Dynamic Trajectory Optimization Research Articles

Dynamic Trajectory Optimization Design for Railway Driver Advisory System

Driver Advisory Systems (DAS) aim to provide reliable and efficient driving instructions to the driver with optimized trajectory. This paper studies trajectory optimization method to achieve energy efficiency and punctuality for DAS. Firstly, the design of offline trajectory optimization is studied, using the Genetic Algorithm (GA) to optimize the energy-efficient trajectory. The performance of offline optimization is evaluated by the application of three different driving styles. Online optimization is constructed to dynamically adjust the trajectory when a driving deviation occurs. The combination of offline optimization and online optimization method is simulated as a dynamic trajectory optimization system, to represent a practical solution for DAS systems to achieve energy efficiency and punctuality by real-time adjustment during the journey. An evaluation of energy saving and computation efficiency for the trajectory optimization is conducted based on a simulation of a real-scale route.

Dynamic programming-based multi-vehicle longitudinal trajectory optimization with simplified car following models

Jointly optimizing multi-vehicle trajectories is a critical task in the next-generation transportation system with autonomous and connected vehicles. Based on a space-time lattice, we present a set of integer programming and dynamic programming models for scheduling longitudinal trajectories, where the goal is to consider both system-wide safety and throughput requirements under supports of various communication technologies. Newell's simplified linear car following model is used to characterize interactions and collision avoidance between vehicles, and a control variable of time-dependent platoon-level reaction time is introduced in this study to reflect various degrees of vehicle-to-vehicle or vehicle-to-infrastructure communication connectivity. By adjusting the lead vehicle's speed and platoon-level reaction time at each time step, the proposed optimization models could effectively control the complete set of trajectories in a platoon, along traffic backward propagation waves. This parsimonious multi-vehicle state representation sheds new lights on forming tight and adaptive vehicle platoons at a capacity bottleneck. We examine the principle of optimality conditions and resulting computational complexity under different coupling conditions.

Dynamic Modeling, Trajectory Optimization, and Control of a Flexible Kiteplane

This paper investigates dynamic modeling, trajectory optimization, and control of a flexible kiteplane used for wind energy harvesting. The individual components of the kiteplane, including flexible wings and a rigid fuselage, are modeled separately and then constrained together using the null-space method. The flexible wings of the kiteplane are modeled as flexible plates, and the Rayleigh–Ritz method is used to discretize the partial differential equation that describes the strain energy stored in the wing. The attitude of the kiteplane is described by the direction cosine matrix (DCM) directly and a proportional-integral-derivative control law that makes use of the DCM is implemented for attitude control. An unsteady aerodynamic model based on Theodorsen’s lift model is used in simulation to allow for an accurate model under transient conditions. An optimal trajectory is found using a simplified dynamic model and solving a finite-dimensional constrained optimization problem. Numerical simulations of the optimal trajectories are performed to demonstrate the kiteplane’s energy-harvesting capability.

Comparison of kinematic and dynamic leg trajectory optimization techniques for biped robot locomotion

The paper presents comparison analysis of two approaches in defining leg trajectories for biped locomotion. The first one operates only with kinematic limitations of leg joints and finds the maximum possible locomotion speed for given limits. The second approach defines leg trajectories from the dynamic stability point of view and utilizes ZMP criteria. We show that two methods give different trajectories and demonstrate that trajectories based on pure dynamic optimization cannot be realized due to joint limits. Kinematic optimization provides unstable solution which can be balanced by upper body movement.

Steady Glide Dynamic Modeling and Trajectory Optimization for High Lift-to-Drag Ratio Reentry Vehicle

Steady glide trajectory optimization for high lift-to-drag ratio reentry vehicle is a challenge because of weakly damped trajectory oscillation. This paper aims at providing a steady glide trajectory using numerical optimal method. A new steady glide dynamic modeling is formulated via extending a trajectory-oscillation suppressing scheme into the three-dimensional reentry dynamics with a spherical and rotating Earth. This scheme comprehensively considers all factors acting on the flight path angle and suppresses the trajectory oscillation by regulating the vertical acceleration in negative feedback form and keeping the lateral acceleration invariant. Then, a study on steady glide trajectory optimization is carried out based on this modeling and pseudospectral method. Two examples with and without bank reversal are taken to evaluate the performance and applicability of the new method. A comparison with the traditional method is also provided to demonstrate its superior performance. Finally, the feasibility of the pseudospectral solution is verified by comparing the optimal trajectory with integral trajectory. The results show that this method not only is capable of addressing the case which the traditional method cannot solve but also significantly improves the computational efficiency. More importantly, it provides more stable and safe optimal steady glide trajectory with high precision.

Research on Dynamic Trajectory Optimization of Hybrid Engine

Dynamic working conditions run through the whole operational process of hybrid engines, which endow great significance to its optimization to obtain the optimal dynamic trajectory of hybrid engines to improve both the economy and emission performance. The motor, responding the torque demand of the vehicle rapidly, provides the possibility to control the engine working along a specific trace. Aiming at the dynamic trajectory optimization of hybrid engines, a dynamic process effect field has been built to analysis dynamic characteristics based on field coordination principle, which transform the dynamic process optimization to path optimization in a field space. Utilizing space trajectory optimization method, the path optimization problem is simplified further to a minimization problem of cumulative number of field effect in a field space and is solved by the steepest gradient method of discrete space, depending on which the optimal trajectories under different objective factors have been achieved. Simulation and experiments results show that the optimal trace algorithm can reach the established goal, which achieves the optimal control in dynamic process.

到着時刻を指定した旅客機の軌道最適化

In the future air transportation system, airspace will be efficiently used and each aircraft can optimize its own performance. Due to limited capacity of the airspace like terminal area, however, some sort of adjustment for each aircraft is necessary to maintain separation among multiple aircraft. Fixed arrival time is a basic solution to the problem. This paper studies the effect of arrival time assignment on the performance by assuming that each aircraft generates its own flight plan by minimizing its fuel consumption. Dynamic programming trajectory optimization is used to calculate the optimal flight profile composed of altitude and velocity. The result shows that the arrival time adjustment is efficiently performed in the descent phase, if the required amount of time to be adjusted is not large.

A Study on Earth-Moon Transfer Orbit Design

Optimal transfer trajectories based on the planar circular restricted three body problem are designed by using mixed impulsive and continuous thrust. Continuous and dynamic trajectory optimization is reformulated in the form of discrete optimization problem. This is done by the method of direct transcription and collocation. It is then solved by using nonlinear programming software. Two very different transfer trajectories can be obtained by the different combinations of the design parameters. Furthermore, it was found out that all designed trajectories permit a ballistic capture by the Moon's gravity. Finally, the required thrust profiles are presented and they are analyzed in detail.

Optimization of area navigation noise abatement approach trajectories

This article describes the development of a novel tool for the design of environmentally optimized area navigation (RNAV) approach procedures. This new development is an extension of a tool called NOISHHH which was developed earlier for the analysis and design of noise abatement procedures around airports. The NOISHHH tool is essentially a framework that combines a noise model, a geographic information system, an emission inventory model, and a dynamic trajectory optimization algorithm to generate flight paths that minimize the noise impact in the vicinity of an airport. The RNAV-extended version of NOISHHH offers the possibility to calculate routes that can be programmed into the flight management system currently available in many aircraft cockpits. The capabilities of the RNAV-compliant version of NOISHHH are illustrated in an example scenario based on an instrument approach to one of the runways of Schiphol airport in the Netherlands.

Optimization of Rotorcraft Simultaneous Noninterfering Noise Abatement Approach Procedures

T HE concept of simultaneous noninterfering (SNI) approaches for rotorcraft is currently being explored in both Europe and the United States. The SNI concept was initially conceived in the United States to enable the integration of both fixed wing and rotorcraft into the terminal airspace system to reduce delays and increase capacity [1]. It comprises primarily specific instrument flight rules (IFR) departure and approach procedures which enable rotorcraft to operate independently from fixed-wing traffic IFR streams. Because of the much lower approach speeds of helicopters, sequencing helicopter operations into the IFR approach stream tends to result in congestion and undesirable delays. At present, helicopter operators often prefer to operate under visual flight rules to avoid complex IFR procedures, but clearly this does not provide a reliable air transport service in all weather conditions. Also, in Europe, research pertaining to SNI operations is well underway, notably in the sixth framework project OPTIMAL (Optimized Procedures and Techniques for Improvement of Approach and Landing) [2]. The main aim of the OPTIMAL project is to increase airport capacity and efficiency, while reducing the noise footprint. A downside of the SNI concept is that new SNI routes will be located in previously unused airspace and consequently may overfly noise-sensitive communities that were not affected by traffic movements before. This, coupled with the fact that helicopter approach operations tend to be relatively noisy, indicates a clear need for optimization of the SNI routes and flight paths such as to reduce the noise impact in the affected residential communities. Optimization of SNI approaches with respect to community noise impact was first explored by Atkins and Xue [3,4]. In [3,4], they present an optimization technique for segmented three-dimensional SNI trajectory design based on an incremental search strategy that combines a k-ary tree with Dijkstra’s algorithm. The objective function is based on a validated rotorcraft noise model as well as terminal area population density data. Fixed-wing airspace corridors were treated as impenetrable obstacles. In this approach, a trajectory is described as a sequence of trimmed flight segments that connect initial approach and landing sites. The number of segments considered in this study remains limited (typicallyfive or less) primarily due to the fact that the computational load increases rapidly with the number of segments. To make the approach numerically tractable, a number of simplifying assumptions were introduced. In particular, it was assumed that transitions between trim states do not appreciably affect solution cost. The optimization of noise abatement procedures for fixed-wing aircraft has received considerablymore attention. In [5], an optimization approach is presented that, similar to [3,4], relies on segmented routes. The segmented routes, optimized using a genetic algorithm, enable a specification of simple procedures that are amenable to fast online computer solutions that can be readily implemented in a guidance system. In [6–8], a noise-optimized approach and departure trajectories are computed based on a direct numerical optimization techniques that enable one to generate (piecewise) continuous optimal trajectories for a point-mass modeled fixed-wing aircraft. The numerical tool that has been used in these particular studies is called NOISHHH. The NOISHHH tool essentially combines a noise model, a dose-response relationship, an emission inventory model, a geographic information system, and a dynamic trajectory optimization algorithm. NOISHHH generates routings and flight paths for both arrivals and departures that minimize the environmental impact in the residential communities surrounding the airport, while satisfying all imposed operational and safety constraints. The present study is aimed at extending the NOISHHH tool to permit the computation of noise-optimized SNI trajectories for rotorcraft. The extension does not only entail a modification of the dynamic vehiclemodel and the operational context, but also involves an adaptation of the implemented noisemodel. The environmentallyoptimized SNI trajectories calculated with the modified version of NOISHHH are illustrated in an example scenario involving an SNI instrument approach of a Robinson R22 helicopter [9] to a helispot on runway 22 of Schiphol airport (Amsterdam) in the Netherlands.

Environmentally Optimized Resolutions of In-Trail Separation Conflicts for Arrival Flights

This paper describes the development of a novel tool that calculates environmentally optimized conflict resolutions for two consecutive arrival flights that feature an in-trail separation conflict. This dual-event tool is an extension of a single-event version of the tool that was developed earlier for the analysis and design of noise-abatement procedures around airports. The new tool combines a noise model, an emissions inventory model, a geographic information system, and a dynamic trajectory optimization algorithm. The optimization algorithm generates routings and flight paths that minimize the environmental impact in the residential communities surrounding the airport while satisfying all imposed operational and safety constraints. The environmentally optimized conflict resolutions calculated with the dual-event version of the tool are illustrated in an example scenario based on an approach to one of the runways of Amsterdam Airport Schiphol in The Netherlands. The results indicate that the optimal resolution strategy heavily depends on the considered aircraft types.

Generic and site-specific criteria in the optimization of noise abatement trajectories

This paper presents a trade-off study that has been conducted using a recently developed tool for the analysis and design of noise abatement procedures around airports. This new tool, NOISHHH, combines a noise model, a geographic information system, and a dynamic trajectory optimization algorithm. NOISHHH features a multi-objective optimization capability that permits exploration of a variety of environmental criteria, including indices that are generic in nature (e.g. noise footprints) as well as site-specific criteria that take into account the population distribution in the areas surrounding the airport. Using this capability a noise performance trade-off was conducted by comparing arrival trajectories that are optimized according to a variety of noise abatement criteria, including both generic and site-specific criteria. The main focus is on providing insight into the sensitivities in the multi-objective noise performance trade-off process. The results are used to illustrate the possibility of synthesizing trajectories that provide a sensible compromise solution among the various noise criteria.

The Dynamic-Q optimization method: An alternative to SQP?

In this paper, a constrained optimization method, called the Dynamic-Q method, is presented. Simply stated, the method consists of applying an existing dynamic trajectory optimization algorithm to successive spherical quadratic approximations of the actual optimization problem. The Dynamic-Q algorithm has the advantage of having minimal storage requirements, thus making it suitable for problems with large numbers of variables. The Dynamic-Q method is tested and results obtained are compared to results for a sequential quadratic programming (SQP) method. Indications are that the new method is robust and efficient, and particularly well suited to practical engineering optimization problems.

Optimal departure trajectories with respect to sleep disturbance

This paper describes on-going research in the field of trajectory optimization with respect to noise. Recently, this resulted in a tool in which the Integrated Noise Model, a Geographic Information System and a dynamic trajectory optimization algorithm are combined. This tool has proved to be effective in analyzing noise abatement procedures for departure. With this tool, optimized departure trajectories were generated by using a composite performance index which incorporated a noise related and a fuel related parameter. This resulted in minimum-fuel trajectories that were locally adjusted for noise considerations. However, such a minimum-fuel trajectory is not very realistic from an operational point of view. Therefore, this study proposes a different composition of the performance index. The performance index that is used in the present study incorporates the deviation from a reference flight path instead of a fuel parameter. In this way, a reference flight can be selected that is more practical. A trajectory optimized using the modified performance index will deviate from the reference track only if this improves the noise impact. It is also shown that, depending on the scenario, two instruments, i.e., a thrust cutback or lateral movement, are employed to a different extent in order to achieve a noise reduction.

Optimization of Noise Abatement Departure Trajectories

This paper describes the development of a new tool that offers significant capabilities for the analysis and design of noise abatement procedures at any given airport. The proposed tool combines a noise model, a geographic information system and a dynamic trajectory optimization algorithm. The optimization algorithm essentially modifies routings and flightpaths such as to minimize the noise impact in the residential communities surrounding the airport, while satisfying all imposed operational and safety constraints. Numerical examples, involving departure trajectories from Amsterdam Airport Schiphol, are included to demonstrate the effectiveness and flexibility of the developed tool. Although the results obtained to date are for departure flights only, the employed methodology tool holds out equal promise for application to approach trajectories. In the numerical examples the characteristics of a Boeing 737-300 aircraft are used.