John E. Hurtado

Decentralized Cooperative-Control Design for Multivehicle Formations

DOI: 10.2514/1.33009 In a decentralized cooperative-control regime, individual vehicles autonomously compute their required control inputs to achieve a group objective. Controlling formations of individual vehicles is one application of decentralized cooperative control. In this paper, cooperative-control schemes are developed for a multivehicle formation problem with information flow modeled by leader–follower subsystems. Control laws are developed to drive position and velocity errors between vehicle pairs to zero. The general control law for the ith vehicle tracks its lead vehicle’s position and velocity, as well as a reference position and velocity that the whole formation follows. Rate-estimation schemes are developed for the general control law using both Luenberger-observer and passive-filtering estimation methods. It is shown that these estimation methods are complicated by the effects that the estimated rates have on formation stability. Finally, the development of a rate-free controller is presented, which does not require state informationfromothervehiclesintheformation.Thecontrolschemesaresimulatedfora five-vehicleformationand are compared for stability and formation convergence.

Increasing Runway Capacity for Continuous Descent Approaches Through Airborne Precision Spacing

NASA Langley Research Center has been developing an operational concept called Airborne Precision Spacing (APS), which combines new avionics and procedures to increase runway arrival capacity through precise inter-aircraft spacing at the runway threshold. However, with increases in traffic volume, noise restrictions threaten to limit operations. Continuous Descent Approaches (CDAs) are efficient arrival routes designed to minimize ground noise, but these routes are not currently operational in a high-density environment. This research evaluates applying the APS precision spacing tool to CDA arrival routes in three test conditions. These test conditions were developed to evaluate the system performance and operational efficiency of the combined concepts. Simulation results indicate that the APS tool is able to minimize inter-aircraft spacing errors at the threshold in the presence ofvarying initial spacing errors.

Stability and Control of Collective Systems

In this paper, decentralized, distributed feedback control laws are presented for cooperative robotic systems whose task is to localize unknown sources. The control laws follow from a second order representation of the source field. The stability of the proposed feedback control laws for the individual robots, and for the entire robot collective, is demonstrated using Lyapunovs direct method and a vector Lyapunov approach. Additional feedback control laws are proposed to achieve an additional level of coordination. In particular, control laws that achieve desired formations surrounding a localized source are developed.

Decentralized Control for a Swarm of Vehicles Performing Source Localization

In this paper, decentralized feedback controls are presented for a swarm of autonomous, robotic vehicles that is tasked with localizing a stationary, time-invariant source. The development of the feedback controls is motivated by classic function-minimization theory and the method is actually suited for a large collection of agents, where collection of agents may refer to, for example, a population of N design points in some variable space. We present the theory that supports the method, some example problems and their simulations to illustrate the method, and discuss some potential applications.

Hamel coefficients for the rotational motion of an N–dimensional rigid body

Many of the kinematic and dynamic concepts relating to rotational motion have been generalized for N–dimensional rigid bodies. In this paper a new derivation of the generalized Euler equations is presented. The development herein of the N–dimensional rotational equations of motion requires the introduction of a new symbol, which is a numerical relative tensor, to relate the elements of an N Ö N skew–symmetric matrix to a vector form. This symbol allows the Hamel coefficients associated with general N–dimensional rotations to be computed. Using these coefficients, Lagranges equations are written in terms of the angular–velocity components of an N–dimensional rigid body. The new derivation provides a convenient vector form of the equations, allows the study of systems with forcing functions, and allows for the sensitivity of the kinetic energy to the generalized coordinates.

Application of the Cayley Form to General Spacecraft Motion

The study of N-dimensional rigid-body motion is a well-developed field of mechanics. Some of the key results for describing the kinematics of these bodies come from the Cayley transform and the Cayley-transform kinematic relationship. Additionally, several forms of the equations of motion for these bodies have been developed by various derivations. By using Cayley kinematics, the motion of general mechanical systems can be intimately related to the motion of higher-dimensional rigid bodies. This is done by associating each point in the configuration space with an N-dimensional orientation. An example of this is the representation of general orbital and attitude motion of a spacecraft as pure rotation of a four-dimensional rigid body. Another example is the representation of a multibody satellite system as a four-dimensional rigid body.

Interior Parameters, Exterior Parameters, and a Cayley-Like Transform

A RGUABLY, the most fundamental representation for describing the relative orientation of a rigid body is the orientation matrix, also called the direction cosine matrix. Few believe, however, that this matrix provides the most convenient parameterization of orientation. For that, many instead turn to one of a collection of three-parameter sets, even though it is known that every three-parameter orientation set will encounter some kind of singularity, a fact shown by Stuelpnagel [1]. Others turn to the Euler parameters, which are a nonsingular four-parameter set. The direct relationship between each of the various parameter sets and the orientationmatrix is considered to be of basic importance. So, too, is the time derivative of such relationships, although the angular velocity vector or matrix is usually substituted for the time derivative of the orientationmatrix. The purpose of this note is to investigate the direct relationship between a particular three-parameter orientation set, viz., the modified Rodrigues parameters (MRP), and the orientation matrix. The modified Rodrigues parameters were originally developed by Wiener [2], rediscovered by Marandi and Modi [3], and investigated quite fully by Tsiotras and Longuski [4] and Schaub and Junkins [5]. Nevertheless, there is more to say.

Linear Feedback Control Using Quasi Velocities

A novel approach for designing feedback controllers for natural mechanical systems using quasi velocities is presented. The approach is relevant to the stabilization and regulation of finite-dimensional multibody systems. In particular the globally asymptotically stable linear feedback of Rodrigues parameters and angular velocity is taken from spacecraft attitude control and applied to a broader class of problems. This controller is shown to have good performance due to the sensitivity of the rotational kinematics to small motions near the reference configuration. Additionally, the concept is extended to systems with more than three degrees of freedom by generalizing the functional form of the three-dimensional rotational kinematics. This defines a new set of quasi velocities that allow globally asymptotically stable linear feedback for any number of degrees of freedom. Anexample shows that the use of these variables in controller design can lead to improved performance.

Aeroelastic Modeling of Large Offshore Vertical-axis Wind Turbines: Development of the Offshore Wind Energy Simulation Toolkit.

The availability of offshore wind resources in coastal regions makes offshore wind energy an attractive opportunity. There are, however, significant challenges in realizing offshore wind energy with an acceptable cost of energy due to increased infrastructure, logistics, and operations and maintenance costs. Vertical-axis wind turbines (VAWTs) are potentially ideal candidates for offshore applications, with many apparent advantages over the horizontal-axis wind turbine configuration in the offshore arena. VAWTs, however, will need to undergo much development in the coming years. Thus, the Offshore Wind ENergy Simulation (OWENS) toolkit is being developed as a design tool for assessing innovative floating VAWT configurations. This paper presents an overview of the OWENS toolkit and provides an update on the development of the tool. Verification and validation exercises are discussed, and comparisons to experimental data for the Sandia National Laboratories 34meter VAWT test bed are presented. A discussion and demonstration of a “loose” coupling approach to external loading modules, which allows a greater degree of modularity, is given. Results for a realistic VAWT structure on a floating platform under aerodynamic loads are shown and coupling between platform and turbine motions is demonstrated. Finally, future plans for development and use of the OWENS toolkit are discussed.

Optimal Nonlinear Feedback Control Design Using a Waypoint Method

This paper discusses an innovative idea of blending the notion of a waypoint scheme with a series solution method developed by the authors for solving the Hamilton―Jacobi―Bellman equation in the context of designing optimal feedback control laws for nonlinear dynamic systems subject to terminal constraints. The overall time interval of the given problem is partitioned into smaller segments, and the series solution method is applied within each segment using stored gains that are computed from one segment only. The methodology is applied to highly nonlinear systems including a minimum orbit transfer problem. Several examples are demonstrated, and the results are compared with the corresponding open-loop solutions to demonstrate the efficacy of the proposed method.