Xiaoli Bai

New Results for Time-Optimal Three-Axis Reorientation of a Rigid Spacecraft

Some new results for a classical minimum-time rest-to-rest maneuver problem are presented. An inertially symmetric rigid body is considered. For the case in which the magnitude of the control is constrained while the control direction is left free, we analytically prove that the eigenaxis maneuver is the time-minimum solution by using Pontryagins principle. For the case in which the three components of the control are independently constrained, we discover six- and seven-switch solutions for reorientation angles of less than 72 deg by using a hybrid numerical approach. The seven-switch solutions are consistent with the classical results, and the six-switch solutions are reported here for the first time. We find that the two sets of solutions are widely separated in state and control spaces. However, the two locally optimum maneuver times are very close to each other, although the six-switch control always has a slightly shorter time. Simulation results that illustrate and validate the new findings are summarized. Although no conclusive proof is available to date, we believe the six-switch maneuvers to be global extrema.

Extended neuro-fuzzy models of multilayer perceptrons☆

In this paper the famous neural model, the multilayer perceptron, is extended to a new neural model that is called the additive-Takagi–Sugeno-type multilayer perceptron. The present study proves that this new model can also act as a universal approximator, and thus it can be used in many fields, such as system modeling and identification. The concept of f-duality and the fuzzy operator interactive-or are used to prove that the proposed neural model is functionally equal to a kind of fuzzy inference system. Further, this paper presents another new neuro-fuzzy model that is called the sigmoid-adaptive-network-based fuzzy inference system. Simulation studies show that our proposed models both have stronger approximation capability than multilayer perceptrons.

Modified Chebyshev-Picard Iteration Methods for Orbit Propagation

Modified Chebyshev-Picard Iteration methods are presented for solving high precision, long-term orbit propagation problems. Fusing Chebyshev polynomials with the classical Picard iteration method, the proposed methods iteratively refine an orthogonal function approximation of the entire state trajectory, in contrast to traditional, step-wise, forward integration methods. Numerical results demonstrate that for orbit propagation problems, the presented methods are comparable to or superior to a state-of-the-art 12th order Runge-Kutta-Nystrom method in a serial processor as measured by both precision and efficiency. We have found revolutionary long solution arcs with more than eleven digit path approximations over one to three lower-case Earth orbit periods, multiple solution arcs can be patched continuously together to achieve very long-term propagation, leading to more than ten digit accuracy with built-in precise interpolation. Of revolutionary practical promise to much more efficiently solving high precision, long-term orbital trajectory propagation problems is the observation that the presented methods are well suited to massive parallelization because computation of force functions along each path iteration can be rigorously distributed over many parallel cores with negligible cross communication needed.

Modified Chebyshev-Picard Iteration Methods for Station-Keeping of Translunar Halo Orbits

The halo orbits around the Earth-Moon libration point provide a great candidate orbit for a lunar communication satellite, where the satellite remains above the horizon on the far side of the Moon being visible from the Earth at all times. Such orbits are generally unstable, and station-keeping strategies are required to control the satellite to remain close to the reference orbit. A recently developed Modified Chebyshev-Picard Iteration method is used to compute corrective maneuvers at discrete time intervals for station-keeping of halo orbit satellite, and several key parameters affecting the mission performance are analyzed through numerical simulations. Compared with previously published results, the presented method provides a computationally efficient station-keeping approach which has a simple control structure that does not require weight turning and, most importantly, does not need state transition matrix or gradient information computation. The performance of the presented approach is shown to be comparable with published methods.

Dynamic Analysis and Control of a Stewart Platform Using A Novel Automatic Dierentiation Method

This paper presents a kinematic based Lagrangian approach to generate the equations of motion and design an adaptive control law for multi-body systems. This methodology is applied to dynamic analysis and controller design study for a Stewart platform. Novel means of utilizing automatic dierentiation are employed to generate and solve the equations of motion, using only high level geometric and kinematic descriptions of the system. Based on deriving and coding only the kinematic descriptions of the system, the nonlinear motion of the platform is solved automatically and the analyst is freed from deriving, coding, and validating the lengthy nonlinear equations of motion. Lyapunov stability theory and concepts from adaptive control are used to formulate a nonlinear feedback control law. The control law is of the model reference adaptive structure, designed to track a prescribed smooth trajectory. By designing an adaptive update rule for the system mass and inertia parameters, the tracking errors are proven to be asymptotically stable for arbitrary parameter errors. Also, a PID adaptive control law is designed to guarantee bounded stability in the presence of bounded disturbances. Numerical results are included to illustrate the performance of the algorithm in the presence of large parameter errors and external disturbance.

Bang-bang Control Design by Combing Pseudospectral Method with a novel Homotopy Algorithm

The bang-bang type of control problem for spacecraft trajectory optimization is solved by using a hybrid approach. First, a pseudospectral method is utilized to generate approximate switching times, control structures, and initial co-states. Second, a homotopy method is used to solve the two-point boundary value problems derived from the Euler-Lagrangian equations. The unknown variables in the homotopy method include both switching times and the unknown initial states and co-states. The homotopy algorithm is made robust to the nonlinearity of the problems by enforcing the constraint satisfaction along the homotopy path. The optimization variables are treated as continuous variables and the flnal solutions have the same accuracy as the ordinary difierential equation solvers. An orbit transfer problem is presented to show the advantages of this hybrid methodology.

Rapid Generation of Time-Optimal Trajectories for Asteroid Landing via Convex Optimization

This paper presents a new method for rapid generation of time-optimal trajectories for asteroid landing via convex optimization. To overcome the nonconvex difficulty due to the free-flight time, a minimum-landing-error problem that can be convexified is proposed to serve as a gateway for solving the time-optimal control problem. The proposed method solves the reduced minimum-landing-error problem via convex optimization first and then searches for the minimum flight time through a combination of extrapolation and bisection methods. The effectiveness of the proposed methodology for rapidly generating time-optimal trajectories is validated through simulations of spacecraft landing on two asteroids with both finite thrust and low thrust.

Decision Support for Optimal Runway Reconfiguration

Runway configuration consists of the specification of active runways and the directions for take-off and landing at an airport. Airports typically have more than one configuration, and the reconfiguration process consists of switching from one configuration to another based on the changes in wind conditions, noise abatement procedures or traffic demand. This paper advances a decision support system that uses a queuing network model of the terminal area to determine the optimal time for reconfiguration to minimize arrival delays. The approach employs the Queuing Network Analyzer formulation, which provides corrections to the Markovian queuing approach to enable independent specification both the mean and variance of inter-arrival and service times. The parameters of the queuing network model are derived from an estimation methodology and the inter-aircraft arrival time distribution are derived from scheduled aircraft arrivals into the terminal area. Operation of the algorithm is demonstrated for the San Francisco Metroplex consisting of San Francisco airport, Oakland International Airport, and Mineta San Jose International Airport, and also the Los Angeles Metroplex consisting of Los Angeles International Airport, Bob Hope Burbank Airport, and John Wayne-Orange County Airport. The simulation results indicate that the proposed approach can provide actionable decisions in the presence of system uncertainties. Differences between the decisions made based on the two different queuing network formulations are given. An approach to derive robust reconfiguration decisions based on a trade-off between optimal mean and variance of the delay times is also illustrated.

Design and Evaluation of LNAV/VNAV Guidance Algorithms for Time-of-Arrival Error Characterization

This paper develops 3D-path tracking algorithms to simulate the Lateral NAVigation (LNAV) and Vertical NAVigation (VNAV) capabilities found in current day aircraft flight management systems. The LNAV/VNAV capability is realized using two modules: (i) Reference Trajectory Synthesis Module, and (ii) LNAV/VNAV Guidance Module. A separate paper deals with the Reference Trajectory Synthesis Module. The focus of the current paper is the design and evaluation of LNAV/VNAV Guidance Module. The guidance module is formulated as a reference-trajectory tracking controller. The control laws are based on single-input single-output linear feedback control principles. The outputs from the guidance module are: (i) bank-angle command, (ii) coefficient-of-lift command, (iii) thrust command, and (iv) spoiler drag command. The guidance module is evaluated on a simulation that models aircraft point-mass dynamics, bank-angle auto-pilot dynamics, pitchaxis auto-pilot dynamics, engine lag dynamics, atmospheric forecast model, and a realistic forecast uncertainty model. Test scenarios include A320 and MD82 aircraft flying along different arrival routes into San Francisco and Los Angeles International airports. MonteCarlo simulation framework is used to estimate the time-of-arrival uncertainty associated with a A320 LNAV/VNAV flight.

Modeling, Control and Simulation of a Novel Mobile Robotic System

We are developing an autonomous mo- bile robotic system to emulate six degree of freedom relative spacecraft motion during proximity opera- tions. A mobile omni-directional base robot provides x, y, and yaw planar motion with moderate accuracy through six independently driven motors. With a six degree of freedom micro-positioning Stewart platform on top of the moving base, six degree of freedom spacecraft motion can be emulated with high accu- racy. This paper presents our approach to dynamic modeling, control, and simulation for the overall sys- tem. Compared with other simulations that intro- duced significant simplifications, we believe that our rigorous modeling approach is crucial for the high fi- delity hardware in-the-loop emulation.