Optimal Trajectory Research Articles

Trajectories of work ability and associated work unit characteristics from pre-COVID to post-COVID pandemic period

ObjectivesTo identify trajectories of work ability from pre-COVID to post-COVID-19 pandemic period and to examine work unit characteristics associated with these trajectories.MethodsThe study population was a cohort of Finnish public sector employees (n=54 651) followed from 2016 until 2022. We used trajectory analysis to identify trajectories of work ability and multinomial regression to examine their associations with prepandemic work unit characteristics and pandemic-related changes at workplaces.ResultsWe identified three trajectories of work ability: (1) suboptimal work ability decreasing over time (12%); (2) relatively consistent good work ability (73%) and (3) consistent optimal work ability (15%). The strongest associations with belonging to the suboptimal work ability trajectory were found for employees in work units characterised by high job strain (OR 2.29, 95% CI 1.82 to 2.88), poor team climate (OR 0.74, 95% CI 0.64 to 0.86) and low organisational justice (OR 0.64, 95% CI 0.57 to 0.72) when compared with the most optimal trajectory. The least favourable work ability trajectory was also associated with team reorganisation (OR 1.22, 95% CI 1.04 to 1.44) and a low share of those working from home (OR 0.86, 95% CI 0.78 to 0.94) during the pandemic.ConclusionPrepandemic psychosocial risk factors and pandemic-induced changes at work were associated with poor and declining work ability during the COVID-19 pandemic. Employers and occupational health services should better identify and support vulnerable employees to enhance their work participation.

Machine-Learning Methods Estimating Flights’ Hidden Parameters for the Prediction of KPIs

Complex microscopic simulation models of strategic Air Traffic Management (ATM) performance assessment and decision-making are hindered by several factors. One of the most important is the existence of hidden parameters—such as aircraft take-off weight (TOW) and the selected cost index (CI)—which, if known, would allow for more effective performance modeling methodologies for assessing Key Performance Indicators (KPIs) at various levels of abstraction/detail, e.g., system-wide, or at the level of individual flights. This research proposes a data-driven methodology for the estimation of flights’ hidden parameters combining mechanistic and advanced Artificial Intelligence/Machine Learning (AI/ML) models. Aiming at microsimulation models, our goal is to study the effect of these estimations on the prediction of flights’ KPIs. In so doing, we propose a novel methodology according to which data-driven methods are trained given optimal trajectories (produced by mechanistic models) corresponding to known hidden parameter values, with the aim of predicting hidden parameters’ values of unseen trajectories. The results show that estimations of hidden parameters support the accurate prediction of KPIs regarding the efficiency of flights: fuel consumption, gate-to-gate time and distance flown.

Design and Optimization of Non-Coplanar Orbits for Orbital Photovoltaic Panel Cleaning Robots

Aiming at the problem that it is difficult for an orbital photovoltaic panel cleaning robot to span a large distance between photovoltaic panels, a method of designing and optimizing a non-coplanar orbit based on Bezier curves is proposed. Firstly, the robot’s motion law is analyzed to obtain trajectory data for a single work cycle. Then, Bezier curves are utilized for trajectory design to ensure a smooth transition during the spanning motion phase. Thirdly, with the average value of the minimum distance between the Bezier curve and the point set data of the spanning motion phase as the optimization objective function, the nonlinear planning based on the SQP algorithm was adopted for the optimization of the upper and lower trajectories. Finally, the results of the case calculations indicate that the standard deviation of the optimized upper and lower trajectories was reduced by 35.63% and 40.57%, respectively. Additionally, the ADAMS simulation validation demonstrates that the trajectory errors of the four wheels decreased by a maximum of 8.79 mm, 23.78 mm, 10.11 mm, and 14.97 mm, respectively, thereby confirming the effectiveness of the trajectory optimization.

Collaborative control framework at isolated signalized intersections under the mixed connected automated vehicles environment

AbstractThis study proposes a collaborative control framework under the mixed traffic environment of connected and automated vehicles and connected human‐driven vehicles, which can simultaneously optimize the signal timing, lane settings, and vehicle trajectories at isolated intersections. Initially, considering the dynamics of traffic demand and incompatible signals, we analyze the vehicle delay of each lane. Based on the delay analysis, the spatiotemporal resource collaborative optimization model of lane setting and signal timing is established to minimize the average delay. Subsequently, in the buffer zone, a graph‐theoretic‐based sorting and platooning model provides a clear and concise representation of the transformation process from the initial state to the target state of vehicles, enabling the platoon formation. Additionally, trajectory optimization is integrated into the collaborative control framework by the optimal control model and car‐following model in the passing zone. Simulation experiments and sensitivity analyses demonstrate the effectiveness of the proposed framework in reducing average vehicle delay, improving fuel consumption, and coping with changing traffic demand at intersections.

Trajectory shaping guidance for impact angle control of planetary hopping robots

This paper presents a novel optimal trajectory-shaping control concept for a planetary hopping robot. The hopping robot suffers from uncontrolled in-flight and undesired after-landing motions, leading to a position drift at landing. The proposed concept thrives on the Generalized Vector Explicit (GENEX) guidance, which can generate and shape the optimal trajectory and satisfy the end-point constraints like the impact angle of the velocity vector. The proposed concept is used for a thruster-based hopping robot, which achieves a range of impact angles, reduces the position drift at landing due to the undesired in-flight and after-landing motions, and handles the error in initial hopping angles. The proposed approach’s conceptual realization is illustrated by lateral acceleration generated using thruster orientation control. Extensive simulations are carried out on horizontal and sloped surfaces with different initial and impact angle conditions to demonstrate the effect of impact angle on the position drift error and the viability of the proposed approach.

Resource Allocation in UAV-D2D Networks: A Scalable Heterogeneous Multi-Agent Deep Reinforcement Learning Approach

In unmanned aerial vehicle (UAV)-assisted device-to-device (D2D) caching networks, the uncertainty from unpredictable content demands and variable user positions poses a significant challenge for traditional optimization methods, often making them impractical. Multi-agent deep reinforcement learning (MADRL) offers significant advantages in optimizing multi-agent system decisions and serves as an effective and practical alternative. However, its application in large-scale dynamic environments is severely limited by the curse of dimensionality and communication overhead. To resolve this problem, we develop a scalable heterogeneous multi-agent mean-field actor-critic (SH-MAMFAC) framework. The framework treats ground users (GUs) and UAVs as distinct agents and designs cooperative rewards to convert the resource allocation problem into a fully cooperative game, enhancing global network performance. We also implement a mixed-action mapping strategy to handle discrete and continuous action spaces. A mean-field MADRL framework is introduced to minimize individual agent training loads while enhancing total cache hit probability (CHP). The simulation results show that our algorithm improves CHP and reduces transmission delay. A comparative analysis with existing mainstream deep reinforcement learning (DRL) algorithms shows that SH-MAMFAC significantly reduces training time and maintains high CHP as GU count grows. Additionally, by comparing with SH-MAMFAC variants that do not include trajectory optimization or power control, the proposed joint design scheme significantly reduces transmission delay.

A Hierarchical Planning Method for AUV Search Tasks Based on the Snake Optimization Algorithm

In a complex and dynamic battlefield environment, enabling autonomous underwater vehicles (AUVs) to reach dynamic targets in the shortest possible time using global autonomous planning is a key issue affecting the completion of search tasks. In this study, ahierarchicalAUV task planning method that uses a combination of hierarchical programming and a snake optimization algorithm is proposed for two typical cases where the platform can provide initial target information. This method decomposes the search task problem into a three-level programming problem, with the outer task planning goal of achieving the shortest encounter time between AUV and dynamic targets; the goal of task planning in the middle layer is to achieve the shortest actual navigation time for AUVs under different operating conditions; and the internal task planning is responsible for considering the comprehensive trajectory optimization under navigation constraints such as threat zone, path length, and path smoothness. The snake optimization algorithm was used for solving each layer of task planning. The feasibility of the proposed method was verified through simulation experiments of AUV search tasks under two types of initial target information conditions. The simulation results show that this method can achieve task planning for AUV searching for dynamic targets under various constraint conditions, optimize the encounter time between AUV and dynamic targets, and have strong engineering practical value. It has certain reference significance for task planning problems similar to underwater unmanned equipment.

Optimal Periodic Control of Unmanned Aerial Vehicles Based on Fourier Integral Pseudospectral and Edge-Detection Methods

The endurance of unmanned aerial vehicles (UAVs) is a critical factor in expanding the scope of their applications. Extended flight times enable UAVs to undertake longer missions, cover larger areas and perform tasks such as persistent surveillance, data collection and search and rescue operations. Optimal trajectory planning is a cost-effective method to significantly enhance UAV endurance and performance by minimizing fuel consumption. This study introduces a novel numerical optimization framework to maximize UAV endurance. Specifically, we address the problem of determining optimal thrust and cruise angle of attack for a UAV in 2D space under specific initial, periodic and boundary conditions. By normalizing the free final time optimal control problem and employing Fourier collocation and quadrature, we transform it into a nonlinear programming problem. A key contribution of this work is accurately detecting and reconstructing the thrust history, including jump discontinuities, directly from Fourier pseudospectral data without smoothing techniques. The proposed method outperforms existing approaches in solving the periodic energy-optimal path planning problem for UAVs, as it effectively reconstructs the bang-bang thrust profile, facilitating rapid and efficient thrust adjustments essential for various flight maneuvers. Furthermore, the algorithm aligns with the UAV model, ensuring seamless integration into real-world control systems. The method’s independence from prediction horizon length, due to the use of Fourier collocation on the normalized interval [Formula: see text], is a notable advantage. This characteristic offers potential for future applications in various fields involving nonsmooth optimal control problems. This research generally provides a valuable tool for researchers and engineers working on UAV design and operation, paving the way for more efficient and effective UAV systems.

A Comprehensive Review of Artificial Intelligence and Machine Learning in Control Theory

Abstract: Traditional control methods, such as proportional-integral-derivative (PID) controllers and linear-quadratic regulators (LQRs), have proven effective for linear and well-modeled systems. However, these methods often perform poorly in nonlinear, complex and dynamic environments. The paper aims to investigate the modern control systems by integrating artificial intelligence (AI) techniques, such as machine learning (ML), reinforcement learning (RL), deep learning, and fuzzy logic, to enhance their adaptive, robust, and predictive capabilities. And it reviews the literature and analyzes AI integration in control systems. The proposed strategies include supervised learning for trajectory optimization and fault detection, reinforcement learning for optimal control in dynamic environments, neural networks for complex nonlinear function approximation, and fuzzy logic for handling uncertainty and imprecise inputs. AI techniques significantly enhance the ability to tackle nonlinear problems and dynamic changes, demonstrating superior performance in applications like self-driving cars adapting to various road conditions and optimal energy distribution in smart grids. Despite the challenges of computational complexity, scalability, and the safety and reliability in the implementation of interpretable AI models, this paper suggests that hybrid approaches combining traditional control and AI techniques, along with the evolution of interpretable AI and convergence with quantum control, hold great promise for advancing AI-driven control systems.

Intelligent Vehicle Trajectory Tracking Based on Horizontal and Vertical Integrated Control

To address the common issues of accuracy and stability in trajectory tracking tasks for autonomous vehicles, this study proposes an innovative composite control strategy that skillfully integrates lateral and longitudinal dynamic control. For lateral control, model predictive control (MPC) theory is introduced to compute the front wheel steering angle that ensures optimal trajectory following. On the longitudinal control level, the vehicle’s acceleration and deceleration logic are finely tuned to ensure precise adherence to the preset speed trajectory. More importantly, by deeply integrating these two control methods, the comprehensive coordination of the vehicle’s lateral and longitudinal movements is achieved. To validate the effectiveness of the proposed control strategy, simulations were conducted using the CarSim and MATLAB/Simulink platforms. The analysis of the simulation results confirms that the proposed method effectively improves speed tracking stability and significantly enhances path tracking accuracy and overall driving stability.

Optimizing Solid Rocket Missile Trajectories: A Hybrid Approach Using an Evolutionary Algorithm and Machine Learning

This paper introduces a novel approach for modeling and optimizing the trajectory and behavior of small solid rocket missiles. The proposed framework integrates a six-degree-of-freedom (6DoF) simulation environment experimentally tuned for accuracy, with a combination of genetic algorithms (GAs) and machine learning (ML) to enhance the performance of the missile path. In the initial phase, a GA is employed to optimize the missile’s trajectory for efficient target acquisition, defining key launch parameters such as the ramp angle and lateral maneuver force to minimize positional errors and to ensure effective target engagement. Following trajectory optimization, the derived data are used to train an ML model that predicts setup parameters, significantly reducing computational costs and time. This close integration enables real-time adjustments for acquiring moving targets, thereby improving accuracy and minimizing maneuvering costs. This study also explores the application of fluidic thrust vectoring for small rockets, providing an innovative solution to enhance maneuverability and control, especially at low speeds. The proposed framework was validated using experimental launch data from the Icarus Team. The methodology offers a robust and cost-effective solution for precision targeting and improved maneuverability in aerospace and defense contexts.

Multitask-Based Anti-Collision Trajectory Planning of Redundant Manipulators

During performing multiple tasks of a redundant manipulator, the obstacles affect the sequential order of task areas and the joint trajectories. The end-effector is constrained to visit multiple task areas with an optimal anti-collision path, while the joints are required to move smoothly and avoid predefined obstacles. A special encoding genetic algorithm (SEGA) is proposed for multitask-based anti-collision trajectory planning. Firstly, the spatial occupancy relationship between obstacles and manipulator is developed utilizing the theory of spherical enclosing box and spatial superposition. The obstacles are detected according to the relative position relationship between linear segments and spheres. Secondly, each joint trajectory between adjacent task areas is depicted with a sixth-degree polynomial. Additionally, each joint trajectory is improved via optimizing the unknown six-order coefficient. By searching for optimal sequential order of task areas, optimal collision detection results, and optimal joint trajectories, the multitask-based anti-collision trajectory planning problem is transformed into a parameter optimization problem. In SEGA, the cost function consists of two parts, including the end-effector path length and the variation of joint angles. Moreover, each chromosome consists of three categories of genes, including the sequential order of task areas, the sequential order of joint configurations corresponding to task areas, and the unknown coefficients for anti-collision joint trajectories. Finally, numerical simulations are carried out to verify the proposed method.

Optimizing rural waste management: Leveraging high-resolution remote sensing and GIS for efficient collection and routing

Accurate assessment of distribution patterns and dynamic insights into rural populations is pivotal for comprehending domestic waste generation, recycling, and transportation in rural territories. Given that the dispersion of rural inhabitants exhibits minimal variation and maintains stability, this research endeavors to establish a pragmatic model for rural domestic waste collection and routing, leveraging the capabilities of very high-resolution remote sensing combined with geographic information system (GIS) techniques. Specifically, the Dilated LinkNet model was employed to discern features such as buildings, roads, water bodies, farmlands, and forests from the high-resolution remote sensing imagery. A novel multiple K-means clustering approach was devised for building segmentation. Within these clusters, an assortment of spatial regulations and evaluations facilitated the judicious selection of environmentally-conscious waste collection sites (WCSs). The Pointer Network, augmented with reinforcement learning, executed a traveling salesman analysis on these chosen WCSs, yielding the optimal collection trajectory. Validated in Huangtu Town, a quintessential rural region in China, our model manifested superior recognition precision, recording IoU accuracies of 0.902, 0.926, 0.933, 0.891, and 0.849 for buildings, roads, water bodies, farmlands, and forests respectively. Notably, when compared to our field survey data, the optimized daily collection route in a rural context decreased from 256.40 km before optimization to 140.44 km, reflecting a substantial reduction of 45.23% in total distance. This study furnishes an effective model that relies solely on information from remote-sensing images for efficient rural waste collection and extends invaluable insights to planners and administrators in the realm of rural and township waste management.

A Hybrid ARO Algorithm and Key Point Retention Strategy Trajectory Optimization for UAV Path Planning

Path planning is a fundamental research issue for enabling autonomous flight in unmanned aerial vehicles (UAVs). An effective path planning algorithm can greatly improve the operational efficiency of UAVs in complex environments like urban and mountainous areas, thus offering more extensive coverage for various tasks. However, existing path planning algorithms often encounter problems such as high computational costs and a tendency to become trapped in local optima in complex 3D environments with multiple constraints. To tackle these problems, this paper introduces a hybrid multi-strategy artificial rabbits optimization (HARO) for efficient and stable UAV path planning in complex environments. To realistically simulate complex scenarios, we introduce spherical and cylindrical obstacle models. The HARO algorithm balances exploration and exploitation phases using a dual exploration switching strategy and a population migration memory mechanism, enhancing search performance and avoiding local optima. Additionally, a key point retention trajectory optimization strategy is proposed to reduce redundant path points, thus lowering flight costs. Experimental results confirm the HARO algorithm’s superior search performance, planning more efficient and stable paths in complex environments. The key point retention strategy effectively reduces flight costs during trajectory optimization, thereby enhancing adaptability.

Center of mass kinematic reconstruction during steady-state walking using optimized template models.

Template models, such as the Bipedal Spring-Loaded Inverted Pendulum and the Virtual Pivot Point, have been widely used as low-dimensional representations of the complex dynamics in legged locomotion. Despite their ability to qualitatively match human walking characteristics like M-shaped ground reaction force (GRF) profiles, they often exhibit discrepancies when compared to experimental data, notably in overestimating vertical center of mass (CoM) displacement and underestimating gait event timings (touchdown/ liftoff). This paper hypothesizes that the constant leg stiffness of these models explains the majority of these discrepancies. The study systematically investigates the impact of stiffness variations on the fidelity of model fittings to human data, where an optimization framework is employed to identify optimal leg stiffness trajectories. The study also quantifies the effects of stiffness variations on salient characteristics of human walking (GRF profiles and gait event timing). The optimization framework was applied to 24 subjects walking at 40% to 145% preferred walking speed (PWS). The findings reveal that despite only modifying ground forces in one direction, variable leg stiffness models exhibited a >80% reduction in CoM error across both the B-SLIP and VPP models, while also improving prediction of human GRF profiles. However, the accuracy of gait event timing did not consistently show improvement across all conditions. The resulting stiffness profiles mimic walking characteristics of ankle push-off during double support and reduced CoM vaulting during single support.

An actuator space optimal kinematic path tracking framework for tendon-driven continuum robots: Theory, algorithm and validation

Path tracking of continuum robots is a fundamental and crucial problem across various applications. In this article, we address this problem by focussing on three aspects. Firstly, we propose an efficient multi-solution inverse kinematics solver for three-section constant curvature robots by bridging the theoretical reduction and the numerical correction. Secondly, we derive a linear tendon-driven actuation model, establishing the connection between the robot configuration space and the actuator space. With this model, we achieve optimal distance planning and optimal time allocation considering the constraints of actuator velocity and acceleration, generating a continuous trajectory directly in the actuator space. Finally, we present our kinematic path tracking framework, which includes offline optimal trajectory planning and online feedforward and feedback control. Experiments are conducted both in simulations and in the real world on our three-section tendon-driven continuum robot. The experiments validate the increased efficiency, higher success rates, and accessibility of multiple solutions offered by our inverse kinematics solver, as well as the optimality in distance planning and time allocation in the actuator space. Performance improvements in tracking accuracy are demonstrated through comparative experiments and the application of our framework in path tracking tasks with obstacles is presented through a case study.

BWSAR: A Single-Drone Search-and-Rescue Methodology Leveraging 5G-NR Beam Sweeping Technologies for Victim Localization

Drones integrated with 5G New Radio (NR) base stations have emerged as a promising solution for efficient victim search and localization in emergency zones where cellular networks are disrupted by natural disasters. Traditional approaches relying solely on uplink Sounding Reference Signal (SRS) for localization face limitations due to User Equipment (UE) power constraints. To overcome this, our paper introduces BWSAR, a novel three-stage Search-and-Rescue (SAR) methodology leveraging 5G-NR beam sweeping technologies. BWSAR utilizes downlink Synchronization Signal Block (SSB) for coarse-grained direction estimation, guiding the drone towards potential victim locations. Subsequently, finer-grained beam sweeping with Positioning Reference Signal (PRS) is employed within the identified direction, enabling precise three-dimensional UE coordinate estimation. Furthermore, we propose a trajectory optimization algorithm to expedite the drone’s navigation to emergency areas. Simulation results underscore BWSAR’s efficacy in reducing positioning errors and completing SAR missions swiftly, within minutes.

Multi-objective optimal trajectory planning for manipulators based on CMOSPBO

Feasible, smooth, and time-jerk optimal trajectory is essential for manipulators utilized in manufacturing process. A novel technique to generate trajectories in the joint space for robotic manipulators based on quintic B-spline and constrained multi-objective student psychology based optimization (CMOSPBO) is proposed in this paper. In order to obtain the optimal trajectories, two objective functions including the total travelling time and the integral of the squared jerk along the whole trajectories are considered. The whole trajectories are interpolated by quintic B-spline and then optimized by CMOSPBO, while taking into account kinematic constraints of velocity, acceleration, and jerk. CMOSPBO mainly includes improved student psychology based optimization, archive management, and an adaptive ε-constraint handling method. Lévy flights and differential mutation are adopted to enhance the global exploration capacity of the improved SPBO. The ε value is varied with iterations and feasible solutions to prevent the premature convergence of CMOSPBO. Solution density estimation corresponding to the solution distribution in decision space and objective space is proposed to increase the diversity of solutions. The experimental results show that CMOSPBO outperforms than SQP, and NSGA-II in terms of the motion efficiency and jerk. The comparison results demonstrate the effectiveness of the proposed method to generate time-jerk optimal and jerk-continuous trajectories for manipulators.

Observer-based fuzzy T–S control with an estimation error guarantee for MPPT of a photovoltaic battery charger in partial shade conditions

To improve the efficiency and performance of a photovoltaic system (PV) an observer-based fuzzy controller design methodology is provided in the study. The desired controller is achieved by employing a combination of linear matrix inequalities (LMIs). The system consists of a photovoltaic generator (PVG) connected to a boost converter. A battery is linked to the boost converter to stock additional energy for further use. A fuzzy controller based on a T–S fuzzy type observer that guarantees a predefined L2 performance is suggested to achieve maximum power point tracking (MPPT) even under changing weather conditions. An optimal trajectory should be tracked to ensure maximum power operation. For this aim, a specific reference fuzzy model is proposed to create the aimed trajectories. Using this method, the system dynamics are precisely reproduced over a large range of operations. The whole T–S fuzzy methodology, suggested in this paper, aims to ensure the most efficient energy recovery to recharge a battery under partially shaded conditions, resulting in high system efficiency. The proposed method is simulated with MATLAB/SIMULINK and the simulation results, with realistic reference trajectories, are driven while taking into account climate variations. The analysis of these simulations, along with a comparison with two other commonly used approaches, led to the conclusion that the suggested strategy succeeded in reducing the tracking time, as well as eliminating the oscillation that often occurs around maximum power point (MPP).

The isoperimetric problem for convex hulls and the large deviations rate functionals of random walks

We study the asymptotic behaviour of the most likely trajectories of a planar random walk that result in large deviations of the area of their convex hull. If the Laplace transform of the increments is finite, such a scaled limit trajectory h solves the inhomogeneous anisotropic isoperimetric problem for the convex hull, where the usual length of h is replaced by the large deviations rate functional ∫01I(h′(t))dt and I is the rate function of the increments. Assuming that the distribution of increments is not supported on a half-plane, we show that the optimal trajectories are convex and satisfy the Euler–Lagrange equation, which we solve explicitly for every I. The shape of these trajectories resembles the optimizers in the isoperimetric inequality for the Minkowski plane, found by Busemann (1947).