Development and Application of Controller for Transition Flight of Tail-Sitter UAV

There is renewed interest in tail-sitter airplanes on account of their vertical takeoff and landing capability as well as their efficient horizontal flight capabilities. The transition from a vertical near-hover mode to a horizontal cruise mode is a critical component of the tail-sitter flight profile. In practice, this transition is often achieved by a stall-and-tumble maneuver, which is somewhat risky and therefore not desirable, so alternative maneuvering strategies along controlled trajectories are sought. Accordingly, this paper presents the synthesis and application of a transition controller to a tail-sitter UAV for the first time. For practical reasons, linear controllers are designed using the PID technique and linked by gain scheduling. The limits of the PID controller are complemented by a so-called $\mathcal{L}_{1}$ adaptive controller that considers the coupling effect, reduces the effort for appropriate gain selection, and improves the tracking performance at different points during operation. Each transition trajectory is controlled by the flight velocity and path angle using dynamic inversion. The transition control law is tested on a tail-sitter UAV, an 18-kg vehicle that has a 2-m wingspan with an aspect ratio of 4.71 and is powered by a 100-cm³ gasoline engine driving an aft-mounted ducted fan. This paper describes not only the synthesis and the onboard implementation of the control law but also the flight testing of the fixed-wing UAV in hover, transition, and cruise modes.     

小型尾坐式飞行器自适应SRUKF姿态算法

针对小型尾坐式飞行器姿态估计问题,设计了由陀螺、加速度计、磁强计组成的姿态测量系统。为了抑制MEMS陀螺漂移导致的姿态误差,以四元数为状态变量,以加速度计和磁强计的输出作为观测变量,建立了滤波模型。采用平方根无迹卡尔曼滤波(SRUKF)对传感器信息进行融合,保证了滤波算法的数值稳定性。由于小型尾坐式飞行器抗干扰能力弱,引入自适应算法,解决了量测信息受到干扰时滤波精度下降的问题,提高了系统的鲁棒性和可靠性。仿真结果表明,存在外界磁场干扰时,姿态误差小于1°。通过实际飞行实验,验证了算法的可行性。     

Optimal 4-D Aircraft Trajectories in a Contrail-sensitive Environment

Aircraft induced contrails present an important source and a growing concern for climate change in aviation. This paper develops a methodology to determine optimal flight trajectories that minimize the total flying cost in a dynamic, contrail-sensitive environment. The total flying costs consist of costs due to fuel burn, crew, passenger travel time, CO₂ emission, and contrail formation. By constructing a multi-layer hexagonal grid structure to represent the airspace, we formulate the single aircraft trajectory optimization problem as a binary integer program that allows for flight altitude and heading adjustment, and contrail information update. Various cost factors are quantified, in particular the one corresponding to aviation-generated contrails, using the Global Warming Potential concept. Computational analyses show that optimal trajectories depend critically upon the time horizon choice for calculating the CO₂ climate impact. Shifting flights to periods with low contrail effect is not justified, given the limited benefit but potentially large passenger schedule delay cost increase. The analyses are further extended to determining the optimal trajectories for multiple flights using a successive optimization procedure.     

Variable Load Factor Guidance for Low-Altitude Fly-to-Point Maneuvers of a Jet Fighter Aircraft

This paper describes the formulation andnumerical investigation of a variable load factor guidance algorithm(variable n-guidance) that allows an aircraft pilotto approximate minimum-time low-altitude quasi-level fly-to-pointmaneuvers of a jet fighter aircraft. The maneuvers studied consistof flight to a point at a radial distance of 50 kft from thestarting point, with the final position vector oriented at 45,90, 135, 180 deg from the initial course and with the requirementthat the initial and final altitudes be the same.First, the fly-to-point maneuver is optimized from the time viewpointwith respect to three controls (angle of attack, power setting,angle of bank) via the sequential gradient-restoration algorithm.Then, from the study of the optimal trajectories, a variablen-guidance algorithm is developed, connecting theload factor to the turn-to-go. This algorithm is implementedvia feedback control and tested. For comparison purposes, a constantn-guidance scheme is also tested. The main conclusionis that the variable n-guidance algorithm producestrajectories that approximate closely the optimal trajectories.On the other hand, the constant n-guidance schemedoes not approximate well the optimal trajectories.     

On numerical algorithm and interactive visualization for optimal control problems

We present methods for the visualization of the numerical solution of optimal control problems. The solution is based on dynamic programming techniques where the corresponding optimal value function is approximated on an adaptively refined grid. This approximation is then used in order to compute approximately optimal solution trajectories. We discuss requirements for the efficient visualization of both the optimal value functions and the optimal trajectories and develop graphic routines that in particular support adaptive, hierarchical grid structures, interactivity and animation. Several implementational aspects using the Graphics Programming Environment ‘GRAPE’ are discussed. Received: 4 December 1997 / Accepted: 5 August 1998     

基于雷达测距的飞行器交会对接误差补偿控制技术

为解决由视线倾角、视线偏角过大造成的飞行器对接存在误差的问题,实现飞行器交会轨迹的精准对接,提出基于雷达测距的飞行器交会对接误差补偿控制技术。建立空间参考坐标系,根据轨道根数计算结果,推导动力学状态方程,实现对飞行器交会对接过程中的动力学作用分析。按照雷达测距原理,计算飞行器的理论飞行时长及雷达装置作用距离,再联合相关参数指标,确定精度极限的取值范围,实现基于雷达测距的对接误差控制。在三坐标测量机结构模型中,定义飞行位姿拟合条件,再根据位姿误差求解结果,实现对误差参数的补偿修正处理,完成基于雷达测距的飞行器交会对接误差补偿控制方法的设计。对比实验结果表明,应用所提方法可以同时将视线倾角、视线偏角的取值控制在0°-45.0°的数值范围之内,能够较好解决飞行器错误对接的问题,符合精准对接飞行器交会轨迹的实际应用需求。     

Attitude Stabilization with Real-time Experiments of a Tail-sitter Aircraft in Horizontal Flight

This paper focusses on the attitude stabilization of a mini tail-sitter aircraft, considering aerodynamic effects. The main characteristic of this vehicle is that it operates in either the hover mode for launch and recovery, or the horizontal mode during cruise. The dynamic model is obtained using the Euler–Lagrange formulation, and aerodynamic effects are obtained by studying the propeller effects. A nonlinear saturated Proportional-Integral-Derivative (SPID) control with compensation of aerodynamic moments is proposed in order to achieve the asymptotic stabilization of the vehicle in horizontal mode. In addition, a homemade inertial measurement unit (HIMU) is built for operating the complete operational range of the vehicle (including vertical and horizontal modes). Finally, simulation results are presented for validating the control law, and practical results are obtained in real-time during the flight.     

Analysis and design of guidance-strategy for dynamic soaring with UAVs

Dynamic soaring is an effective method to extract energy from wind shear to reduce energy consumption and extend flight duration. However, the design of the guidance-strategy for autonomous dynamic soaring is still suffering from the heavy computation load. In order to solve this problem, the aim of this paper is to propose a simple method to generate the guidance-strategy for autonomous dynamic soaring. Firstly, the flight path of dynamic soaring is modeled and solved by an open source optimal software named GPOPS. Secondly, the cycle of dynamic soaring is divided into four piecewise trajectories, and the characteristics of each are determined by some simple equations. Thirdly, the guidance-strategy based on the results of these equations is summarized. Simulation results indicate that the proposed guidance-strategy can present the characteristics of optimal flight very well, and it is practical and easy to be implemented by the on-board computer of Unmanned Aerial Vehicles for its simplicity.     

L ∞-error estimates of higher order mixed finite element approximations for elliptic optimal control problems

In this paper, we investigate the L ^∞-error estimates of the numerical solutions of linear-quadratic elliptic control problems by using higher order mixed finite element methods. The state and co-state are approximated by the order k Raviart-Thomas mixed finite element spaces and the control variable is approximated by piecewise polynomials of order k (k≥1). Optimal L ^∞-error estimates are derived for both the control and the state approximations. These results are seemed to be new in the literature of the mixed finite element methods for optimal control problems.     

The AutoSOAR autonomous soaring aircraft part 2: Hardware implementation and flight results

Autonomous soaring has the potential to greatly improve both the range and endurance of small robotic aircraft. This paper describes the results of a test flight campaign to demonstrate an autonomous soaring system that generates a dynamic map of lift sources (thermals) in the environment and uses this map for on‐line flight planning and decision making. The aircraft is based on a commercially available radio‐controlled glider; it is equipped with an autopilot module for low‐level flight control and on‐board computer that hosts all autonomy algorithms. Components of the autonomy algorithm include thermal mapping, explore/exploit decision making, navigation, optimal airspeed computation, thermal centering control, and energy state estimation. A finite state machine manages flight behaviors and switching between behaviors. Flight tests at Aberdeen Proving Ground resulted in 7.8 h flight time with the autonomous soaring system engaged, with three hours spent climbing in thermals. Postflight computation of energy state and frequent observations of groups of birds thermalling with our aircraft indicate that it was effectively exploiting available energy.     

推力矢量垂直短距飞机轨迹优化与控制

推力矢量垂直短距起降(V/STOL)飞机是一种兼顾巡航飞行速度和起降灵活性的新型飞机.本文首先建立了包含执行器饱和的V/STOL飞机动力学模型;然后针对V/STOL飞机在过渡过程阶段面临的强耦合、强非线性的特点,使用梯度下降法进行最优过渡过程轨迹优化并采用适应性矩估计算法(Adam)加速了优化过程;在此基础上,以最优轨迹为基础设计前馈控制器,同时通过对比真实飞行状态与所设计的最优状态给出反馈补偿量,保证了实际的过渡过程沿着最优轨迹进行.经过仿真实验可以发现,该方法具有过渡过程时间短、姿态平稳、鲁棒性强的优点.     

Solving dynamic portfolio choice problems by recursing on optimized portfolio weights or on the value function?

Most dynamic programming methods deployed in the portfolio choice literature involve recursions on an approximated value function. The simulation-based method proposed recently by Brandt, Goyal, Santa-Clara, and Stroud (Review of Financial Studies, 18, 831–873, 2005), relies instead on recursive uses of approximated optimal portfolio weights. We examine the relative numerical performance of these two approaches. We show that when portfolio weights are constrained by short sale restrictions for example, iterating on optimized portfolio weights leads to superior results. Value function iterations result in a lower variance but disproportionately higher bias of the solution, especially when risk aversion is high and the investment horizon is long.     

Velocity profile optimization of on road vehicles: Pontryagin's Maximum Principle based approach

Driving profile of on road vehicles has shown to have significant effect on fuel economy. This paper discusses the development of Pontryagin's Maximum Principle (PMP) based solution to determine the energy optimal velocity profile by incorporating the gear shifting, speed limit and road grade constraints simultaneously. In the proposed approach the real world road grade profile and speed limits are approximated by a set of piece-wise constant functions and the corresponding first order necessary conditions are derived. By solving a number of differential equations an analytical solution is generated. Therefore, the computation time of the solution is extremely fast. To verify the global optimality of the solution, the results are compared with dynamic programming (DP) solution that solves the complex and non-linear representative model of the actual test vehicle. The comparison results prove that the generated optimal speed trajectories are very close to global optimal solution.     

ROBUST NONLINEAR CONTROLLER DESIGN FOR A LONGITUDINAL FLIGHT CONTROL PROBLEM

In this paper, the H_∞ approximate I/O linearization formulation and μ‐synthesis are employed to design a nonlinear controller for an aircraft longitudinal flight control problem. We propose modified nonlinear H_∞ controller formulas to approximately linearize the system and use μ‐synthesis to address tracking, regulation, and robustness issues.     

Robust identification method for nonlinear model structures and its application to high-performance aircraft

A common assumption is that the model structure is known for modelling high performance aircraft. In practice, this is not the case. Actually, structure identification plays the most important role in the processing of nonlinear system modelling. The integration of mode structure identification and parameter estimation is an efficient method to construct the model for high performance aircraft, which is nonlinear and also contains uncertainties. This article presents an efficient method for identifying nonlinear model structure and estimating parameters for high-performance aircraft model, which contains uncertainties. The parameters associated with nonlinear terms are considered one after the other if they should be included in the nonlinear model until a stopping criterion is met, which is based on Akaike's information criterion. A numerically efficient U-D factorisation is presented to avoid complex computation of high-order matrices. The proposed method is applied to flight test data of a high-performance aircraft. The results demonstrate that the proposed method could obtain the good aircraft model with a reasonably good fidelity based on the comparison with flight test data.     

多目标规划模型在航迹规划中的应用

智能飞行器是由动力装置驱动,并在计算机系统自动引导进行的。航迹规划是实现飞行器智能导航并成功完成任务的技术保障。本文针对智能飞行器飞行过程中受到飞行器的最小转弯角限制以及定位误差的影响,提出了基于A*算法的多目标规划的数据模型以及寻求最优航迹规划路径的算法,并用两个校正点数据集进行了验证。结果显示,改进后的A*算法可以快速地规划出满足限制条件的最优路径。     

The AutoSOAR autonomous soaring aircraft,part 1: Autonomy algorithms

Autonomous soaring has the potential to greatly improve both the range and endurance of small robotic aircraft. This paper describes an autonomous soaring system that generates a dynamic map of lift sources (thermals) in the environment and uses this map for online flight planning and decision making. Components of the autonomy algorithm include thermal mapping, explore/exploit decision making, navigation, optimal airspeed computation, thermal centering control, and energy state estimation. A finite state machine manages the aircraft behavior during flight and determines when changing behavior is appropriate. A complete system to enable autonomous soaring is described with special attention paid to practical considerations encountered during flight testing. A companion paper describes the hardware implementation of this system and the results of a flight test campaign conducted at Aberdeen Proving Ground in September 2015.     

A frequency‐constrained geometric Pontryagin maximum principle on matrix Lie groups

We present a geometric discrete‐time Pontryagin maximum principle (PMP) on matrix Lie groups that incorporates frequency constraints on the control trajectories in addition to pointwise constraints on the states and control actions directly at the stage of the problem formulation. This PMP gives first‐order necessary conditions for optimality and leads to two‐point boundary value problems that may be solved by numerical techniques to arrive at optimal trajectories. We demonstrate our theoretical results with numerical simulations on the optimal trajectory generation of a wheeled inverted pendulum and an attitude control problem of a spacecraft on the Lie group SO(3).     

Design of a robust controller for a supersonic aircraft using H∞ approach

In this paper an H_∞ optimal, robust flight control system design for a supersonic aircraft has been described. Separate controllers are designed for longitudinal and lateral motions. A general two-degrees-of-freedom controller is proposed, where feedback control is designed for robust performance augmentation, while a series compensator is used to ensure that requisite handling qualities. Three alternative methods to achieve performance robustness have been discussed. The results obtained are very encouraging. It is hoped that this will equip the flight control engineers with an alternative to the conventional methods.     

Tree-Based Parallel Algorithm Design

In this paper a systematic method for the design of efficient parallel algorithms for the dynamic evaluation of computation trees and/or expressions is presented. This method involves the use of uniform closure properties of certain classes of unary functions. Using this method, optimal parallel algorithms are given for many computation tree problems which are important in parallel algebraic and numerical computation, and parallel code generation on exclusive read and exclusive write parallel random access machines. Our algorithmic result is complemented by a P-complete tree problem. Received February 13, 1995; revised March 25, 1996.