tolerant attitude stabilization control for flexible spacecraft with the angular velocity magnitude eliminated. The Note is organized as follows. Section II presents the mathematical model and attitude control problems formation of a flexible spacecraft under normal and faulty actuator conditions. Section III presents the proposed fault-tolerant attitude stabilization controller without velocity magnitude in the presence of two types of actuator faults. Simulation results to demonstrate various features of the proposed scheme are given in Sec. IV followed by conclusions in Sec. V.

Derivative-Free Model Reference Adaptive Control

Abstract: A derivative-free, delayed weight update law is developed for model reference adaptive control of continuous-time uncertain systems, without assuming the existence of constant ideal weights. Using a Lyapunov―Krasovskii functional it is proven that the error dynamics are uniformly ultimately bounded, without the need for modification terms in the adaptive law. Estimates for the ultimate bound and the exponential rate of convergence to the ultimate bound are provided. Also discussed are employing various modification terms for further improving performance and robustness of the adaptively controlled system. Examples illustrate that the proposed derivative-free model reference adaptive control law is advantageous for applications to systems that can undergo a sudden change in dynamics.

Density Functions for Mesh Refinement in Numerical Optimal Control

Abstract: needed to understand how the density/monitor functions can be used in numerical optimal control and how they can influence the accuracy and robustness of numerical optimal control algorithms Furthermore, the choice of “good” density/monitor functions for mesh discretization of optimal control problems seems to be open Inthispaperweattempttoprovideapartialanswertotheprevious questions We introduce a method to distribute the mesh points efficiently using density/monitor functions Although different monitor functions can be used for mesh generation, an appropriate choice of a monitor function can generate a better quality mesh, and can improve the accuracy of the solution along with the speed of convergence Hence, the problem of mesh generation can be treated asaproblemof findinganappropriatedensity/monitorfunctionTwo possible choices of density functions are used in the numerical examples, based on the discrete control/state histories from the previousiterationduringthemeshrefinementprocessTheproposed method avoids the numerical integration step and the use of ODE solversforthesystemdynamicsaswasdonein[8]Yet,itgeneratesa mesh with a suitable level of adaptive discretization that provides sharp resolution around the places where the control switches or the trajectory meets/leaves state constraints, thus resulting in better accuracy of the overall final solution Numerical examples are presented to demonstrate the advantage of the proposed method, and comparisons are provided against the industry-standard sparse optimal control software (SOCS)

Autonomous Exploration of a Wind Field with a Gliding Aircraft

Abstract: Soaring is the process of exploiting favorable wind conditions to extend flight duration. This paper presents an approach for simultaneously mapping and using a wind field for soaring with an unpowered aircraft. Previous research by the authors and others has addressed soaring in known wind fields. However, an adequate estimate of the wind field is required in order to generate energy-gain paths. Conversely, the exploration required to generate a useful map estimate requires energy. This work aims to address these problems simultaneously by attempting to maintain and improve a model-free wind map based on observations collected during the flight and to use the currently available map to generate energy-gain paths. Wind estimation is performed using Gaussian process regression. A path planner generates and selects paths based on energy efficiency and field exploration. The method is tested in simulation with wind fields consisting of single and multiple stationary thermal bubbles. The use of soaring flight with consistent improvement in map quality and accuracy is demonstrated in a number of scenarios.

Aircraft Trajectory Optimization and Contrails Avoidance in the Presence of Winds

Abstract: There are indications that persistent contrails can lead to adverse climate change, although the complete effect on climate forcing is still uncertain. A flight trajectory optimization algorithm with fuel and contrails models, which develops alternative flight paths, provides policy makers the necessary data to make tradeoffs between persistent contrails mitigation and aircraft fuel consumption. This study develops an algorithm that calculates wind-optimal trajectories for cruising aircraft while avoiding the regions of airspace prone to persistent contrails formation. The optimal trajectories are developed by solving a non-linear optimal control problem with path constraints. The regions of airspace favorable to persistent contrails formation are modeled as penalty areas that aircraft should avoid and are adjustable. The tradeoff between persistent contrails formation and additional fuel consumption is investigated, with and without altitude optimization, for 12 city-pairs in the continental United States. Without altitude optimization, the reduction in contrail travel times is gradual with increase in total fuel consumption. When altitude is optimized, a two percent increase in total fuel consumption can reduce the total travel times through contrail regions by more than six times. Allowing further increase in fuel consumption does not seem to result in proportionate decrease in contrail travel times.

Kinematic analysis and control design for a nonplanar multirotor vehicle

Abstract: A new class of nonplanar multirotor rotary vehicle is introduced that has the capability of independent control of both thrust and torque vectors in three dimensions. The vehicle configuration is based around the use of six thrust producing rotors arranged in pairs on three separate reference planes. Variable thrust can be provided via fixedpitch/variable-speed rotors or variable-pitch/fixed-speed rotors. The orientation of rotor reference planes affects the orthogonality of force and torque control, and it is shown how maneuverability can be traded with propulsive efficiency. The static mapping between force and torque control outputs and rotor inputs is derived from rotor geometry and a simple rotor aerodynamic model that does not include interference between rotors or fuselage drag and does not explicitly include induced-velocity effects. Controllers are synthesized for both position and attitude control, with acceptable stability demonstrated via Lyapunov analysis. Vehicle closed-loop dynamic response is investigated in simulation, and controller performance is shown to meet design requirements in the presence of unmodeled rotor inertia effects. Experimental results on a static test rig confirm that the simplified rotor aerodynamic modeling used for control synthesis is adequate for symmetric flight conditions around hover. A free flying prototype has been flight-tested in hover, showing that practical vehicles are possible, accepting the fact that increased control capability comes at the expense of reduced payload and duration, compared with a conventional helicopter.

Globally Asymptotic Stabilization of Spacecraft with Simple Saturated Proportional-Derivative Control

Abstract: ATTITUDE stabilization of a rigid body has been a subject that has attracted a considerable amount of interest in the control of rigid spacecraft and aircraft. Several control techniques that stabilize the arbitrary attitude motion of a spacecraft can be found in the literature. For example, Egeland and Godhavn [1] establish the passivity between the angular velocity vector and the Euler parameter vector, and they propose an adaptive control to complete the global asymptotic stabilization of a rigid spacecraft. Using the same idea, Lizarraide and Wen [2] develop velocity-free controllers. The results in [1,2] were later extended by Tsiotras [3]. Fjellstad and Fossen [4] show that linear proportional-derivative (PD) control law is able to asymptotically stabilize the attitude motion of a rigid body by using minimal three-dimensional parameterizations for the kinematics. The attitude stabilization of a rigid body, using the unit quaternion and the angular velocity in the feedback control law, has been investigated by many researchers, and a wide class of controllers has been proposed (see, for instance, [5–7]). Because of its inherent robustness with respect to external disturbances and uncertainties, various optimal control schemes have been proposed for solving the attitude stabilization problem for rigid spacecraft [8–10]. While these control schemes are simple, elegant, and intuitively appealing, there is an implicit assumption in the development of these schemes that the spacecraft actuators are able to provide any requested joint torque. This assumption can lead to difficulties in practice since the available torque amplitude is limited in actual spacecraft. Moreover, it is known that control system design approaches that do not incorporate input constraints directly into the design suffer from important performance limitations [11,12]. For example, if the controller commands more torque than the actuators can supply from the typical control methods, degraded or unpredictable motion and thermal or mechanical failure may result [13]. Recognizing these difficulties, several solutions that take into account actuator constraints have been proposed. Specifically, Tsiotras and Luo [14] developed a saturation control law for an underactuated rigid spacecraft. This control law is completed by using a nonstandard attitude representation, which allows the decomposition of general motion into two rotations. Boskovic et al. [15] formulated two robust sliding mode controllers for global asymptotic stabilization of spacecraft in the presence of control input saturation and uncertainties, based on the variable-structure control approach. Wallsgrove and Akella [16] developed a smooth attitude stabilizing control containing hyperbolic tangent functions. The controller can be viewed as a smooth analog of the variable-structure approach, with the degree of sharpness of the control permitted to vary with time according to a set of user-defined parameters. Belta [17] proposes a saturated controller for driving the system from initial to final regions of the state space locally. The saturated control law is constructed based on a control of multiaffine systems. Guerrero-Castellanos et al. [18] investigated the global stabilization of a rigid spacecraft with a bounded quaternion-based feedback. Recently, Ali et al. [19] presented a method to design a bounded control for spacecraft attitude maneuver with backstepping control. This Note complements and extends the results presented in [3] to the bounded input cases. In particular, two very simple saturated PD (SPD) controllers are proposed to ensure global asymptotic stabilization of rigid spacecraft subject to actuator saturation, in terms of the Euler parameter kinematic parameterizations. The contribution of this Note is twofold. Comparing with similar work presented in [3], the proposed controls are bounded; thus, they can remove the possibility of degraded or unpredictable motion and actuator failure due to excessive torque input levels. This is accomplished by selecting control gains a priori. The fact that the proposed controllers can be a priori bounded is a significant added advantage. The practical implications are that the actuators can be appropriately sized without an ad hoc saturation scheme to protect the actuator. In comparison with the available saturated controls for stabilization of spacecraft, the proposed saturated controllers do not refer to the model parameters in the control formulations and are very simple; thus, they are readily implemented. It is proven that spacecraft systems subject to actuator constraints can be globally asymptotically stabilized via the proposed SPD controls by using Lyapunov’s direct method and LaSalle’s invariance principle. Simulations are included to illustrate the effectiveness of the proposed approaches.

Robust Roll Autopilot Design for Tactical Missiles

Abstract: In this paper, a robust roll autopilot based on the extended state observer technique is proposed. The autopilot is robust to uncertainties, external disturbances, the airframe flexibility, and fast unmodeled sensor lags. The external disturbances and the parametric uncertainties in the roll loop are treated as a composite disturbance and the extended state observer is used to estimate the composite disturbance and the states of the system in an integrated manner. The estimated disturbance and the estimated states are used to robustify linear quadratic regulator autopilots designed for nominal systems. The closed-loop stability of the observer-controller combination is proved. Simulation results are presented to demonstrate the efficacy of the extended state observer in estimation of the uncertainties and the states, and in meeting the objectives of the design. Lastly, the proposed design is compared with some well-known designs reported in the literature.

Cooperative Target Localization with a Communication-Aware Unmanned Aircraft System

Abstract: This paper presents an approach to generating information-gathering trajectories for a cooperative unmanned aircraft system that takes into account the reliability of multihop networked communication. The algorithms presented here implicitly consider the communication limitations of the aircraft within a path-planning algorithm in which there is a position dependency on both the sensing and communication capabilities of the network. A communication-aware performance metric is derived by combining the extended information filter with a packet- erasure channel model and stochastic model of packet routing. Informative trajectories that maximize this metric are generated by a distributed, hierarchical planning algorithm. Flight results are used to characterize the communication channel model for use in a multivehicle simulation. Finally, simulation studies are used to evaluate the path-planning approach through the specific application of stationary WiFi source localization. These studies show that the approach leads to improved estimation performance relative to path-planning that does not consider communication reliability. Further, the approach leads to the emergence of natural roles whereby some of the aircraft contribute largely to the sensing portion of the objective, while others improve communication reliability by serving mainly as communication relays.

Model-Free Control Design for Multi-Input Multi-Output Aeroelastic System Subject to External Disturbance

Abstract: In this paper, a class of aeroelastic systems with an unmodeled nonlinearity and external disturbance is considered. By using leading- and trailing-edge control surface actuations, a full-state feedforward/feedback controller is designed to suppress the aeroelastic vibrations of a nonlinear wing section subject to external disturbance. The fullstate feedback control yields a uniformly ultimately bounded result for two-axis vibration suppression. With the restriction that only pitching and plunging displacements are measurable while their rates are not, a high-gain observer is used to modify the full-state feedback control design to an output feedback design. Simulation results demonstrate the efficacy of the multi-input multi-output control toward suppressing aeroelastic vibration and limit cycle oscillations occurring in pre and postflutter velocity regimes when the system is subjected to a variety of external disturbance signals. Comparisons are drawn with a previously designed adaptive multi-input multi-output controller.

Susceptibility of F/A-18 Flight Controllers to the Falling-Leaf Mode: Linear Analysis

Abstract: The F/A-18 Hornet aircraft with the original flight control law exhibited a nonlinear out-of-control phenomenon known as the falling-leaf mode. This unstable mode was suppressed by modifying the control law. This paper employs the falling-leaf phenomenon as an example to investigate the applicability of linear analysis tools for detecting inherently nonlinear phenomenon. A high-fidelity nonlinear model of the F/A-18 is developed for controller analysis using F/A-18 High-Alpha Research Vehicle aerodynamic data in the open literature. A variety of linear analysis methods are used to investigate the robustness properties of the original (baseline) and the revised F/A-18 flight control law at different trim points. Classical analyses, e.g., gain and phase margins, do not indicate a significant improvement in robustness properties of the revised control law over the baseline design. However, advanced robustness analyses, e.g., μ analysis, indicate that the revised control law is better able to handle the cross-coupling and variations in the dynamics than the baseline design.