A penalized nonparametric method for nonlinear constrained optimization based on noisy data

The objective of this study is to find a smooth function joining two points A and B with minimum length constrained to avoid fixed subsets. A penalized nonparametric method of finding the best path is proposed. The method is generalized to the situation where stochastic measurement errors are present. In this case, the proposed estimator is consistent, in the sense that as the number of observations increases the stochastic trajectory converges to the deterministic one. Two applications are immediate, searching the optimal path for an autonomous vehicle while avoiding all fixed obstacles between two points and flight planning to avoid threat or turbulence zones.     

Flight Control of Biomimetic Air Vehicles Using Vibrational Control and Averaging

A combination of vibrational inputs and state feedback is applied to control the flight of a biomimetic air vehicle. First, a control strategy is developed for longitudinal flight, using a quasi-steady aerodynamic model and neglecting wing inertial effects. Vertical and forward motion is controlled by modulating the wings’ stroke and feather angles, respectively. Stabilizing control parameter values are determined using the time-averaged dynamic model. Simulations of a system resembling a hawkmoth show that the proposed controller can overcome modeling error associated with the wing inertia and small parameter uncertainties when following a prescribed trajectory. After introducing the approach through an application to longitudinal flight, the control strategy is extended to address flight in three-dimensional space.     

Quasi-steady flight to quasi-steady flight transition for abort landing in a windshear: Trajectory optimization and guidance

This paper is concerned with the optimal transition and the near-optimum guidance of an aircraft from quasi-steady flight to quasi-steady flight in a windshear. The abort landing problem is considered with reference to flight in a vertical plane. In addition to the horizontal shear, the presence of a downdraft is considered.It is assumed that a transition from descending flight to ascending flight is desired; that the initial state corresponds to quasi-steady flight with absolute path inclination of –3.0 deg; and that the final path inclination corresponds to quasi-steady steepest climb. Also, it is assumed that, as soon as the shear is detected, the power setting is increased at a constant time rate until maximum power setting is reached; afterward, the power setting is held constant. Hence, the only control is the angle of attack. Inequality constraints are imposed on both the angle of attack and its time derivative.First, trajectory optimization is considered. The optimal transition problem is formulated as a Chebyshev problem of optimal control: the performance index being minimized is the peak value of the modulus of the difference between the instantaneous altitude and a reference value, assumed constant. By suitable transformations, the Chebyshev problem is converted into a Bolza problem. Then, the Bolza problem is solved employing the dual sequential gradient-restoration algorithm (DSGRA) for optimal control problems.Two types of optimal trajectories are studied, depending on the conditions desired at the final point. Type 1 is concerned with gamma recovery (recovery of the value of the relative path inclination corresponding to quasi-steady steepest climb). Type 2 is concerned with quasi-steady flight recovery (recovery of the values of the relative path inclination, the relative velocity, and the relative angle of attack corresponding to quasi-steady steepest climb). Both the Type 1 trajectory and the Type 2 trajectory include three branches: descending flight, nearly horizontal flight, and ascending flight. Also, for both the Type 1 trajectory and the Type 2 trajectory, descending flight takes place in the shear portion of the trajectory; horizontal flight takes place partly in the shear portion and partly in the aftershear portion of the trajectory; and ascending flight takes place in the aftershear portion of the trajectory. While the Type 1 trajectory and the Type 2 trajectory are nearly the same in the shear portion, they diverge to a considerable degree in the aftershear portion of the trajectory.Next, trajectory guidance is considered. Two guidance schemes are developed so as to achieve near-optimum transition from quasi-steady descending flight to quasi-steady ascending flight: acceleration guidance (based on the relative acceleration) and gamma guidance (based on the absolute path inclination).The guidance schemes for quasi-steady flight recovery in abort landing include two parts in sequence: shear guidance and aftershear guidance. The shear guidance is based on the result that the shear portion of the trajectory depends only mildly on the boundary conditions. Therefore, any of the guidance schemes already developed for Type 1 trajectories can be employed for Type 2 trajectories (descent guidance followed by recovery guidance). The aftershear guidance is based on the result that the aftershear portion of the trajectory depends strongly on the boundary conditions; therefore, the guidance schemes developed for Type 1 trajectories cannot be employed for Type 2 trajectories. For Type 2 trajectories, the aftershear guidance includes level flight guidance followed by ascent guidance. The level flight guidance is designed to achieve almost complete velocity recovery; the ascent guidance is designed to achieve the desired final quasi-steady state.The numerical results show that the guidance schemes for quasi-steady flight recovery yield a transition from quasi-steady flight to quasi-steady flight which is close to that of the optimal trajectory, allows the aircraft to achieve the final quasi-steady state, and has good stability properties.This research was supported by NASA Langley Research Center, Grant No. NAG-1-516, by Boeing Commercial Airplane Company, and by Air Line Pilots Association.The authors are indebted to Dr. R. L. Bowles (NASA-LRC) and Dr. G. R. Hennig (BCAC) for helpful discussions.     

Path planning for robots under stochastic uncertainty *

In order to reduce large online measurement and correction expenses, the a priori informations on the random variations of the model parameters of a robot and its working environment are taken into account already at the planning stage. Thus, instead of solving a deterministic path planning problem with a fixed nominal parameter vector, here, the optimal velocity profile along a given trajectory in work space is determined by using a stochastic optimization approach. Especially, the standard polygon of constrained motion-depending on the nominal parameter vector-is replaced by a more general set of admissible motion determined by chance constraints or more general risk constraints. Robust values (with respect to stochastic parameter variations) of the maximum, minimum velocity, acceleration, deceleration, resp., can be obtained then by solving a univariate stochastic optimization problem Considering the fields of extremal trajectories, the minimum-time path planning problem under stochastic uncertainty can be solved now by standard optimal deterministic path planning methods     

Optimum maneuvers of a skip vehicle with bounded lift constraints

This paper presents the analytical solutions of the problem of optimum maneuvering of a glide vehicle flying in the hypervelocity regime. The investigation is based on the approximation of Allen and Eggers; namely, that along the fundamental part of a reentry or ascent trajectory, the aerodynamic forces greatly exceed the components of the gravitational force in the directions tangent and normal to the flight path.The problem consists of finding an optimal control law for the lift such that the final velocity or the final altitude is maximized. This problem can be viewed as bringing the vehicle to the best condition for interception, penetration, or making an evasive maneuver.If the range is free, the optimal lift control is obtained in closed form. If the lift control is bounded, then bounded control is optimal whenever it is reached. The switching sequences for different cases are discussed, and it is shown that there are at most two switchings. Bounded lift control is always at the ends of the optimal trajectory; for the case of two switchings, the optimal trajectory has an inflection point.The authors wish to thank the National Aeronautics and Space Administration for the Grant No. NGR-06-003-033 under which this work was carried out.     

The P1 and P2 approximations of the spherical harmonic method as applied to radiative heat transfer computations with allowance for strong blowing from the surface of a vehicle moving in the Jovian atmosphere

The spherical harmonics method in the P₁ and P₂ approximations is used to analyze radiative heat transfer for a space vehicle entering a planet’s atmosphere. Strong blowing of ablated materials from the vehicle surface is taken into account by using a two-layer flow model without allowance for the viscosity and thermal conduction of the gas. The heating and ablation of a multilayered thermal protection system are determined simultaneously with the vehicle’s flight trajectory, which is calculated taking into account the mass loss due to the ablation. The approach is illustrated by computing the flight of a space vehicle shaped as a spherical segment or a spherically blunted cone entering the Jovian atmosphere at a speed of 60 km/s and an entry angle of ?5°.     

Stochastic air freight hub location and flight routes planning

This paper introduced a stochastic programming model to address the air freight hub location and flight routes planning under seasonal demand variations. Most existing approaches to airline network design problems are restricted to a deterministic environment. However, the demand in the air freight market usually varies seasonally. The model is separated into two decision stages. The first stage, which is the decision not affected by randomness, determines the number and the location of hubs. The second stage, which is the decision affected by randomness, determines the flight routes to transport flows from origins to destinations based upon the hub location and realized uncertain scenario. Finally, the real data based on the air freight market in Taiwan and China is used to test the proposed model.     

Quasi-steady flight to quasi-steady flight transition in a windshear: Trajectory optimization and guidance

This paper is concerned with the near-optimum guidance of an aircraft from quasi-steady flight to quasi-steady flight in a windshear. The take-off problem is considered with reference to flight in a vertical plane. In addition to the horizontal shear, the presence of a downdraft is considered. It is assumed that the power setting is held at the maximum value and that the aircraft is controlled through the angle of attack. Inequality constraints are imposed on both the angle of attack and its time derivative.First, trajectory optimization is considered. The optimal transition problem is formulated as a Chebyshev problem of optimal control: the performance index being minimized is the peak value of the modulus of the difference between the absolute path inclination and a reference value, assumed constant. Two types of optimal trajectories are studied: type 1 is concerned with gamma recovery (recovery of the initial value of the relative path inclination); and type 2 is concerned with quasisteady flight recovery (recovery of the initial values of the relative velocity, the relative path inclination, and the relative angle of attack). The numerical results show that the type 1 trajectory and the type 2 trajectory are nearly the same in the shear portion, while they diverge to a considerable degree in the aftershear portion of the optimal trajectory.Next, trajectory guidance is considered. A guidance scheme is developed so as to achieve near-optimum quasi-steady flight recovery in a windshear. The guidance scheme for quasi-steady flight recovery includes three parts in sequence. The first part refers to the shear portion of the trajectory and is based on the result that this portion of the trajectory depends only mildly on the boundary conditions; therefore, any of the guidance schemes already developed for type 1 trajectories can be employed (for instance, variable gamma guidance). The second part (constant gamma guidance) refers to the initial aftershear portion of the trajectory and is designed to achieve almost velocity recovery. The third part (constant rate of climb guidance) refers to the final aftershear portion of the trajectory and is designed to achieve almost complete restoration of the initial quasi-steady state.While the shear guidance and the initial aftershear guidance employ constant gain coefficients, the final aftershear guidance employs a variable gain coefficient. This is done in order to obtain accuracy and prompt response, while avoiding oscillations and overshoots. The numerical results show that the guidance scheme for quasi-steady flight recovery yields a transition from quasi-steady flight to quasi-steady flight which is close to that of the optimal trajectory, ensures the restoration of the initial quasi-steady state, and has good stability properties.This paper is based on Refs. 1 and 2.This research was supported by NASA-Langley Research Center, Grant No. NAG-1-516, and by Boeing Commercial Aircraft Company. The authors are indebted to Dr. R. L. Bowles, NASA-Langley Research Center, for helpful discussions.     

基于贝叶斯网络的飞行不安全事件风险评估研究

飞行不安全事件会导致飞行事故和飞行事故症候,为了保障飞行安全,对飞行不安全事件的风险因素进行风险评估,对风险大的因素进行有效的管理,可以降低飞行不安全事件的发生.首先从飞行不安全事件的责任类别角度,总结了飞行不安全事件的32个风险因素,归属9类责任,建立了基于贝叶斯网络的飞行不安全事件风险评估模型;其次根据2011年1到11月的民用航空不安全事件的统计结果,利用Microsoft Excel软件和编写VB语言程序通过输入风险因素的先验概率,计算出目标事件即飞行不安全事件发生的概率和风险因素的重要性指标值,最后利用贝叶斯网络模型对飞行不安全事件的风险因素进行评价,得出影响较大的风险因素有6个,分别为爆胎/轮胎脱层/扎破、系统失效、通信中断、外来物击伤、雷击、危险接近/飞行冲突.针对影响较大的风险因素,应增强机务部门对航空器轮胎、机载设备系统、通信系统的检修质量、提高对天气观测和预报的准确度、加强机组培训、优化空管指挥方案.     

基于动态列生成算法的飞机排班问题研究

飞机排班是航空运输生产计划的重要环节,对航空公司的正常运营和整体效益有着决定性影响;飞机排班通常构建为大规模整数规划问题,是航空运筹学研究的重要课题,构建的模型属于严重退化的NP-Hard问题.在考虑对多种机型的飞机进行排班时,大大增加了问题的复杂性.针对航空公司实际情况,建立多种机型的飞机排班模型;为实现模型的有效求解,提出了基于约束编程的动态列生成算法;即用约束编程快速求解航班连线(航班串)并计算航班串简约成本,动态选择列集并与限制主问题进行迭代.最后,利用国内某航空公司干线航班网络实际数据验证模型和算法的有效性.     

智能网联下无人车配送路径优化

结合智能网联无人车实时信息共享与路径选择的特点,研究其配送路径优化问题。通过引进关键点更新策略,制定路径预规划阶段和路径实时调整阶段无人车路径选择策略,提出智能网联环境下基于实时交通信息的车辆路径问题两阶段模型。其中,路径预规划阶段模型确定初始路径与每辆车服务的客户点,路径实时调整阶段模型对每辆车的路径实时调整。对于该优化模型设计遗传算法进行求解,并通过算例验证了模型与算法的可行性。研究结果表明,本文构建的无人车配送优化模型,有效的结合了无人车实时通信与路径选择的特点,节省了无人车配送时间。研究对于无人车在第三方物流配送领域的推广应用具有一定的探索意义。     

Numerical analysis of the oscillation susceptibility along the path of longitudinal flight equilibria of a reentry vehicle

In this paper, it is shown that when the automatic flight control system (AFCS) is decoupled, then on the path of longitudinal flight equilibria of the ALFLEX reentry vehicle, there exist saddle–node bifurcations resulting in oscillations: when the elevator angle exceeds the bifurcation value, the angle of attack and pitch rate oscillate with the same period, while the pitch angle increases or decreases infinitely. Hence, the orbit of the system is spiraling. It is also shown that a mild (non-catastrophic) stability loss occurs due to the bifurcations. Based on this analysis, an automatic flight control design is developed.     

Cell-to-cell mapping method for time-optimal trajectory planning of multiple robot arm systems

This paper presents the results obtained by applying the cell-to-cell mapping method to solve the problem of the time-optimal trajectory planning for coordinated multiple robotic arms handling a common object along a specified geometric path. Based on the structure of the time-optimal trajectory control law, the continuous dynamic model of multiple arms is first approximated by a discrete and finite cell-to-cell mapping on a two-dimensional cell space over a phase plane. The optimal trajectory and the corresponding control are then determined by using the cell-to-cell mapping and a simple search algorithm. To further improve the computational efficiency and to allow for parallel computation, a hierarchical search algorithm consisting of a multiple-variable optimization on the top level and a number of cell-to-cell searches on the bottom level is proposed and implemented in the paper. Besides its simplicity, another distinguishing feature of the cell-to-cell mapping methods is the generation of all optimal trajectories for a given final state and all possible initial states through a single searching process. For most of the existing trajectory planning methods, the planning process can be started only when both the initial and final states have been specified. The cell-to-cell method can be generalized to any optimal trajectory planning problem for a multiple robotic arms system.     

Emergency Logistics Planning in Natural Disasters

Logistics planning in emergency situations involves dispatching commodities (e.g., medical materials and personnel, specialised rescue equipment and rescue teams, food, etc.) to distribution centres in affected areas as soon as possible so that relief operations are accelerated. In this study, a planning model that is to be integrated into a natural disaster logistics Decision Support System is developed. The model addresses the dynamic time-dependent transportation problem that needs to be solved repetitively at given time intervals during ongoing aid delivery. The model regenerates plans incorporating new requests for aid materials, new supplies and transportation means that become available during the current planning time horizon. The plan indicates the optimal mixed pick up and delivery schedules for vehicles within the considered planning time horizon as well as the optimal quantities and types of loads picked up and delivered on these routes. In emergency logistics context, supply is available in limited quantities at the current time period and on specified future dates. Commodity demand is known with certainty at the current date, but can be forecasted for future dates. Unlike commercial environments, vehicles do not have to return to depots, because the next time the plan is re-generated, a node receiving commodities may become a depot or a former depot may have no supplies at all. As a result, there are no closed loop tours, and vehicles wait at their last stop until they receive the next order from the logistics coordination centre. Hence, dispatch orders for vehicles consist of sets of “broken” routes that are generated in response to time-dependent supply/demand. The mathematical model describes a setting that is considerably different than the conventional vehicle routing problem. In fact, the problem is a hybrid that integrates the multi-commodity network flow problem and the vehicle routing problem. In this setting, vehicles are also treated as commodities. The model is readily decomposed into two multi-commodity network flow problems, the first one being linear (for conventional commodities) and the second integer (for vehicle flows). In the solution approach, these sub-models are coupled with relaxed arc capacity constraints using Lagrangean relaxation. The convergence of the proposed algorithm is tested on small test instances as well as on an earthquake scenario of realistic size.     

Optimal planning of network structures within an exchange area

The cost-optimal planning and capacity extension of a given network structure is described by a mixed-integer program. The decision variables in this model are first discrete digital systems (PCM) set up on existing cable lines and secondly new cable links required in the future. Furthermore, this formulation takes account of the circuit capacity of the system and path diversification required for reliability reasons. This planning model describes a real-world problem that can be formulated not only mathematically as a true reproduction of reality but can also be solved in a closed form within reasonable computer time. Opposite to the operational planning methods, this model allows a global cost-optimal network to be obtained, which is subject to a certain set of constraints.     

模糊计划评审技术(F-PERT)中关键路径的规划解法

研究了模糊计划评审技术中关键路径的求解方法 .首先建立了模糊计划网络图中寻找关键路径的规划模型 ,指出该规划模型在模糊排序规则下可以转化为多目标线性规划问题 ,并给出了该类多目标线性规划问题的求解步骤 .最后的算例表明 ,文中提出的方法是切实可行的 .     

A light-propagation model for aircraft trajectory planning

Predicted air traffic growth is expected to double the number of flights over the next 20 years. If current means of air traffic control are maintained, airspace capacity will reach its limits. The need for increasing airspace capacity motivates improved aircraft trajectory planning in 4D (space+time). In order to generate sets of conflict-free 4D trajectories, we introduce a new nature-inspired algorithm: the light propagation algorithm (LPA). This algorithm is a wavefront propagation method that yields approximate geodesic solutions (minimal-in-time solutions) for the path planning problem, in the particular case of air-traffic congestion. In simulations, LPA yields encouraging results on real-world traffic over France while satisfying the specific constraints in air-traffic management.     

Dynamic Location-routeing Problems

Dynamic location-routeing problems involve the determination of the least-cost sequence of depot, vehicle fleet and route configurations in a distribution system, over a given planning horizon. This paper presents two solution approaches to such problems. The first is an exact method which is appropriate for small-scale problems. It consists of representing the problem by a suitable network and of solving to optimality an integer linear programme associated with the network. In the second approach, some of the system costs are approximated, and a global solution is then obtained by determining a shortest path on a directed graph. Under some hypotheses, this approach is suitable for large-scale problems. It is illustrated on a simple example.     

On air traffic flow management with rerouting. Part I: Deterministic case

In this paper a deterministic mixed 0-1 model for the air traffic flow management problem is presented. The model allows for flight cancelation and rerouting, if necessary. It considers several types of objective functions to minimize, namely, the number of flights exceeding a given time delay (that can be zero), separable and non-separable ground holding and air delay costs, penalization of alternative routes to the scheduled one for each flight, time unit delay cost to arrive to the nodes (i.e., air sectors and airports) and penalization for advancing arrival to the nodes over the schedule. The arrival and departure capacity at the airports is obviously considered, as well as the capacity of the different sectors in the airspace, being allowed to vary along the time horizon. So, the model is aimed to help for better decision-making regarding the ground holding and air delays imposed on flights in an air network, on a short term policy for a given time horizon. It is so strong that there is no additional cut appending, nor does it require the execution of the branch-and-bound phase to obtain the optimal solution for the problem in many cases of the testbeds with which we have experimented. In the other cases, the help of the cut identifying and heuristic schemes of the state-of-the art optimization engine of choice is required in order to obtain the solution of the problem, and the branch-and-bound phase is not required either. An extensive computational experience is reported for large-scale instances, some of which have been taken from the literature and some others were coming from industry.     

Solving the vehicle routing problem with time windows and multiple routes exactly using a pseudo-polynomial model

In this paper, we address a variant of the vehicle routing problem called the vehicle routing problem with time windows and multiple routes. It considers that a given vehicle can be assigned to more than one route per planning period. We propose a new exact algorithm for this problem. Our algorithm is iterative and it relies on a pseudo-polynomial network flow model whose nodes represent time instants, and whose arcs represent feasible vehicle routes. This algorithm was tested on a set of benchmark instances from the literature. The computational results show that our method is able to solve more instances than the only other exact method described so far in the literature, and it clearly outperforms this method in terms of computing time.