Trajectory Optimization Framework Research Articles

Well Trajectory Optimization under Geological Uncertainties Assisted by a New Deep Learning Technique

Summary The large number of geological realizations and well trajectory parameters make field development optimization under geological uncertainty a time-consuming task. A novel deep learning-based surrogate model with a novel well trajectory parametrization technique is proposed in this study to optimize the trajectory of wells under geological uncertainty. The proposed model is a deep neural network with ConvLSTM layers to extract the most salient features from highly channelized and layered reservoirs efficiently. ConvLSTM layers are used because they can extract spatiotemporal features simultaneously since layered reservoirs can be regarded as a time series of spatially distributed reservoir properties. The proposed surrogate model could predict the individual objective function with a coefficient of determination of 0.96. After verifying the validity of the surrogate model, four approaches were used to optimize well trajectories. Two of the approaches consumed all available realizations (surrogate model-based and simulation-based approaches), while the remaining two used a subset of realizations. The selection of the subset was based on the cumulative oil production (COP) and the diffusive time of flight (DTOF). Results showed that although the surrogate model used all realizations, it could provide similar results to the simulation-based optimization with only a 5% computational cost of the simulation-based approach. The novelty of this work lies in its proposal of an innovative surrogate model to improve the analysis of channelized and layered reservoirs and its introduction of a novel well trajectory optimization framework that effectively addresses the challenge of optimizing well trajectories in complex three-dimensional spaces, a problem not adequately tackled in previous works.

A Decision Support Framework for Aircraft Arrival Scheduling and Trajectory Optimization in Terminal Maneuvering Areas

This study introduces a decision support framework that integrates aircraft trajectory optimization and arrival scheduling to facilitate efficient management of descent operations for arriving aircraft within terminal maneuvering areas. The framework comprises three modules designed to tackle specific challenges in the descent process. The first module formulates and solves a trajectory optimization problem, generating a range of candidate descent trajectories for each arriving aircraft. The options for descent operations include step-down descent operation, Continuous Descent Operation (CDO), and CDO with a lateral path stretching strategy. The second module addresses the assignment of conflict-free trajectories to aircraft, determining precise arrival times at each waypoint. This is achieved by solving an aircraft arrival scheduling problem. To overcome computational complexities, a novel variable neighborhood search algorithm is proposed as the solution approach. This algorithm utilizes three neighborhood structures within an extended relaxing and solving framework, and incorporates a tabu search algorithm to enhance the efficiency of the search process in the solution space. The third module focuses on comparing the total cost incurred from flight delays and fuel consumption across the three descent operations, enabling the selection of the most suitable operation for the descent process. The decision support framework is evaluated using real air traffic data from Guangzhou Baiyun International Airport. Experimental results demonstrate that the framework effectively supports air traffic controllers by scheduling more cost-efficient descent operations for arrival aircraft.

Affine Formation Maneuver Control for Multi-Agent Based on Optimal Flight System

The use of affine maneuver control to maintain the desired configuration of unmanned aerial vehicle (UAV) swarms has been widely practiced. Nevertheless, the lack of capability to interact with obstacles and navigate autonomously could potentially limit its extension. To address this problem, we present an innovative formation flight system featuring a virtual leader that seamlessly integrates global control and local control, effectively addressing the limitations of existing methods that rely on fixed configuration changes to accommodate real-world constraints. To enhance the elasticity of an algorithm for configuration change in an obstacle-laden environment, this paper introduces a second-order differentiable virtual force-based metric for planning local trajectories. The virtual field comprises several artificial potential field (APF) forces that adaptively adjust the formation compared to the existing following control. Then, a distributed and decoupled trajectory optimization framework that considers obstacle avoidance and dynamic feasibility is designed. This novel multi-agent agreement strategy can efficiently coordinate the global planning and local trajectory optimizations of the formation compared to a single method. Finally, an affine-based maneuver approach is employed to validate an optimal formation control law for ensuring closed-loop system stability. The simulation results demonstrate that the proposed scheme improves track accuracy by 32.92% compared to the traditional method, while also preserving formation and avoiding obstacles simultaneously.

From External Interaction to Internal Inference: An Intelligent Learning Framework for Spectrum Sharing and UAV Trajectory Optimization

From External Interaction to Internal Inference: An Intelligent Learning Framework for Spectrum Sharing and UAV Trajectory Optimization

Trajectory optimization for collaborative recovery of parafoil systems using unmanned vessel

Traditional trajectory optimization methods for the parafoil system set fixed-point landing as the objective. However, in recent payload fairing recovery missions, the recovery system comprising two parafoils is collaboratively recovered by a mobile vehicle, posing new challenges to the current trajectory optimization technique. In order to recover two parafoil systems autonomously with an unmanned surface vessel, this paper presents a trajectory optimization framework composed of three following component processes consecutively. Firstly, a feasibility judgment algorithm based on reachable boundary estimation is designed to determine the possibility of recovering two parafoil systems. Secondly, the decoupled-then-simultaneous strategy is proposed to enhance the convergence of solving the collaborative recovery problem. Thirdly, the finite-element collocation approach is utilized to convert the formulated trajectory optimization problems into nonlinear programming (NLP) problems, which are solved by a highly efficient NLP solver. Simulation results show that the proposed trajectory optimization framework can efficiently generate the optimal trajectory for recovering two parafoil systems with a vessel.

RoLoMa: robust loco-manipulation for quadruped robots with arms

Deployment of robotic systems in the real world requires a certain level of robustness in order to deal with uncertainty factors, such as mismatches in the dynamics model, noise in sensor readings, and communication delays. Some approaches tackle these issues reactively at the control stage. However, regardless of the controller, online motion execution can only be as robust as the system capabilities allow at any given state. This is why it is important to have good motion plans to begin with, where robustness is considered proactively. To this end, we propose a metric (derived from first principles) for representing robustness against external disturbances. We then use this metric within our trajectory optimization framework for solving complex loco-manipulation tasks. Through our experiments, we show that trajectories generated using our approach can resist a greater range of forces originating from any possible direction. By using our method, we can compute trajectories that solve tasks as effectively as before, with the added benefit of being able to counteract stronger disturbances in worst-case scenarios.

Novel learning framework for optimal multi-object video trajectory tracking

BackgroundWith the rapid development of Web3D, virtual reality, and digital twins, virtual trajectories and decision data considerably rely on the analysis and understanding of real video data, particularly in emergency evacuation scenarios. Correctly and effectively evacuating crowds in virtual emergency scenarios are becoming increasingly urgent. One good solution is to extract pedestrian trajectories from videos of emergency situations using a multi-target tracking algorithm and use them to define evacuation procedures. MethodsTo implement this solution, a trajectory extraction and optimization framework based on multi-target tracking is developed in this study. First, a multi-target tracking algorithm is used to extract and preprocess the trajectory data of the crowd in a video. Then, the trajectory is optimized by combining the trajectory point extraction algorithm and Savitzky–Golay smoothing filtering method. Finally, related experiments are conducted, and the results show that the proposed approach can effectively and accurately extract the trajectories of multiple target objects in real time. ResultsIn addition, the proposed approach retains the real characteristics of the trajectories as much as possible while improving the trajectory smoothing index, which can provide data support for the analysis of pedestrian trajectory data and formulation of personnel evacuation schemes in emergency scenarios. ConclusionsFurther comparisons with methods used in related studies confirm the feasibility and superiority of the proposed framework.

Trajectory Optimization Framework for Rehabilitation Robots With Multi-Workspace Objectives and Constraints

Trajectory Optimization Framework for Rehabilitation Robots With Multi-Workspace Objectives and Constraints

Incorporation of Rigid Body Dynamics into Indirect Hypersonic Trajectory Optimization

This investigation demonstrates hypersonic trajectory optimization using planar rigid body dynamics within the indirect trajectory optimization framework. Employing rigid body dynamics captures the coupling between the optimal trajectory, the vehicle geometry, mass distribution, and control configuration. This provides trajectories that implicitly account for the maneuverability of the vehicle, wherein the vehicle is guaranteed to follow the angle-of-attack profile. This is unlike point-mass dynamics, wherein the angle-of-attack or angle-of-attack rate is directly used as the control variable, and maneuverability must be accounted for using bounds on these quantities. This is not straightforward because these bounds are dependent on flight conditions and are not constant for the entire trajectory. As a result, point-mass dynamics can produce infeasible solutions if these bounds are not properly handled. When using rigid body dynamics, these bounds are a consequence of the flight dynamics and are not required to be explicitly enforced, thereby circumventing the challenge with dynamic bounds on angle-of-attack and angle-of-attack rate altogether. Additionally, optimal trajectories calculated using rigid body dynamics more accurately reflect the drag penalties incurred when maneuvering the vehicle, such as when deflecting the aerodynamic control surfaces. The incurred drag penalties become critical in high-performance applications, wherein the terminal velocity is required to be maximized. Also, because the trajectory is coupled to the vehicle geometry, mass distribution, and control architecture, the optimal trajectory can be concurrently analyzed with the vehicle configuration, thereby enabling multidisciplinary design analysis. Despite these benefits offered by employing rigid body dynamics in trajectory optimization, there is limited literature in this regard, and none of them explored in this investigation employs indirect methods. This investigation fills this gap in the indirect trajectory optimization arena.

Stress flow guided non-planar print trajectory optimization for additive manufacturing of anisotropic polymers

When manufacturing parts using material extrusion additive manufacturing and anisotropic polymers, the mechanical properties of a manufactured component are strongly dependent on the print trajectory orientation. We conduct non-planar slicing and optimize the print trajectories to maximize the alignment between the material deposition direction and the stress flow induced by a predefined load case. The trajectory optimization framework considers manufacturability constraints in the form of uniform layer height and line spacing. We demonstrate the method by manufacturing a load bearing mechanical bracket using a 5-axis 3D printer and a liquid crystal polymer material. The failure strength and stiffness of the optimized bracket are improved by a factor of 44 and 6 respectively when compared with conventional printing.

MAESTRO-X: Distributed Orchestration of Rotary-Wing UAV-Relay Swarms

This work details a scalable framework to orchestrate a swarm of rotary-wing UAVs serving as cellular relays to facilitate beyond line-of-sight connectivity and traffic offloading for ground users. First, a Multiscale Adaptive Energyconscious Scheduling and TRajectory Optimization (MAESTRO) framework is developed for a single UAV. Aiming to minimize the time-averaged latency to serve user requests, subject to an average UAV power constraint, it is shown that the optimization problem can be cast as a semi-Markov decision process, and exhibits a multiscale structure: outer actions on radial wait velocities and terminal service positions minimize the longterm delay-power trade-off, optimized via value iteration; given these outer actions, inner actions on angular wait velocities and service trajectories minimize a short-term delay-energy cost; finally, rate adaptation is embedded along the trajectory to leverage air-to-ground channel propagation conditions. A novel hierarchical competitive swarm optimization scheme is developed in the inner optimization, to devise high-resolution trajectories via iterative pair-wise updates. Next, MAESTRO is eXtended to UAV swarms (MAESTRO-X) via scalable policy replication, enabled by a decentralized command-and-control network augmented with: (1) spread maximization to proactively position UAVs to serve future requests; (2) consensus-driven conflict resolution to orchestrate scheduling decisions based on delay-energy costs including queuing dynamics; (3) adaptive frequency reuse to improve spectrum utilization across the network; and (4) a piggybacking mechanism allowing UAVs to serve multiple ground users simultaneously. Numerical evaluations show that, for user requests of 10 Mbits, generated according to a Poisson arrival process with rate 0.2 req/min/UAV, single-agent MAESTRO offers 3.8× faster service than a high-altitude platform and 29% faster than a static UAV deployment; moreover, for a swarm of 3 UAV-relays, MAESTRO-X delivers data payloads 4.7× faster than a successive convex approximation scheme; and remarkably, a single UAV optimized via MAESTRO outclasses 3 UAVs optimized via a deep-Q network by 38%.

Robust estimation of distribution algorithms via fitness landscape analysis for optimal low-thrust orbital maneuvers

One particular kind of evolutionary algorithms known as Estimation of Distribution Algorithms (EDAs) has gained the attention of the aerospace industry for its ability to solve nonlinear and complicated problems, particularly in the optimization of space trajectories during on-orbit operations of satellites. This article describes an effective method for optimizing the trajectory of a spacecraft using an evolutionary approach based on EDAs, incorporated with fitness landscape analysis (FLA). The approach utilizes flexible operators that are paired with seeding and selection mechanisms of EDAs. Initially, the orbit transfer problem is mathematically modeled and the objectives and constraints are identified. The landscape feature of the search space is analyzed via the dispersion metric to measure the modality and ruggedness of the search domain. The obtained information are used as feedback in developing adaptive operators for truncation factor and constraints separation threshold of the employed EDA. A framework for spacecraft trajectory optimization has been presented where the dispersion value for a space mission is estimated using a k-nearest neighbors (k-NN) algorithm. The suggested method is used to solve several problems related to low-thrust orbit transfer of satellites in Earth’s orbit. Results demonstrate that the suggested framework for trajectory design and optimization of space transfers is effective enough to offer fuel-efficient and energy-efficient maneuvers for different thrust levels of the propulsion system. Moreover, the performance of the proposed approach is evaluated against non-adaptive EDA and other advanced evolutionary algorithms. The obtained results certify that the proposed adaptive evolutionary approach is superior in identifying feasible minimum-fuel and minimum-energy transfer trajectories.

Stochastic optimization of three-dimensional non-Cartesian sampling trajectory.

Optimizing three-dimensional (3D) k-space sampling trajectories is important for efficient MRI yet presents a challenging computational problem. This work proposes a generalized framework for optimizing 3D non-Cartesian sampling patterns via data-driven optimization. We built a differentiable simulation model to enable gradient-based methods for sampling trajectory optimization. The algorithm can simultaneously optimize multiple properties of sampling patterns, including image quality, hardware constraints (maximum slew rate and gradient strength), reduced peripheral nerve stimulation (PNS), and parameter-weighted contrast. The proposed method can either optimize the gradient waveform (spline-based freeform optimization) or optimize properties of given sampling trajectories (such as the rotation angle of radial trajectories). Notably, the method can optimize sampling trajectories synergistically with either model-based or learning-based reconstruction methods. We proposed several strategies to alleviate the severe nonconvexity and huge computation demand posed by the large scale. The corresponding code is available as an open-source toolbox. We applied the optimized trajectory to multiple applications including structural and functional imaging. In the simulation studies, the image quality of a 3D kooshball trajectory was improved from 0.29 to 0.22 (NRMSE) with Stochastic optimization framework for 3D NOn-Cartesian samPling trajectorY (SNOPY) optimization. In the prospective studies, by optimizing the rotation angles of a stack-of-stars (SOS) trajectory, SNOPY reduced the NRMSE of reconstructed images from 1.19 to 0.97 compared to the best empirical method (RSOS-GR). Optimizing the gradient waveform of a rotational EPI trajectory improved participants' rating of the PNS from "strong" to "mild." SNOPY provides an efficient data-driven and optimization-based method to tailor non-Cartesian sampling trajectories.

Densely rewarded reinforcement learning for robust low-thrust trajectory optimization

To overcome the time-consuming training caused by the sparse reward function in reinforcement learning, an efficient dense reward framework for robust low-thrust trajectory optimization is proposed. The dense reward functions are designed separately for the deterministic and considered uncertain scenarios, including state uncertainties, observation uncertainties and execution uncertainties. For the uncertainties, the dense reward function is designed to diminish the deviation with respect to the isochronous nominal state along the corresponding deterministic optimal trajectory at each step, rendering the reward function no longer sparse and suitable for complex multirevolution problems. In addition, a multistage reward function of the terminal constraints for the rendezvous missions is designed by incorporating some exponential acceleration terms, enabling significant improvement in training efficiency as the terminal errors become low. In addition, a dense reward function for the deterministic scenario is also proposed via the introduction of empirical forbidden zones and an exponential term. The effectiveness and efficiency of the proposed method is demonstrated in a simple Earth-Mars mission and a complex Earth-Venus multirevolution mission. The promising results verify the significant effect of the proposed method in speeding up the process of training an initial incapable agent to an ‘expert’ while guaranteeing or even improving the performance.

Flight data clustering for offline evaluation of real-time trajectory optimization framework

Real-time Trajectory Optimization (RTOP) is a machine learning-based flight path optimization framework that automatically performs in-flight re-planning continuously with the latest weather information. The framework leverages three core algorithms: (1) a supervised learning algorithm to predict winds, (2) an unsupervised learning algorithm to forecast areas of convective weather, and (3) a graph-based pathfinding algorithm to generate optimized flight trajectories. This research first proposes a methodology that uses an unsupervised learning-based clustering algorithm with the concept of Hausdorff distance to appropriately select representative flight cases to build up confidence in statistical analysis. Second, this research conducts an operational evaluation of the RTOP framework with the selected representative flight cases to highlight the statistical significance of simulation results and indicate the expected savings. The results show that optimized flight trajectories generated by the RTOP framework reduce the duration of the en-route phase up to 2% compared to the real-world flight trajectories in most cases.

Multi-IRS and Multi-UAV-Assisted MEC System for 5G/6G Networks: Efficient Joint Trajectory Optimization and Passive Beamforming Framework

This article presents a multi-intelligent reflecting surface (IRS)- and multi-unmanned aerial vehicle (UAV)-assisted mobile edge computing (MEC) system for 5G/6G networks. In the studied system, multiple UAVs are integrated for providing services to large-scale user equipment (UEs) with the help of multiple IRSs. This article aims to minimize the overall cost including energy consumption, completion time, and maintenance cost of UAVs by jointly optimizing the trajectories of UAVs and phase shifts of IRSs. When solving this problem, one has to count in mind the deployment of stop points (SPs) of UAVs, and consider the association among UEs, and UAVs (i.e., which UE will send data to which UAV at which SP), the order of SPs, and the phase shifts of IRSs. Therefore, traditional optimization techniques may not solve the above-mentioned problem in an efficient way. To tackle the above-mentioned problem, this article proposes an algorithm called TPaPBA that consists of four phases. The first phase optimizes the SPs’ deployment via using a differential evolution algorithm having variable population size. As a result, all the SPs of UAVs can be obtained. Then, the second phase optimizes the association among UEs, SPs, and UAVs. Specifically, TPaPBA first adopts a clustering algorithm to optimize the SPs-UAVs association, and then a close criterion is introduced to optimize UEs-SPs association. Subsequently, third phase adopts a low-complexity greedy algorithm to optimize the order of SPs for UAVs. Finally, the phase shifts of IRSs are optimized to enhance the data rate between UEs and UAVs. The simulation results of TPaPBA on ten instances having UEs ranging from 100 to 1000, reveals that TPaPBA has significantly improved the system performance contribution and outperforms other approaches in terms of reducing the overall cost of UAVs.

A data-driven trajectory optimization framework for terminal maneuvering area operations

The contradiction between air traffic capacity and demand constrains the development of the civil aviation industry. This paper proposes a Data-Driven Trajectory Optimization Framework for Terminal Maneuvering Area operations (DDTO-TMA) to enhance the capacity of Terminal Maneuvering Area (TMA). First, a Wasserstein-distance-based spectral clustering algorithm is applied to divide historical trajectories into several groups based on flight performance. Then, based on clustering results, a set of candidate Four-Dimensional Trajectories (4DTs) is created via flyable trajectories expansion. Finally, a combined algorithm with Mahalanobis-distance-based conflict detection and Pareto frontier determination is designed to identify optimal trajectories from candidate 4DTs in an efficient way. Two validations have been performed for Guangzhou Baiyun International Airport (ZGGG) TMA. The first validation evaluates the performance of the proposed DDTO-TMA. The results show that the DDTO-TMA can generate optimal trajectories that are not only of the interest of most stakeholders but also conflict-free. Besides, with the increase in the size of the historical trajectory set, the performance of DDTO-TMA gradually increases. The second validation estimates the improvement of a TMA operation after adopting DDTO-TMA. The results illustrate that, compared with the baseline, the proposed DDTO-TMA could enhance the arrival capacity by 30% without sacrificing stakeholders' interests. Furthermore, the proposed optimal trajectory generator can be easily transferred to different airports due to its data-driven characteristics.

Transition Flight Trajectory Optimization for a Flapping-Wing Micro Air Vehicle with Unsteady Vortex-Lattice Method

Flapping-wing micro air vehicles (FWMAVs) have the capability of performing various flight modes like birds and insects. Therefore, it is necessary to understand the various flight modes of FWMAVs in order to fully utilize the capability of the vehicle. The unique flight modes of FWMAVs can be studied through the trajectory optimization. This paper proposes a trajectory optimization framework of an FWMAV. A high-fidelity simulation model is included in the framework to sufficiently consider the complicated dynamics of the FWMAV. The unsteady aerodynamics are modeled with the unsteady panel method (UPM) and the unsteady vortex-lattice method (UVLM). The effect of wing inertia is also considered in the simulation model. In this study, transition flight trajectories are searched with the proposed framework. An optimal control problem is formulated for the transition flight from hovering to forward flight and transcribed to the parameter optimization problem with the direct shooting method. The cost function is defined as energy consumption. The same converged solution can be obtained with different initial guesses. The optimization results show that the FWMAV utilizes the pitch-up maneuver to increase altitude, although the forward speed is reduced. This pitch-up maneuver is performed more actively when the target velocity of transition is low, or the wind condition is favorable to acceleration.

Online environmentally adaptive trajectory planning for rotorcraft unmanned aerial vehicles

PurposeThis paper aims to propose an environmentally adaptive trajectory planning system considering the dynamic characteristics of unmanned aerial vehicles (UAVs) and the distance between obstacles and the UAV. The system generates a smooth and safe flight trajectory online.Design/methodology/approachFirst, the hybrid A* search method considering the dynamic characteristics of the quadrotor is used to find the collision-free initial trajectory. Then, environmentally adaptive velocity cost is designed for environment-adaptive trajectory optimization using environmental gradient data. The proposed method adaptively adjusts the autonomous flight speed of the UAV. Finally, the initial trajectory is applied to the multi-layered optimization framework to make it smooth and dynamically viable.FindingsThe feasibility of the designed system is validated by online flight experiments, which are in unknown, complex situations.Practical implicationsThe proposed trajectory planning system is integrated into a vision-based quadrotor platform. It is easily implementable onboard and computationally efficient.Originality/valueA hybrid A* path searching method is proposed to generate feasible motion primitives by dispersing the input space uniformly. The proposed method considers the control input of the UAV and the search time as the heuristic cost. Therefore, the proposed method can provide an initial path with the minimum flying time and energy loss that benefits trajectory optimization. The environmentally adaptive velocity cost is proposed to adaptively adjust the flight speed of the UAV using the distance between obstacles and the UAV. Furthermore, a multi-layered environmentally adaptive trajectory optimization framework is proposed to generate a smooth and safe trajectory.

Concurrent Trajectory Optimization and Aircraft Design for the Air Cargo Challenge Competition

A coupled aerostructural aircraft design and trajectory optimization framework is developed for the Air Cargo Challenge competition to maximize the expected score based on cargo carried, altitude achieved and distance traveled. Its modular architecture makes it easily adaptable to any problem where the performance depends not only on the design of the aircraft but also on its flight trajectory. It is based on OpenAeroStruct, an aerostructural solver that uses analytic derivatives for efficient gradient-based optimization. A trajectory optimization module using a collocation method is coupled with the option of using b-splines to increase computational efficiency together with an experimentally-based power decay model that accurately determines the aircraft propulsive response to control input depending on the battery discharge level. The optimization problem totaled 206 variables and 283 constraints and was solved in less than 7 h on a standard computer with 12% reduction when using b-splines for trajectory control variables. The results revealed the need to consider the multi-objective total score to account for the different score components and highlighted the importance of the payload level and chosen trajectory. The wing area should be increased within allowable limits to maximize payload capacity, climb to maximum target height should be the focus of the first 60 s of flight and full throttle should be avoided in cruise to reduce losses and extend flight distance. The framework proved to be a valuable tool for students to easily obtain guidelines for both the model aircraft design and control to maximize the competition score.