Kamesh Subbarao

Adaptive Output Feedback Control for Spacecraft Rendezvous and Docking Under Measurement Uncertainty

An output feedback structured model reference adaptive control law has been developed for spacecraft rendezvous and docking problems. The effect of bounded output errors on controller performance is studied in detail. Output errors can represent an aggregation of sensor calibration errors, systematic bias, or some stochastic disturbances present in any real sensor measurements or state estimates. The performance of the control laws for stable, bounded tracking of the relative position and attitude trajectories is evaluated, considering unmodeled external as well as parametric disturbances and realistic position and attitude measurement errors. Essential ideas and results from computer simulations are presented to illustrate the performance of the algorithm developed in the paper.

Backstepping Approach for Controlling a Quadrotor Using Lagrange Form Dynamics

The dynamics of a quadrotor are a simplified form of helicopter dynamics that exhibit the same basic problems of underactuation, strong coupling, multi-input/multi-output design, and unknown nonlinearities. Control design for the quadrotor is more tractable yet reveals corresponding approaches for helicopter and UAV control design. In this paper, a backstepping approach is used for quadrotor controller design. In contrast to most other approaches, we apply backstepping on the Lagrangian form of the dynamics, not the state space form. This is complicated by the fact that the Lagrangian form for the position dynamics is bilinear in the controls. We confront this problem by using an inverse kinematics solution akin to that used in robotics. In addition, two neural nets are introduced to estimate the aerodynamic components, one for aerodynamic forces and one for aerodynamic moments. The result is a controller of intuitively appealing structure having an outer kinematics loop for position control and an inner dynamics loop for attitude control. The control approach described in this paper is robust since it explicitly deals with unmodeled state-dependent disturbances and forces without needing any prior knowledge of the same. A simulation study validates the results obtained in the paper.

Structured H 1 Command and Control-Loop Design for Unmanned Helicopters

The aim of this paper is to present rigorous and efficient methods for designing flight controllers for unmanned helicopters that have guaranteed performance, intuitive appeal for the flight control engineer, and prescribed multivariableloopstructures.Helicopterdynamicsdonotdecoupleastheydoforthe fixed-wingaircraftcase,andso the design of helicopter flight controllers with a desirable and intuitive structure is not straightforward. We use an H1 output-feedback design procedure thatis simplified in the sense that rigorous controller designs are obtained by solving only two coupled-matrix design equations. An efficient algorithm is given for solving these that does not require initial stabilizing gains. An output-feedback approach is given that allows one to selectively close prescribed multivariable feedbackloopsusing areducedsetof thestates ateach step.At eachstep,shaping filtersmay beadded thatimproveperformanceandyieldguaranteedrobustnessandspeedofresponse.ThenetresultyieldsanH1 design with a control structure that has been historically accepted in the flight control community. As an example, a design forstationkeepingandhoverofanunmannedhelicopterispresented.Theresult isastationkeeping hovercontroller withrobustperformanceinthepresenceofdisturbances(includingwindgusts),excellentdecoupling,andgoodspeed of response.

H-Infinity Static Output-feedback Control for Rotorcraft

The problem of stabilization of an autonomous rotorcraft platform in a hover configuration subject to external disturbances is addressed. Necessary and sufficient conditions are presented for static output-feedback control of linear time-invariant systems using the H-Infinity approach. Simplified conditions are given which only require the solution of two coupled matrix design equations. This paper also proposes a numerically efficient solution algorithm for the coupled design equations to determine the output-feedback gain. A major contribution is that an initial stabilizing gain is not needed. The efficacy of the control law and the disturbance accommodation properties are shown on a rotorcraft design example. The helicopter dynamics do not decouple as in the fixed-wing aircraft case, so that the design of helicopter flight controllers with a desirable intuitive structure is not straightforward. In this paper an output feedback approach is given that allows one to selectively close prescribed multivariable feedback loops using a reduced set of the states. Shaping filters are added that improve performance and yield guaranteed robustness and speed of response. This gives direct control over the design procedure and performance. Accurate identification of the System parameters is a challenging task for rotorcraft control, addition of loop shaping facilitates implementation engineers to counteract unmodeled high frequency dynamics. The net result yields control structures that have been historically accepted in the flight control community.

Modeling of Flight Dynamics of Morphing Wing Aircraft

Aircraft with variable wing geometry (morphable wings) are of considerable interest, not only formission-specific optimization but for enhanced maneuverability as well. In the nascent field of mini or micro unmanned aerial vehicles, large and rapid changes inwing geometry are achievable, resulting in significant changes of the dynamics of the vehicle. In this paper, a simulationmethodology suitable for such aircraft is presented, accounting for the changes in both the aerodynamic and inertial properties. Because of the complexity of the possible wing configurations, the aerodynamics are simulated using an unsteady vortex-lattice approach, solved concurrently with six-degree-offreedom ( ) nonlinear equations of motion. The time dependence of the inertia tensor andmotion ofmass within the body frame are explicitly taken into account, resulting in additional body-frame forces andmoments. The simulation methodology is applied to various gull-wing configurations, and the flight dynamics are analyzed through nonlinear simulation.

Aircraft conflict detection and resolution using mixed geometric and collision cone approaches

This paper considers the problem of avoidance of conflict or collision between two aircraft in a 3-D environment utilizing current positions and velocities using a mixed geometric and collision cone approach. Analytical results are obtained for certain special cases and numerical optimization techniques are used to search for solutions to the most general cases. The results are optimal as they tend to minimize the velocity vector changes and thus result in minimum deviations from nominal trajectory so as to avoid conflict. It is assumed that the aircraft is able to change its velocity, heading and elevation angles independently and all combinations of these three degrees of freedom are investigated for obtaining the resolution strategies. The simulation results also include explicit bounds on the airspeeds (lower and upper limits) and turning rates to enforce realistic scenarios.

A novel parameter projection mechanism for smooth and stable adaptive control

Abstract A novel parameter projection technique for handling uncertain parameters with a priori available upper and lower bounds is the subject of this paper. It is a wellknown fact that the conventional parameter projection method employed in certainty equivalence adaptive control is able to guarantee global asymptotic stability only after compromising control smoothness. In contrast, the technique presented in this paper preserves both stability and smoothness guarantees for the closed-loop adaptive system. The novelty of the proposed adaptive control formulation comes through our deliberate introduction of a nonlinear re-parameterization of uncertainty, thereby amounting to a significant shift from the classical certainty equivalence methodology. The proposed controller is non-overparameterized and has the potential to significantly improve transient performance because of full and proper utilization of all the available prior information on the unknown parameters. The technical descriptions are further elaborated via the Duffing nonlinear oscillator example to highlight the advantages of this new approach.

Modeling of Dynamic Loading of Morphing-Wing Aircraft

The simulation of dynamic loads and required power is essential for the design of any morphing wing aircraft, since it ultimately determines the feasibility of a given morphing configuration. In this paper a methodology suitable for numerical calculation of the dynamic loads for a morphing-wing aircraft is presented. The approach taken is one of extending Rigid Body Dynamics to include time-varying terms. The dynamic loads are derived from Lagrange’s Equations of a morphing aircraft, modeled as a system of rigid bodies connected by actuated rotational and translational joints. The overall flight dynamics are also treated using the Extended Rigid Body Dynamics approach, introducing morphing forces and moments to model the correct dynamics for a morphing aircraft. Aerodynamic loads are computed using a Vortex-Lattice method. The overall model is applied to a gullwing aircraft performing a set of morphing-induced maneuvers. The resulting loads are analyzed, and the strict power requirements of the gull-wing aircraft are explained.

Queueing Network Models of the National Airspace System

Understanding the relationships between trajectory uncertainties due to aviation operations, precision of navigation and control, and the traffic flow efficiency are central to the design of next generation Air Transportation Systems. Monte-Carlo simulations using air traffic simulation software packages can be used to quantify these effects. However, they are generally time consuming, and do not provide explicit relationships for comparing various technology options. On the other hand, queuing models of the air traffic system can rapidly demonstrate the influence of trajectory uncertainties on traffic flow efficiency, facilitating tradeoff studies in an effective and time-efficient manner. A methodology for incorporating the trajectory uncertainty models into queuing network models of the air traffic at national, regional and local scales is discussed. Usefulness of these models in assessing the impact of uncertainties on traffic flow efficiency is illustrated.

Nonlinear 3-D trajectory guidance for unmanned aerial vehicles

In this paper, we propose a backstepping based nonlinear guidance controller, designed for 3-D path tracking for a UAV. The guidance law design assumes first order dynamics for the speed, heading and elevation angles. We demonstrate closed loop stability via Lyapunov analysis. The efficacy of the controller is demonstrated for two cases, namely the straight path following and a curved path following.