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Demand is growing for unmanned air vehicles (UAVs) with greater autonomy, including the ability to navigate without GPS information, such as indoors. In this work, a novel visual odometry algorithm...

The solution to the simultaneous stabilization problem of a finite set of MIMO unstable plants considered in this Note is based on the frequency-shaped central plant and its sufficiency condition for simultaneous stabilization. The novel method proposed in this Note to acquire the frequency-shaped central plant from a finite set of MIMO unstable plants used v-gap metric between the plants, the frequency-shaping of the plants that used the pre- and post-compensators, and the robust stabilization theory. An optimization problem is formulated to obtain the pre- and post-compensators that reduce the minimum among the maximum v-gap metrics of all the frequency-shaped plants as well as induce required frequency characteristics on all the plants in the set without instigating pole-zero cancellation with any plants in the set. A novel iterative algorithm is developed to solve this optimization problem to attain the compensators. The plant with a maximum v-gap metric that is the minimum among the maximum v-gap metrics of all the frequency-shaped plants is identified as the frequency-shaped central plant. Also, the sufficiency condition of the frequency-shaped central plant is the most suitable sufficiency condition for the simultaneous stabilization. The capability of the iterative algorithm presented in this Note is demonstrated by a realistic design example. For that, the simultaneous stabilization of the finite set of MIMO unstable plants of the NAV is accomplished. The limitation of the method presented in this Note is that it is only applicable to the plants that have similar frequency characteristics. The present work is supported by National Programme for Micro Air Vehicle program. The authors thank Aeronautics Research and Development Board, New Delhi, for partial funding.

Because of the highly integrated nature of their dynamics, flapping-wing micro air vehicles exhibit significant coupling, including interactions between aeroelastic wing behavior, actuator dynamics...

The current work is concerned with longitudinal trajectory tracking control and simulation of a flapping-wing micro air vehicle. For the purpose of accurate simulation studies, a nonlinear and time...

A computationally tractable nonlinear aeroelastic model of a bioinspired flapping-wing micro air vehicle, which includes motor dynamics and is suitable for control evaluation, is developed in this ...

Incremental nonlinear dynamic inversion is a sensor-based control approach that promises to provide high-performance nonlinear control without requiring a detailed model of the controlled vehicle. In the context of attitude control of micro air vehicles, incremental nonlinear dynamic inversion only uses a control effectiveness model and uses estimates of the angular accelerations to replace the rest of the model. This paper provides solutions for two major challenges of incremental nonlinear dynamic inversion control: how to deal with measurement and actuator delays, and how to deal with a changing control effectiveness. The main contributions of this article are 1) a proposed method to correctly take into account the delays occurring when deriving angular accelerations from angular rate measurements; 2) the introduction of adaptive incremental nonlinear dynamic inversion, which can estimate the control effectiveness online, eliminating the need for manual parameter estimation or tuning; and 3) the incorporation of the momentum of the propellers in the controller. This controller is suitable for vehicles that experience a different control effectiveness across their flight envelope. Furthermore, this approach requires only very coarse knowledge of model parameters in advance. Real-world experiments show the high performance, disturbance rejection, and adaptiveness properties.

In this paper, a novel method for aerodynamic model identification of a micro-air vehicle is proposed. The principal contribution is a technique of wind estimation that provides information about the existing wind during flight when no air-data sensors are available. The estimation technique employs multi-objective optimization algorithms that utilize identification errors to propose the wind-speed components that best fit the dynamic behavior observed. Once the wind speed is estimated, the flight experimentation data are corrected and utilized to perform an identification of the aircraft model parameters. A multi-objective optimization algorithm is also used, but with the objective of estimating the aerodynamic stability and control derivatives. Employing data from different flights offers the possibility of obtaining sets of models that form the Pareto fronts. Deciding which model best adjusts to the experiments performed (compromise model) will be the ultimate task of the control engineer., The authors would like to thank the Spanish Ministry of Innovation and Science for providing funding through grant BES-2012-056210 and projects TIN-2011-28082 and ENE-25900. We also want to acknowledge the Generalitat Valenciana for financing this work through project PROMETEO/2012/028.

This paper describes a technique, called quarter-cycle constant period frequency modulation, to control the motion of wings on a flapping wing micro-air vehicle. This technique allows control over the wingbeat period and three additional points (the two zero crossings and the reversal of wing direction) within a single wingbeat cycle, allowing modulation of the wing’s velocity to provide direct control over six degrees of freedom of overall vehicle motion. Using a blade element based aerodynamic model, both instantaneous and cycle-averaged forces and moments are analytically computed for a specific type of wingbeat motion that enables nearly decoupled, multi-degrees of freedom control of an aircraft. Wing motion is controlled using oscillators whose frequencies and three additional parameters change once per wingbeat cycle. A control oriented dynamic model of the vehicle is derived, which is based on a cycle-averaged representation of the forces and moments, and control derivatives are calculated. A cycle...

This paper presents optimization of conventional fixed-wing aircraft perching, stability analysis of optimal perching maneuvers, and tracking formulation of the perching trajectory. Perching maneuvers are optimized to minimize undershoot or altitude gain during the climbing phase, where gravity is used to decelerate the aircraft. A single-phase formulation minimizing the trajectory length of the maneuver is proposed to simplify the optimization formulation and solution procedure. Compared with the existing two-phase approach, where the maneuver is optimized separately in its dive and climb phases, this single-phase formulation is shown to provide lower undershoot perching solutions. Stability analysis of the optimal perching trajectories is performed using contraction theory. It is shown that the perching solutions are in general unstable and will diverge during the terminal phase in the presence of state perturbations. To address this instability and avoid deviation from the desired landing point, a traj...

Flapping wing micro air vehicles continue to be a growing field, with ongoing research into unsteady, low Reynolds number aerodynamics, microfabrication, and fluid–structure interaction. However, research into flapping wing control of such micro air vehicles continues to lag. Existing research uniformly consists of proposed control laws that are validated by computer simulations of quasi-steady blade-element formulas. Such simulations use numerous assumptions and cannot be trusted to fully describe the flow physics. Instead, such control laws must be validated on hardware. In earlier work, a novel control technique, biharmonic amplitude and bias modulation, was proposed and analyzed with these same quasi-steady blade-element formulas. In this work, the biharmonic amplitude and bias modulation control technique was implemented on a flapping wing prototype (4 cm wing length) and tested on a six-component force/torque sensor. Experiments verified that the prototype can generate nearly uncoupled forces and mo...

The navigation of a small unmanned aerial vehicle is challenging due to a large influence of wind to its kinematics. When the kinematic model is reduced to two dimensions, it has the form of the Dubins kinematic vehicle model. Consequently, this paper addresses the problem of minimizing the expected time required to drive a Dubins vehicle to a prescribed target set in the presence of a stochastically varying wind. First, two analytically-derived control laws are presented. One control law does not consider the presence of the wind, whereas the other assumes that the wind is constant and known a priori. In the latter case it is assumed that the prevailing wind is equal to its mean value; no information about the variations of the wind speed and direction is available. Next, by employing numerical techniques from stochastic optimal control, feedback control strategies are computed. These anticipate the stochastic variation of the wind and drive the vehicle to its target set while minimizing the expected tim...

Recent studies of vision-based navigation and guidance for robotic vehicles have been inspired by the biological systems found in flying insects. The wide-field integration of optic flow is one pre-existing method, in which the sensed optic flow is integrated along with sensitivity functions to mimic the action of directionally sensitive cells observed in some insects’ visual systems. This study re-examines the wide-field integration method and reformulates the problem from a summation rather than an integral. This reformulation allows the wide-field integration measurement outputs to be directly compared with nonintegrated optic flow measurements. The method using nonintegrated optic flow measurements is shown to have some practical advantages, such as eliminating the need to define input sensitivity functions and having a measurement Jacobian that is easier to derive analytically. Also, the state estimates obtained with the nonintegrated method are proven to have minimum variance compared with those fro...

This work considers the trimmed periodic orbits of flapping-wing micro air vehicles, and details the tradeoff between the stability of those orbits (via Floquet theory), their size, and the power needed to sustain them. The nonlinear equations of motion of a body with two rigid flapping wings are coupled to a blade element aerodynamic method, and the periodic shooting method is used to locate the orbit. Analytical sensitivities of the relevant flight metrics, including the Floquet multipliers, are derived with respect to kinematic variables, which enables a gradient-based optimization for maximum stability, minimum power, or minimum orbit size. This is done for hovering, climbing, and forward flight; comparisons between the required kinematics and the resulting flight behavior for each optimal case provide insight into the conflicting metrics. Notably, the optimizer is able to locate designs that are stable in an open-loop sense. However, this effort is not meant to replace the inclusion of a dedicated cl...

The multibody flight dynamics of flapping-wing micro air vehicles are inherently complex. Stability analyses and control algorithms are best applied to equations of motion in first-order form. This paper presents a method for approximating the first-order equations of motion for a flapping-wingmicro air vehicle. The first-order equations of motion are derived from a coupled, multibody representation of the system. The first-order equations are analyzed using an approximation method called quarter-cycle averaging. The quarter-cycle averaging method is necessary because the classical averaging techniques are not available. The quarter-cycle approximation method is applied to representations of hovering flight and forward flight. The method enables the calculation of equilibrium points for the averaged system.Forbothflight regimes, the quarter-cycle approximatiomethodprovides anorder ofmagnitude improvement in accuracy when compared to local averaging.

Many recent studies on autonomous spacecraft landing use computer vision methods to improve the accuracy of the state estimates used for landing. Typically, these studies integrate the vision module with other exteroceptive sensors such as laser or radar altimeters. This is a sensible approach for the main landing system of a large spacecraft. However, for a backup emergency system or for much smaller spacecrafts, a solution entirely based on vision and proprioceptive sensors (e.g. gyros) could lead to significant mass savings. Small flying animals are capable of safe and accurate landings while relying only on proprioceptive and visual information. Since this capability holds a promise of landing safely with limited sensors and processing, it has served as inspiration for recent spacecraft landing studies. The focus of these studies has been on the use of ventral optic flow, a measure of the translational velocity divided by the height. Bees are known to use optic flow for controlling their speed and height, also when landing. In particular, when landing, they keep the ventral optic flow constant. Valette et al. study a control law that implements this strategy, simulating landings on the moon. The disadvantages of the sole use of ventral optic flow for landing are two-fold. First, the vertical dynamics of the lander is left free. The ventral flow can have the same constant value for a trajectory in which the lander ascends while accelerating and a trajectory in which the lander descends while decelerating. Thus, one has to directly or indirectly assume some type of descent profile, for example by introducing a pitch law for the spacecraft. Without the use of additional exteroceptive information to compute an optimal pitch profile, this leads to a considerable expense of propellant and to undefined final low-gate conditions. Second, in the case of a straight vertical landing the ventral flow is zero. In such a case, e.g. in the terminal phase of an asteroid landing scenario, the ventral flow does not provide any information on how to land the spacecraft. Advanced Concepts Team, European Space Agency, dario.izzo@esa.int Exteroceptive sensors observe entities external to the spacecraft, while proprioceptive sensors measure quantities within the spacecraft “body”.

cially pertinent in the application of unmanned aircraft used for collecting targeted observations in a hurricane. The presence of such a oweld may inhibit a vehicle from making forward progress relative to a ground-xed frame, thus limiting the directions in which it can travel. Using a selfpropelled particle model in which each particle moves at constant speed relative to the ow, this paper presents results for motion coordination in a strong, known oweld. We present the particle model with respect to inertial and rotating reference frames and provide for each case a set of conditions on the oweld that ensure trajectory feasibility. Results from the Lyapunov-based design of decentralized control algorithms are presented for circular, folium, and spirograph trajectories, which are selected for their potential use as hurricane sampling trajectories. The theoretical results are illustrated using numerical simulations in an idealized hurricane model.

Research into insect-sized flappingwingmicro air vehicles has exploded over the last decade, yetmost of this work has focused on simply achieving flight, while leaving the issue of how to control it to future researchers. Here, previous work in the field of flapping wing control is summarized and each proposed technique is evaluated according to how many body forces and moments it can directly influence on the micro air vehicle and how complicated a wing flapping mechanism is needed to implement it. Though some promising techniques have been proposed, none satisfactorily address all of the design criteria; therefore, a new technique is proposed, biharmonic amplitude andbiasmodulation. This technique is analyzedwith quasi-steady blade-element techniques and shown to provide direct influence over five micro air vehicle body forces and moments in hover while requiring only two actuators. Furthermore, it is applicable to a wing flapping mechanism operating at its resonant frequency, which reduces the energetic cost of control for the micro air vehicle.

Neuromorphic architectures to robust and adaptive navigation based on visual clues have been proposed as automated landing systems. In particular, constant-optic-flow descents have been studied in relation to their bioinspired nature and to their promise for a substantial hardware and software simplification. The main body of work on the topic considers Earth-based systems as applications, such as micro air vehicles, and has only lately looked at planetary landings, but never in relation to their mass optimality. In this paper, constant-optic-flow descents are studied with respect to optimality, first from a theoretical point of view using Pontryagin’s maximum principle and then performing a numerical investigation on some selected cases (Apollo-like) anda comparison with unconstrained descents. The propellant mass introduced by forcing a constant optic flow during a lunar descent is estimated for typical high-gate/low-gate conditions. The effect of constraining the spacecraft pitch law during the constant-optic-flow descent is also studied, showing that an optimal pitch law is essential to lower the overall mass consumption and that linear or exponential laws may not be adequate. A guidance algorithm is then presented and discussed for use in automated planetary landing when a constant optic flow is regulated.

rst principles are described. An example is presented where simulation results are compared to experimental measurements. The results show that the dierential equations correctly predict major trends in observed motor speed and wing spar structural deformation over the course of each wingbeat. The results show that when pairing ight-weight motors and wings, signicant variations in drive motor speed occur during each wingbeat. It is shown that coupling between motor speed, wing loads, and structural exibility cause the aerodynamic forces encountered by the wing spars to depart from those predicted by rigid-spar and constant-velocity-motor-based kinematic simulations.

I NSECTS display remarkable agility and flight-path control in the execution of their everyday tasks, all in the face of significant environmental uncertainties. Maneuvering forces are typically generated by small kinematic perturbations to high-frequency wing motions, such as changes in stroke amplitude, timing of wing rotation, or stroke plane tilting [1]. This clever approach of coupling high-frequency actuation with low-frequency rigid-body motion eliminates the need in most species for active sensing on and active deformation of the wing surface, otherwise evident in their avian [2] and mammalian [3] aerobatic counterparts. Previous analysis of insect-inspired flapping-wing locomotion has examined wing kinematic trajectories from the perspective of maximizing lift [4,5] or minimizing required power [6]. With the introduction of new tools to extract the finewingstroke towingstroke kinematics of insects from high-speed videography [7,8], a number of species-specific control strategies for maneuvering have been identified. In addition, with the development of microscale vehicles that can potentially generate lift forces greater than their weight [9], stability and control aspects of the problem are now a focal point of research. Despite the critical need, the inherent complexity of small-scale flapping flight aerodynamics has obscured a control-theoretic analysis of both biologically relevant and engineered wing kinematic perturbation strategies.While the detailed aerodynamic mechanisms involved in small-scale flight are still an area of active research [10], recent efforts have in fact yielded several approaches for extraction of reduced-order linear time-invariant (LTI) flight dynamics, either for single-degree-of-freedom experimental cases [11,12], direct analytic methods [13], or more general computationally [14] and spectrally derived models [15]. Such formulations are amenable to application of linear control analysis tools, and they should provide the next level of insight. Reachability (or more traditionally, controllability) characterizes the amount of control one has over the state of a system through the choice of the input. This is an important topic for small-scale flapping-wingmicro air vehicle (MAV)designers for several reasons. Size, weight, and power (SWAP) constraints are very stringent at this scale, and reductions in complexity that promote robustness and weight reduction are encouraged. In addition, these vehicles are intended to operate in gusty and possibly cluttered environments, and a high level of platformmaneuverability and actuation authority will be crucial to achieving robust flight-path control in the face of these uncertainties. This Note explores the reachable state space associated with biologically inspired kinematic control strategies seen in longitudinal motion about hover. In Sec. II, a frequency-based system identificationmethodology for identifying the stability derivatives of a small-scale flapping microsystem about hover is outlined, along with the control derivatives for biologically relevant wing kinematic perturbations for maneuvering. Section III applies controllability analysis tools to interpret these biologically relevant control strategies for MAV design, using the example of an MAV with Drosophila-like parameters.

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.

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.

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.

A method for determining the location of a stationary ground target when imaged from the air using a camera-equipped micro air vehicle is developed. The ground object's elevation is assumed known. Rather than a "one-shot" affair, multiple bearing measurements of the ground object taken as the aircraft flies around the target are used. This makes it possible for the adverse effects of both the random measurement errors and the systematic measurement errors (i.e., attitude sensors' biases) to be mitigated. The main result of this paper is that when bearing measurements of a target are taken over time, the target's position and the micro air vehicle's systematic attitude-measurement errors can be jointly estimated using linear regression. As a result,the target is accurately geolocated and the attitude sensors are calibrated. If only one snap bearing measurement of the target can be taken, the attitude sensors will be calibrated before arrival at the target area using an initial point The technique was successfully tested on actual flight data collected during multiple micro air vehicle operations for cooperative geolocation of unknown targets.

A very important subproblem in the task assignment problem for unmanned air vehicles is the evaluation of costs for the state transitions of a directed graph. Usually a Dubins vehicle flying in the absence of wind is considered in the computation of costs. However, when a prevailing wind vector field is considered, the costs taken on very different values and the task assignment problem can have very different solutions. In this paper, we consider the problem of constructing minimum-time trajectories for a Dubins vehicle in the presence of a time-varying wind vector field. We present results on the existence and uniqueness of minimum-time solutions for a Dubins vehicle flying in a general time-varying wind vector field under some technical conditions. These results extend the conclusions of the well-known Dubins theorem. We also propose an algorithm for obtaining the minimum-time solution for an unmanned air vehicle and prove its convergence. We also present the results of numerical experiments that show that the importance of considering wind vector fields while planning the tour for an unmanned air vehicle.

The effectiveness of open-box micro air vehicles to deliver light, small payloads of high importance to specific ground coordinates is investigated through dynamic simulation. The open box exhibits interesting and varied flight dynamic behavior as key design parameters are changed. For example, the open box can achieve a coning behavior, a corkscrewing behavior, or glide much like a conventional aircraft to the ground by merely shifting the mass center location. The four rear flaps of the air vehicle can be used to control the box and affords the aircraft greater control authority than dispersion caused by typical atmospheric winds. This control mechanism can also be used as a braking system, which can greatly arrest the descent rate before ground impact. These dynamic qualities make the open box a promising airdrop vehicle which can cut through atmospheric winds towards the target before decelerating and gently landing.

plane. This paper explores both of these robustness issues using results from a micro air vehicle simulation model developed at the NASA Langley Research Center. In particular, a hierarchy of dynamic models, ranging from a random walk model to a high-fidelity nonlinear micro air vehicle model, is employed in the Kalman filter for a simulated micro air vehicle trajectory with varying levels of measurement noise. It is demonstrated that the visionbased measurement updates in the filter are capable of compensating for significant modeling errors and filter initialization errors. As would be expected, superior overall results are achieved using higher-fidelity dynamic modelsintheKalman filter.Theworkpresentedinthispaperrepresentsthe firststeptowardtheultimateobjectiveof incorporating vision-based state estimation into the design of autonomous flight control systems for micro air vehicles operating in urban environments.