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Results for “Trajectory Optimization”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Trajectory design via unsupervised probabilistic learning on optimal manifolds

Abstract This article illustrates the use of unsupervised probabilistic learning techniques for the analysis of planetary reentry trajectories. A three-degree-of-freedom model was employed to generate optimal trajectories that comprise the training datasets. The algorithm first extracts the intrinsic structure in the data via a diffusion map approach. We find that data resides on manifolds of much lower dimensionality compared to the high-dimensional state space that describes each trajectory. Using the diffusion coordinates on the graph of training samples, the probabilistic framework subsequently augments the original data with samples that are statistically consistent with the original set. The augmented samples are then used to construct conditional statistics that are ultimately assembled in a path planning algorithm. In this framework, the controls are determined stage by stage during the flight to adapt to changing mission objectives in real-time.

42 ENGINEERING↗
DOE OSTI2018

Optimal velocity prediction for fuel economy improvement of connected vehicles

With the advancement of vehicle-to-vehicle and vehicle-to-infrastructure technologies, more and more real-time information regarding traffic and transportation system will be available to vehicles. This paper presents the development of a novel algorithm that uses available velocity bounds and powertrain information to generate an optimal velocity trajectory over a prediction horizon. When utilised by a vehicle, this optimal velocity trajectory reduces fuel consumption. The objective of this optimisation problem is to reduce dynamic losses, required tractive force, and completing trip distance with a given travel time. Sequential quadratic programming method is employed for this nonlinearly constrained optimisation problem. When applied to a GM Volt-2, the generated velocity trajectory saves fuel compared to a real-world drive cycle. The simulation results confirm the fuel consumption reduction with the rule-based mode selection and the energy management strategy of a GM Volt 2 model in Autonomie.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2019

DEVELOPING A TRAFFIC SIGNAL ECO-COOPERATIVE ADAPTIVE CRUISE CONTROL SYSTEM FOR BATTERY ELECTRIC VEHICLES

This study developed an eco-driving strategy for battery electric vehicles (BEVs) in the vicinity of signalized intersections, known as BEV Eco-Cooperative Adaptive Cruise Control at Intersections (Eco-CACC-I). The system computes a real-time, energy-optimized vehicle trajectory using a BEV vehicle dynamics and energy consumption model. In the proposed approach, the relationship between vehicle speed, acceleration level, and tractive/resistance forces on the vehicle follows the vehicle dynamics model. The Virginia Tech Comprehensive Power-based Electric Vehicle Energy Consumption Model (VT-CPEM) is used to compute the instantaneous battery energy consumption, with the consideration of battery energy regeneration during braking. The Eco-CACC-I energy-optimum trajectory computation is formulated as an optimization problem with constraints. Considering that the optimization solution needs to be computed at a rapid frequency (e.g., 10 Hz) for real-time applications, an A-star algorithm was used here to expedite the computational speed. Lastly, the proposed BEV Eco-CACC-I system was tested in simulation by considering the impacts of various road grades, speed limits, and signal timings. Simulations for an Internal Combustion Engine Vehicles (ICEVs) was conducted to compare with the BEV test results. The results of the comparison indicate that the energy-optimum solution for BEVs is different from that for ICEVs and thus demonstrating the need for vehicle-tailored optimum trajectories.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2015

Nonparametric variational optimization of reaction coordinates

State of the art realistic simulations of complex atomic processes commonly produce trajectories of large size, making the development of automated analysis tools very important. A popular approach aimed at extracting dynamical information consists of projecting these trajectories into optimally selected reaction coordinates or collective variables. For equilibrium dynamics between any two boundary states, the committor function also known as the folding probability in protein folding studies is often considered as the optimal coordinate. To determine it, one selects a functional form with many parameters and trains it on the trajectories using various criteria. A major problem with such an approach is that a poor initial choice of the functional form may lead to sub-optimal results. Here, we describe an approach which allows one to optimize the reaction coordinate without selecting its functional form and thus avoiding this source of error.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

The Hamiltonian property of the flow of singular trajectories

Pontryagin's maximum principle reduces optimal control problems to the investigation of Hamiltonian systems of ordinary differential equations with discontinuous right-hand side. An optimal synthesis is the totality of solutions to this system with a fixed terminal (or initial) condition, which fill a region in the phase space one-to-one. In the construction of optimal synthesis, singular trajectories that go along the discontinuity surface N of the right-hand side of the Hamiltonian system of ordinary differential equations, are crucial. The aim of the paper is to prove that the system of singular trajectories makes up a Hamiltonian flow on a submanifold of N. In particular, it is proved that the flow of singular trajectories in the problem of control of the magnetized Lagrange top in a variable magnetic field is completely Liouville integrable and can be embedded in the flow of a smooth superintegrable Hamiltonian system in the ambient space. Bibliography: 17 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

A Tchebycheff-based multi-objective combined with a PSO–SQP dynamic real-time optimization framework for cycling energy systems

The aim in this work is to develop an optimization framework to address cycling of baseload energy systems due to the penetration of renewables into the grid. The developed strategy corresponds to a multi-objective and dynamic real-time optimization (MOO-DRTO) framework applied to a postcombustion MEA-based CO 2 capture process from a baseload coal-fired power plant under cycling conditions. A Tchebycheff-based method is used for the multi-objective optimization (MOO) component. Also, a hybrid approach consisting of Particle Swarm Optimization (PSO) and Sequential Quadratic Programming (SQP) is implemented for the first time in process systems engineering to solve the dynamic real-time optimization (DRTO) component. The objectives considered in the MOO-DRTO framework are economic and environmental. The proposed MOO-DRTO strategy is successfully implemented and 24-h optimal output trajectories for the carbon capture system under cycling are generated. Also, the optimal compromise is chosen from the Pareto front according to a set of selected weights for the objectives with minimal interaction between the framework and decision maker. The results indicated that the developed framework has potential to be extended to plant-wide optimization applications under cycling.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

TH-C-12A-05: Dynamic Couch Motion for Improvement of Radiation Therapy Trajectories in DCA and VMAT

Purpose: To investigate the potential improvement in dosimetric external beam radiation therapy plan quality using an optimized dynamic gantry and couch motion trajectory which minimizes exposure to the organs at risk. Methods: Patient-specific anatomical information of head-and-neck and cranial cancer patients was used to quantify the geometric overlap between target volumes and organs-at-risk (OARs) based on their two-dimensional projection from source to a plane at isocentre as a function of gantry and couch angle. QUANTEC dose constraints were then used as weighting factors for the OARs to generate a map of couch-gantry coordinate space indicating degree of overlap at each point in space. A couch-gantry collision space was generated by direct measurement on a Varian Truebeam linac using an anthropomorphic solid-water phantom. A dynamic, fully customizable algorithm was written to generate a navigable ideal trajectory for the patient specific couch-gantry space. The advanced algorithm includes weighting factors which can be used to balance the implementation of absolute minimum values of overlap, with the clinical practicality of largescale couch motion and delivery time. Optimized trajectories were calculated for cranial DCA treatments and for head-and-neck VMAT treatments and compared to conventional DCA and VMAT treatment trajectories. Results: Comparison of optimized treatment trajectories with conventional treatment trajectories indicates a decrease in dose to the organs-at-risk between 4.64% and 6.82% (2.39 and 3.52 Gy) of the prescription dose per patient per organ at risk. Conclusion: Using simultaneous couch and gantry motion during radiation therapy to minimize the geometrical overlap in the beams-eye-view target volumes and the organs-at-risk can have an appreciable dose reduction to organs-at-risk.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2022

Multistage Stabilized Continuation for Indirect Optimal Control of Three-Dimensional Hypersonic Trajectories

This work presents the development of a multistaged stabilized continuation for the three-dimensional unpowered hypersonic trajectory planning problem using indirect optimal control methods. The stabilized continuation method is noniterative and guaranteed to terminate within a finite number of floating point operations, thereby making it well suited for onboard autonomous implementations. Here, we present a multistage formulation of the stabilized continuation scheme that involves starting with a “loose” integration tolerance during the first stage and ramping up toward a “strict” integration tolerance through subsequent stages. An important benefit of this approach is that even when the solution to the underlying optimal control problem is numerically unstable, such as with the hypersonic vehicle footprint generation problem, the stabilized continuation algorithm is shown to be successful in finding a solution while providing some additional insights into the underlying cause of the numerical instability.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2023

Integrate FARM with PID controllers: IES Simulation Ecosystem Control System Development

The FARM (Feasible Actuator Range Modifier) software module is a component of the RAVEN-based FORCE framework for analysis of Integrated Energy Systems (IES). FARM was designed to support the HERON software module in the solution of the optimal dispatch problem for IES units. As the result of HERON-FARM dispatch simulation, the set-point trajectories are optimized to meet constraints on both the production variables (i.e., the variables to be optimized such as the electrical power, the hydrogen production rate, etc.) and the process variables tied to the service life of equipment (e.g., steam flowrate, vessel pressure, turbine firing temperature, etc.) at a coarse time resolution (every 10 or 100 seconds) over long time horizons (several days or weeks). In case the operational constraints need to be met at finer time resolution, the computational burden of HERON-FARM would linearly increase with the sampling rate, and sub-optimal solutions might be obtained. System responses characterized by overshoots and damped oscillations temporarily violating the imposed constraints might occur during abrupt power transients. In this report, a hierarchical control system architecture for the operation of the Dynamic Energy Technology and Integration Laboratory (DETAIL) facility constructed at INL was proposed. First, the preliminary studies on the proposed control strategy for operating the facility and the designed PI controllers were reviewed. In particular, the current approach for generating the set-point trajectories was studied, and its limits were identified. To this aim, the inclusion of a Supervisory Control layer embedding a modified version of the FARM algorithm for preserving the system safe operation over both long and real-time horizons was proposed. In this way, FARM would be applied twice, i.e., the original version (“FARM Validator”) aiding the solution of the power dispatch problem, and the modified version (“FARM Supervisory” coordinating the PI controllers to address the real-time control tasks. Despite the kernel of the two modules is the same algorithm, their roles, tasks, and capabilities are quite different. A detailed description of the role of FARM at addressing low-level control tasks is provided, along with tentative operational procedures for training the models embedded into the algorithm by using the collected experimental data.

42 ENGINEERING↗
DOE OSTI2024

A windowed mean trajectory approximation for condensed phase dynamics

We propose a trajectory-based quasi-classical method for approximating dynamics in condensed phase systems. Building upon the previously developed optimized mean trajectory approximation that has been used to compute linear and nonlinear spectra, we borrow some ideas from filtering trajectory methods to obtain a novel semiclassical method for the dynamical propagation of density matrices. This new approximation is tested rigorously against standard multistate electronic models, spin-boson models, and models of the Fenna–Matthews–Olson complex. For dissipative systems, the current method is significantly better or as good as many other semiclassical methods available, especially at low temperatures and for off-diagonal density matrix elements, whereas for scattering models, the current method bears similar limitations as mean-field propagation schemes. All results are tested against the numerically exact hierarchical equations of motion method. In conclusion, the new method shows excellent agreement across various parameter regimes with numerically exact results, highlighting the robustness and accuracy of our approach.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2019

Online Primal-Dual Methods With Measurement Feedback for Time-Varying Convex Optimization

This paper addresses the design and analysis of feedback-based online algorithms to control systems or networked systems based on performance objectives and engineering constraints that may evolve over time. The emerging timevarying convex optimization formalism is leveraged to model optimal operational trajectories of the systems, as well as explicit local and network-level operational constraints. Departing from existing batch and feed-forward optimization approaches, the design of the algorithms capitalizes on an online implementation of primal-dual projected-gradient methods; the gradient steps are, however, suitably modified to accommodate feedback from the system in the form of measurements - hence, the term 'online optimization with feedback.' By virtue of this approach, the resultant algorithms can cope with model mismatches in the algebraic representation of the system states and outputs, they avoid pervasive measurements of exogenous inputs, and they naturally lend themselves to a distributed implementation. Under suitable assumptions, analytical convergence claims are established in terms of dynamic regret. Furthermore, when the synthesis of the feedback-based online algorithms is based on a regularized Lagrangian function, Q-linear convergence to solutions of the time-varying optimization problem is shown.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

The optimal rolling of a sphere, with twisting but without slipping

The problem of a sphere rolling on the plane, with twisting but without slipping, is considered. It is required to roll the sphere from one configuration to another in such a way that the minimum of the action is attained. We obtain a complete parametrization of the extremal trajectories and analyse the natural symmetries of the Hamiltonian system of the Pontryagin maximum principle (rotations and reflections) and their fixed points. Based on the estimates obtained for the fixed points we prove upper estimates for the cut time, that is, the moment of time when an extremal trajectory loses optimality. We consider the problem of re-orienting the sphere in more detail; in particular, we find diffeomorphic domains in the pre-image and image of the exponential map which are used to construct the optimal synthesis. Bibliography: 15 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Improved Sensitivity Relations in State Constrained Optimal Control

Sensitivity relations in optimal control provide an interpretation of the costate trajectory and the Hamiltonian, evaluated along an optimal trajectory, in terms of gradients of the value function. While sensitivity relations are a straightforward consequence of standard transversality conditions for state constraint free optimal control problems formulated in terms of control-dependent differential equations with smooth data, their verification for problems with either pathwise state constraints, nonsmooth data, or for problems where the dynamic constraint takes the form of a differential inclusion, requires careful analysis. In this paper we establish validity of both ‘full’ and ‘partial’ sensitivity relations for an adjoint state of the maximum principle, for optimal control problems with pathwise state constraints, where the underlying control system is described by a differential inclusion. The partial sensitivity relation interprets the costate in terms of partial Clarke subgradients of the value function with respect to the state variable, while the full sensitivity relation interprets the couple, comprising the costate and Hamiltonian, as the Clarke subgradient of the value function with respect to both time and state variables. These relations are distinct because, for nonsmooth data, the partial Clarke subdifferential does not coincide with the projection of the (full) Clarke subdifferential on the relevant coordinate space. We show for the first time (even for problems without state constraints) that a costate trajectory can be chosen to satisfy the partial and full sensitivity relations simultaneously. The partial sensitivity relation in this paper is new for state constraint problems, while the full sensitivity relation improves on earlier results in the literature (for optimal control problems formulated in terms of Lipschitz continuous multifunctions), because a less restrictive inward pointing hypothesis is invoked in the proof, and because it is validated for a stronger set of necessary conditions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

A Method of Optimal Control for Class 8 Vehicle Platoons Over Hilly Terrain

This work develops and implements an NMPC control system to facilitate fuel-optimal platooning of Class 8 vehicles over challenging terrain. Prior research has shown that Cooperative Adaptive Cruise Control (CACC), which allows multiple Class 8 vehicles to follow in close succession, can save between 3 and 8% in overall fuel consumption on flat terrain. However, on more challenging terrain, e.g. rolling hills, platooning vehicles can experience diminished fuel savings, and, in some cases, an increase in fuel consumption relative to individual vehicle operation. This research explores the use of Nonlinear Model Predictive Control (NMPC) with predefined route grade profiles to allow platooning vehicles to generate an optimal velocity trajectory with respect to fuel consumption. In order to successfully implement the NMPC system, a model relating vehicle velocity to fuel consumption was generated and validated using experimental data. Additionally, the predefined route grade profiles were created by using the vehicle's GPS velocity over the desired terrain. The real-time NMPC system was then implemented on a two-truck platoon operating over challenging terrain, with a reference vehicle running individually. The results from NMPC platooning are compared against fuel results from a classical proportional-integral-derivative (PID) headway control method. Furthermore, this comparison yields the comparative fuel savings and energy efficiency benefit of NMPC system. In the final analysis, significant fuel savings of greater than 14 and 20% were seen for the lead and following vehicles relative to their respective traditional cruise control and platooning architectures.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2019

Flexibility Reserve in Power Systems: Definition and Stochastic Multi-Fidelity Optimization

This paper defines flexibility reserve trajectory as a single reserve product that not only supplies the energy imbalance in real-time operation but also the resulting ramping requirements by embedding the flexible ramping trajectories as time derivative of the reserve trajectories. Further, a stochastic optimization model is proposed for multi-fidelity co-optimization of energy and flexibility reserve in day-ahead power systems operation. The proposed model integrates operation decisions with different levels of modeling fidelity in a single stochastic optimization problem. More specifically, day-ahead energy trajectories, day-ahead flexibility reserve capacity trajectories, and real-time flexibility reserve deployment trajectories are modeled by Bernstein polynomials with different degrees as required to match the load and renewable generation with different levels of variability in day-ahead and real-time operations. The proposed model is implemented on the IEEE reliability test system using load and solar generation data of California ISO, where the numerical results demonstrate that the proposed model schedules a reserve capacity that more accurately matches the real-time energy imbalance and ramping requirements of net-load, while reducing the total operation cost of the system.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2022

Advances in Secure 5G Network for a Nationwide Drone Corridor

Recent research has validated the proposal to add a separate set of antennas for 5G coverage in the air, while the conventional set of antennas continues to provide coverage on the ground, for a nationwide drone corridor for 5G cellular drones. More importantly, this drone corridor can be made secure and reliable by adapting the drone trajectories to avoid interference and security attacks, and with advanced precoding and physical layer security. Energy efficiency can also be improved with low-resolution massive multiple-input multiple-output (MIMO) systems that utilize low resolution digital to analog converters. This paper describes additional research findings to further support the creation of this nationwide drone corridor. We design optimal drone trajectory within the drone corridor to improve safety for pedestrians and vehicles on the ground. We derive the optimum antenna uptilt angle to minimize outage probability for a given drone corridor. We also study the placement of intelligent reflector surfaces in an urban drone corridor in order to improve the multi-path scattering and hence the spatial multiplexing gains for serving drones. We calculate trajectories to maximize data rate in the presence of smart interference when drones are used as relays and each drone may be deployed in the paths of data flows from multiple BSs to multiple UEs. Next we demonstrate how the use of the additional set of antennas along with the 3GPP standard based subframe blanking method can minimize the interference from ground reflection of the radio frequency (RF) radiation from the downtilted antennas. The paper concludes with plans to continue with experimental studies to advance this work further.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2020

Dynamic Queue Prediction at Signalized Intersections with Fusing Sensory Information and Connected Vehicles

Queue length is one of the most essential metrics for indicating traffic conditions at signalized intersections. Most existing studies mainly focus on queue length estimation in a retrieving way which cannot effectively predict the future state of vehicle in queue. This paper proposes an innovative dynamic queue prediction model in a vehicle-infrastructure cooperative way. The proposed dynamic queue predictor can customize the queue prediction using the trajectories of preceding vehicles from radar detection with varying information from loop detectors and connected vehicles (CVs). The dynamic queue prediction accuracy can be further improved with at least one present CV in the same cycle. With the accurate dynamic queue prediction, we present a case study of Queue-Aware Eco-Approach and Departure (QEAD) to provide an online optimal vehicle trajectory considering both the signal status and preceding vehicle's future status in queue. The proposed framework and algorithms are of pragmatic significance and one of its advanced features is the ability to work under low penetration rate of CVs. The test using Next Generation SIMulation (NGSIM) dataset and a case study in VISSIM microscopic simulation show promising results.

Ye, Fei↗