Michael W. Oppenheimer

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 constantperiod 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 bobweight 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 bladeelement theory, while the other is driven by an empirical representation of an unsteady aerodynamic model that was derived from experiments.

Integrated Adaptive Guidance and Control for Re-Entry Vehicles with Flight Test Results

To enable autonomous operation of future reusable launch vehicles, reconfiguration technologies will be needed to facilitate mission recovery following a major anomalous event. The Air Force’s Integrated Adaptive Guidance and Control program developed such a system for Boeing’s X-40A, and the total in-flight simulator research aircraft was employed to flight test the algorithms during approach and landing. The inner loop employs a modelfollowing/dynamic-inversion approach with optimal control allocation to account for control-surface failures. Further, the reference-model bandwidth is reduced if the control authority in any one axis is depleted as a result of control effector saturation. A backstepping approach is utilized for the guidance law, with proportional feedback gains that adapt to changes in the reference model bandwidth. The trajectory-reshaping algorithm is known as the optimum-path-to-go methodology. Here, a trajectory database is precomputed off line to cover all variations under consideration. An efficient representation of this database is then interrogated in flight to rapidly find the “best” reshaped trajectory, based on the current state of the vehicle’s control capabilities. The main goal of the flight-test program was to demonstrate the benefits of integrating trajectory reshaping with the essential elements of control reconfiguration and guidance adaptation. The results indicate that for more severe, multiple control failures, control reconfiguration, guidance adaptation, and trajectory reshaping are all needed to recover the mission.

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

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.

Control Allocation for Over-actuated Systems

Much emphasis has been placed on over-actuated systems for air vehicles. Over-actuating an air vehicle provides a certain amount of redundancy for the flight control system, thus potentially allowing for recovery from off-nominal conditions. Due to this redundancy, control allocation algorithms are typically utilized to compute a unique solution to the over-actuated problem. Control allocators compute the commands that are applied to the actuators so that a certain set of forces or moments are generated by the control effectors. Usually, control allocation problems are formulated as optimization problems so that all of the available degrees of freedom can be utilized and, when sufficient control power exists, secondary objectives can be achieved. In this work, a survey of control allocation techniques is given

Dynamics and Control of a Minimally Actuated Biomimetic Vehicle: Part II - Control

A control strategy is proposed for a minimally-actuated flapping-wing micro air-vehicle (FWMAV). The proposed vehicle is similar to the Harvard RoboFly that accomplished the first takeoff of an insect scale flapping wing aircraft, except that it is equipped with independently actuated wings and the vehicle center-of-gravity can be manipulated for control purposes. Using the results from the derivation of the aerodynamic forces and moments from Part I, a control allocation strategy and a feedback control law are designed that enables the vehicle to achieve untethered, stabilized flight about a hover condition. The control laws are designed to make use of three actuators, two of which control the angular position of the wing in the stroke plane, and one that moves a bob-weight that manipulates the vehicle center-of-gravity. The Split-Cycle Constant-Period Frequency Modulation technique, introduced in Part I, is used to allow each wing to generate nonzero cycle-averaged rolling and yawing moments. The technique achieves this objective by varying the frequency of the oscillators, that drive each wing throughout the wing-beat cycles, such that the dynamic pressure acting on each wing during the upstroke is different from that which acts on the

Dynamics and Control of a Minimally Actuated Biomimetic Vehicle: Part I - Aerodynamic Model

An aerodynamic model for the forces and moments acting on a minimally actuated flapping wing micro air vehicle (FWMAV) are derived from blade element theory. The proposed vehicle is similar to the Harvard RoboFly that accomplished the first takeoff of an insect scale flapping wing aircraft, except that it is equipped with independently actuated wings and the vehicle center-of-gravity can be manipulated for control purposes. Using a blade element-based approach, both instantaneous and cycle-averaged forces and moments are computed for a specific type of wing beat motion that enables nearly decoupled, multi-degree-of-freedom control of the aircraft. The wing positions are controlled using oscillators whose frequencies change once per wing beat cycle. A new technique is introduced, called Split-Cycle Constant-Period Frequency Modulation, that has the desirable property of providing a high level of control input decoupling for vehicles without active angle-of-attack control. Like the RoboFly, the wing angle-ofattack variation is passive by design, and is a function of the instantaneous angular velocity of the wing in the stroke plane. A control-oriented dynamic model of the vehicle is derived, which is based on a cycle-averaged � Senior Aerospace Engineer, Control Design and Analysis Branch, 2210 Eighth Street, Ste. 21, Air Force

Model-Predictive Dynamic Control Allocation Scheme for Reentry Vehicles

Allocation of control authority among redundant control effectors, under hard constraints, is an important component of the inner loop of a reentry vehicle guidance and control system. Whereas existing control allocation schemes generally neglect actuator dynamics, thereby assuming a static relationship between control surface deflections and moments about a three-body axis, in this work a dynamic control allocation scheme is developed that implements a form of model-predictive control. In the approach proposed here, control allocation is posed as a sequential quadratic programming problem with constraints, which can also be cast into a linear complementarity problem and therefore solved in a finite number of iterations. Accounting directly for nonnegligible dynamics of the actuators with hard constraints, the scheme extends existing algorithms by providing asymptotic tracking of time-varying input commands for this class of applications. To illustrate the effectiveness of the proposed scheme, a high-fidelity simulation for an experimental reusable launch vehicle is used, in which results are compared with those of static control allocation schemes in situations of actuator failures.

A Flexible Hypersonic Vehicle Model Developed with Piston Theory

Abstract : For high Mach number flows, M>4, piston theory has been used to calculate the pressures on the surfaces of a vehicle. In a two-dimensional inviscid flow, a perpendicular column of fluid stays intact as it passes over a solid surface. Thus, the pressure at the surface can be calculated assuming the surface were a piston moving into a column of fluid. In this work, first-order piston theory is used to calculate the forces, moments, and stability derivatives for longitudinal motion of a hypersonic vehicle. Piston theory predicts a relationship between the local pressure on a surface and the normal component of fluid velocity produced by the surfaces motion. The advantage of piston theory over other techniques, such as Prandtl-Meyer flow, oblique shock, or Newtonian impact theory, is that unsteady aerodynamic effects can be included in the model. The unsteady effects, considered in this work, include perturbations in the linear velocities and angular rates, due to rigid body motion. A flexible vehicle model is developed to take into account the aeroelastic behavior of the vehicle. The vehicle forebody and aftbody are modeled as cantilever beams fixed at the center-of-gravity. Piston theory is used to account for the changes in the forces and moments due to the flexing of the vehicle. Piston theory yields an analytical model for the longitudinal motion of the vehicle, thus allowing design trade studies to be performed while still providing insight into the physics of the problem.

A Hypersonic Vehicle Model Developed With Piston Theory

Abstract : For high Mach number flows, M greater or equal to 4, piston theory has been used to calculate the pressures on the surfaces of a vehicle. In a two-dimensional flow, a perpendicular column of fluid stays intact as it passes over a solid surface. Thus, the pressure at the surface can be calculated assuming the surface were a piston moving into a column of fluid. In this work, first-order piston theory is used to calculate the forces, moments, and stability derivatives for longitudinal motion of a hypersonic vehicle. Piston theory predicts a relationship between the local pressure on a surface and the normal component of fluid velocity produced by the surfaces motion. The advantage of piston theory over other techniques, such as Prandtl-Meyer flow or Newtonian impact theory, is that unsteady aerodynamic effects can be included in the model. The unsteady effects, considered in this work, include perturbations in the linear velocities and angular rate. This provides a more accurate model that agrees more closely with models derived using computational fluid dynamics or those derived by solving Euler equations. Additionally, piston theory yields an analytical model for the longitudinal motion of the vehicle, thus allowing design trade studies to be performed while still providing insight into the physics of the problem.

Integrated control of brake and steer by wire system using optimal control allocation methods

A method, computer usable medium including a program, and a system for braking a vehicle during brake failure. The method and computer usable medium include the steps of determining a brake force lost corresponding to a failed brake, and determining a brake force reserve corresponding to at least one non-failed brake. At least one commanded brake force is determined based on the brake force lost and the brake force reserve. Then at least one command brake force is applied to the at least one non-failed brake wherein at least one of an undesired yaw moment and a yaw moment rate of change are limited to predetermined values. The system includes a plurality of brake assemblies wherein a commanded brake force is applied to at least one non-failed brake.