Trajectory Optimization Method Research Articles

Uncertainty Aware Forward and Inverse Kinematics for Tendon-Driven Continuum Robots via Mixture Density Networks

Tendon-driven continuum robot kinematic models are frequently computationally expensive, inaccurate due to unmodeled effects, or both. In particular, unmodeled effects produce uncertainties that arise during the robot’s operation that lead to variability in the resulting geometry. We propose a novel solution to these issues through the development of a Gaussian mixture kinematic model. We train a mixture density network to output a Gaussian mixture model representation of the robot geometry given the current tendon displacements. This model computes a probability distribution that is more representative of the true distribution of geometries at a given configuration than a model that outputs a single geometry, while also reducing the computation time. We demonstrate uses of this model through both a trajectory optimization method that explicitly reasons about the workspace uncertainty to minimize the probability of collision and an inverse kinematics method that maximizes the likelihood of occupying a desired geometry.

Research on Intelligent Optimization of Wellbore Trajectory in Complex Formation

Borehole trajectory optimization is a key issue in oil and gas drilling engineering. The traditional wellbore trajectory design method faces great challenges in optimizing the trajectory length and complexity, and it is difficult to meet the actual engineering requirements. In this paper, the three-stage wellbore trajectory optimization problem is studied, and a multi-objective optimization model including two objective functions of trajectory length and trajectory complexity is constructed. In this paper, an improved multi-objective particle swarm optimization algorithm is proposed, which combines the clustering strategy to improve the diversity of solutions, and enhances the local search ability and global convergence performance of the algorithm through the elite learning strategy. In order to verify the performance of the algorithm, comparative experiments were carried out using classical multi-objective benchmark functions. The results showed that the improved algorithm is superior to the traditional method in terms of diversity and convergence of solutions. Finally, the proposed algorithm was applied to the actual three-stage wellbore trajectory optimization problem. In summary, the research results of this paper provide theoretical support and engineering practice methods for wellbore trajectory optimization, and serve as an important reference for further improving the efficiency and quality of wellbore trajectory design.

Reinforcement learning‐based trajectory planning for continuous digging of excavator working devices in trenching tasks

AbstractThis paper addresses the challenge of real‐time, continuous trajectory planning for autonomous excavation. A hybrid method combining particle swarm optimization (PSO) and reinforcement learning (RL) is proposed. First, three types of excavation trajectories are defined for different geometric shapes of the digging area. Then, an excavation trajectory optimization method based on the PSO algorithm is established, resulting in optimal trajectories, the sensitive parameters, and the corresponding variation ranges. Second, an RL model is built, and the optimization results obtained offline are used as training samples. The RL‐based method can be applied for continuous digging tasks, which is beneficial for improving the overall efficiency of the autonomous operation of the excavator. Finally, simulation experiments were conducted in four distinct conditions. The results demonstrate that the proposed method effectively accomplishes excavation tasks, with trajectory generation completed within 0.5 s. Comprehensive performance metrics remained below 0.14, and the excavation rate exceeded 92%, surpassing or matching the performance of the optimization‐based method and PINN‐based method. Moreover, the proposed method produced consistently balanced trajectory performance across all sub‐tasks. These results underline the method's effectiveness in achieving real‐time, multi‐objective, and continuous trajectory planning for autonomous excavators.

SDA-RRT*Connect: A Path Planning and Trajectory Optimization Method for Robotic Manipulators in Industrial Scenes with Frame Obstacles

The trajectory planning of manipulators plays a crucial role in industrial applications. This importance is particularly pronounced when manipulators operate in environments filled with obstacles, where devising paths to navigate around obstacles becomes a pressing concern. This study focuses on the environment of frame obstacles in industrial scenes. At present, many obstacle avoidance trajectory planning algorithms struggle to strike a balance among trajectory length, generation time, and algorithm complexity. This study aims to generate path points for manipulators in an environment with obstacles, and the trajectory for these manipulators is planned. The search direction adaptive RRT*Connect (SDA-RRT*Connect) method is proposed to address this problem, which adaptively adjusts the search direction during the search process of RRT*Connect. In addition, we design a path process method to reduce the length of the path and increase its smoothness. As shown in experiments, the proposed method shows improved performances with respect to path length, algorithm complexity, and generation time, compared to traditional path planning methods. On average, the configuration space’s path length and the time of generation are reduced by 38.7% and 57.4%, respectively. Furthermore, the polynomial curve trajectory of the manipulator was planned via a PSO algorithm, which optimized the running time of the manipulator. According to the experimental results, the proposed method costs less time during the manipulator’s traveling process with respect to other comparative methods. The average reduction in running time is 45.2%.

Online Trajectory Optimization of an ASV Based on an Improved RBFNN

Optimization based on conventional neural networks can only guarantee calculation speed. However, the accuracy of network prediction is also a key index in online trajectory optimization. This paper proposes a novel online trajectory optimization approach based on an Improved Radial Basis Function Neural Network (IRBFNN). First, multiple optimal trajectories for different variations of Air-Breathing Supersonic Vehicles (ASVs) are generated, considering attitude, and collected as the dataset. Then, an IRBFNN is trained to predict trajectories online with the above dataset, in which an enhanced loss function is introduced to improve prediction accuracy. Finally, numerical simulations are presented to demonstrate the feasibility and superiority of the proposed online trajectory optimization method. The open-source code of the proposed method is shared in the form of a link to showcase its implementation.

Multi-Objective Trajectory Optimization for Rigid-Flexible Coupling Spray-Painting Robot Integrated with Coating Process Constraints

Robot-automated spraying is widely used in various fields, such as the automotive, metalworking, furniture, and aerospace industries. Spraying quality is influenced by multiple factors, including robot speed, acceleration, end-effector trajectory, and spraying process constraints. To achieve high-quality spraying under the influence of multiple factors, this study proposes a multi-objective optimization method for the spraying trajectory that integrates spraying process constraints into the optimization process. First, a 7-degree-of-freedom rigid-flexible coupling serial spray painting robot system is introduced, which includes a motion decoupling mechanism and a tension amplification mechanism. Subsequently, a paint deposition model for the spray gun was established, and the influence of process constraints on spraying quality was analyzed. Trajectory planning for the spray painting robot, based on the septic B-spline interpolation method, was then performed. Based on this foundation, objective functions and constraint equations for spraying trajectory optimization were established. A multi-objective trajectory optimization method for spraying by the robot is proposed based on the NSGA-II, which integrates the spraying process constraints. Finally, a prototype system of a 7-degree-of-freedom rigid-flexible coupling serial spray painting robot was constructed. Simulations and spraying experiments were conducted to verify the effectiveness of the proposed multi-objective trajectory optimization method. This paper presents a multi-objective optimization method for the spraying trajectory of a robot. In the proposed method, the optimized spraying trajectory is generated with the spraying process as the constraint and time, energy consumption, and impact during the spraying operation of the robot as the optimization objectives.

Granularity Optimization of Travel Trajectory Based on Node2vec: A Case Study on Urban Travel Time Prediction

Intersections are known to cause significant changes in traffic states. However, existing link-level trajectory optimization methods often overlook intersection information, making it challenging to preserve key traffic state features during the optimization process. To address this limitation, a novel approach is proposed that integrates node2vec and K-means algorithms. First, the role of intersections in linking road segments is considered. The node2vec algorithm is employed to capture the deep spatial similarity between links while weakening the adjacency relationship between links before and after intersections. This process generates feature representations for each link. Subsequently, clustering centers are initialized at the intersections, and K-means clustering is applied based on these link feature representations. Through this method, consecutive links within a trajectory that belong to the same cluster are merged, thus optimizing the granularity of the trajectory. Finally, experimental analysis and validation are conducted using link-level travel trajectory data from Shenzhen. The results demonstrate that, under optimal conditions, the mean absolute error (MAE), the mean absolute percentage error (MAPE), and the root mean square error (RMSE) values are reduced by 8.91%, 9.44%, and 8.96%, respectively, while computational efficiency is increased by 30.08%. The proposed trajectory granularity optimization method, which accounts for the existence of intersections, not only effectively retains the key traffic state features from the original trajectory but also significantly reduces training time while improving the model’s prediction accuracy.

Optimization Method for the Attack Trajectory of Loitering Munitions Based on Damage Pre-assessment

Abstract In order to take into account the traditional terminal damage research while designing the trajectory of loitering munitions, this paper deduces a quantitative method which takes the detonation decision of loitering munitions as the input and outputs the damage effect on the power system of the target vehicle. A two-layer optimization model aiming at improving the damage effect and reducing the trajectory length is established, and a trajectory optimization method based on genetic algorithm is designed. The results of numerical simulation show that this optimization method can effectively and stably improve the damage effect of loitering munitions on the power system of the target vehicle, and the genetic algorithm can quickly converge to obtain the optimal trajectory solution. The work contributes to the application of terminal damage research in the overall design of loitering munitions and lays a good foundation for promoting the intelligent damage research of loitering munitions.

A Physics-Informed Indirect Method for Trajectory Optimization

A Physics-Informed Indirect Method for Trajectory Optimization

On Transforming Reinforcement Learning With Transformers: The Development Trajectory.

Transformers, originally devised for natural language processing (NLP), have also produced significant successes in computer vision (CV). Due to their strong expression power, researchers are investigating ways to deploy transformers for reinforcement learning (RL), and transformer-based models have manifested their potential in representative RL benchmarks. In this paper, we collect and dissect recent advances concerning the transformation of RL with transformers (transformer-based RL (TRL)) to explore the development trajectory and future trends of this field. We group the existing developments into two categories: architecture enhancements and trajectory optimizations, and examine the main applications of TRL in robotic manipulation, text-based games (TBGs), navigation, and autonomous driving. Architecture enhancement methods consider how to apply the powerful transformer structure to RL problems under the traditional RL framework, facilitating more precise modeling of agents and environments compared to traditional deep RL techniques. However, these methods are still limited by the inherent defects of traditional RL algorithms, such as bootstrapping and the "deadly triad". Trajectory optimization methods treat RL problems as sequence modeling problems and train a joint state-action model over entire trajectories under the behavior cloning framework; such approaches are able to extract policies from static datasets and fully use the long-sequence modeling capabilities of transformers. Given these advancements, the limitations and challenges in TRL are reviewed and proposals regarding future research directions are discussed. We hope that this survey can provide a detailed introduction to TRL and motivate future research in this rapidly developing field.

Optimizing Well Trajectories for Enhanced Oil Production in Naturally Fractured Reservoirs: Integrating Particle Swarm Optimization with an Innovative Semi-Analytical Model Framework

Summary Well trajectory optimization is a crucial component in the drilling engineering of naturally fractured reservoirs. The complex heterogeneity and anisotropy of such reservoirs significantly affect the pressure drop distribution within the well and, consequently, the oil well’s output, impacting the economic benefits of the well. Therefore, optimizing the well segment trajectory is key to efficient reservoir development. However, traditional well trajectory optimization methods primarily focus on geological structures and drilling engineering costs, often overlooking future production benefits of the oil well. This paper proposes a new method that first establishes a semi-analytical production prediction model capable of describing complex well trajectories. Although the semi-analytical model has unique advantages in well trajectory description, it typically treats the reservoir as a homogeneous entity, which complicates handling complex reservoir characteristics. To overcome this limitation, we combined optimization algorithms and neural networks to construct a framework for addressing reservoir heterogeneity (Semianalytical Model Framework for Unconventional Wells in Heterogeneous Reservoirs, USAMF-HR), enhancing the semi-analytical model’s ability to describe reservoir heterogeneity. Building on this framework, we applied the particle swarm optimization (PSO) algorithm and introduced constraints on the rationalization of initial well trajectories, as well as limits on particle movement speed and displacement, with the maximization of net present value (NPV) as the objective function, to optimize well trajectory coordinates. Through specific case analysis, the reasonableness and practicality of this method have been verified. The results show that this method can quickly and effectively plan the optimal well trajectory, significantly increasing productivity while reducing costs.

Flight trajectory optimization study of a variable-cycle turbine-based combined cycle engine hypersonic vehicle based on airframe/engine integration

Abstract To investigate the optimal flight trajectory for hypersonic vehicle and Turbine-Based Combined Cycle (TBCC) engine to enhance mission efficacy, a performance calculation model of a variable-cycle TBCC engine is developed utilizing the method of airframe/engine integrated performance analysis. Employing the Radau pseudospectral method for trajectory optimization, the study of the hypersonic vehicle involves the angle of attack, the scramjet engine equivalence ratio, and the core driven fan stage (CDFS) stator vane angle as control variables. Two optimization scenarios were considered: minimizing climb time and maximizing range. The findings indicate that by optimally adjusting the angle of attack and the scramjet engine’s equivalence ratio, the vehicle’s climb time can be reduced by up to 33.68 %, and the total flight duration by 8.07 %. Moreover, optimizing these variables, along with CDFS stator vane angle, can decrease fuel consumption during climb and potentially extend cruising distance by 8.56 %, increasing overall range by 3.63 %.

Implementations of the Universal Birkhoff Theory for Fast Trajectory Optimization

This is Part II of a two-part paper. Part I presented a universal Birkhoff theory for fast and accurate trajectory optimization. The theory rested on two main hypotheses. In this paper, it is shown that if the computational grid is selected from any one of the Legendre and Chebyshev families of node points, be it Lobatto, Radau, or Gauss, then the resulting collection of trajectory optimization methods satisfies the hypotheses required for the universal Birkhoff theory to hold. All of these grid points can be generated at an O(1) computational speed. Furthermore, all Birkhoff-generated solutions can be tested for optimality by a joint application of Pontryagin’s- and covector-mapping principles, where the latter was developed in Part I. More importantly, the optimality checks can be performed without resorting to an indirect method or even explicitly producing the totality of necessary conditions that result from an application of Pontryagin’s principle. Numerical problems are solved to illustrate all these ideas in addition to demonstrating near-exponential rates of convergence. The examples are chosen to particularly highlight three practically useful features of Birkhoff methods: 1) bang-bang optimal controls can be produced without suffering any Gibbs phenomenon, 2) discontinuous and even Dirac delta covector trajectories can be well approximated, and 3) extremal solutions over dense grids can be computed in a stable and efficient manner.

Kinematics modeling and trajectory optimization for precision grinding of variable-parameter helical grooves

End mills with variable helix angles in a certain range can suppress the cutting vibration, and the change of the core radius can improve the cutting rigidity and realize the best match between the rigidity and the chip removal performance. However, the existing process cannot accurately realize the continuous variable helix angle along the cutting edge. Moreover, the change in helix angle and core radius increases the difficulty of calculating the grinding trajectory and makes it difficult to control the rake angle accurately, and that results in the performance of this end mill cannot be accurately guaranteed. Therefore, this paper proposed a kinematics modeling and trajectory optimization method for the precision grinding of variable-parameter helical grooves. Firstly, a general grinding kinematics model is established by geometric analysis. Secondly, with the rake angle, helix angle, and core radius as constraints, models are constructed to solve the location and direction parameters of the grinding wheel. Then, the calculation and optimization method of the grinding trajectory for variable-parameter helical grooves is developed. Finally, the experimental verification is carried out and the results show that the maximum rake angle error is 0.09°, the maximum helix angle error is 0.08°, and the maximum core radius error is 0.053 mm. It indicates the grinding kinematics model and the trajectory optimization are correct. This process can also be used to grind complex helical grooves on custom cutting tools such as drills and screw taps.

Dynamic Control Method for CAV-Shared Lanes at Intersections in Mixed Traffic Flow

The existing signal control methods for mixed traffic related to connected automated vehicles (CAVs) and connected human-driven vehicles (CHVs) at intersections fail to tap the traffic potential of CAV-dedicated lanes. Accordingly, a dynamic allocation method of CAV-shared lanes is proposed, and the method of traffic flow scheduling and CAV trajectory optimization for multilane intersections with CAV-shared lanes is constructed to improve the traffic performance. The simulation results show that the optimization strategy proposed in this study can reduce the average delay at the intersection to varying degrees compared with the control strategy, using (a) the dynamic CAV-dedicated lane allocation method and (b) the shared-phase dedicated-lane method. Although the stops of CAVs will increase, the time utilization rate of most approach lanes is considerably improved, particularly CAV-shared lanes that can effectively improve the intersection performance. Further analysis shows that the number of CAV-shared lanes is closely dependent on the CAV penetration rate. The method proposed in this study is suitable for multilane intersections with a high CAV penetration rate.

Optimization and Control Strategies for Mechanical Vehicle Trajectory Research

With the rapid advancement of contemporary transportation and automation technology, the optimization of mechanical vehicle trajectories and control strategies have gradually become a focal area of research. Precise trajectory optimization not only enhances the driving efficiency of vehicles but also significantly reduces energy consumption and safety hazards. This paper reviews the basic theory of mechanical vehicle motion trajectories, focusing on the methods of trajectory optimization and control strategies. It covers model-based trajectory optimization, data-driven optimization methods, and various control strategies. Through an analysis of existing research, it points out the challenges and prospects of applying trajectory optimization and control strategies in complex environments.

Optimization of paddle trajectory for fin-wheel underwater robot

Purpose The purpose of this paper is to investigate the oscillating trajectory of the paddle of a fin-wheel underwater robot to enhance its propulsion efficiency in water. This robot can be used for underwater detection and military operations. Design/methodology/approach By studying the propulsion mode of underwater fin-based robots, it is found that such robots periodically generate a large reverse thrust during the swing process, resulting in low propulsion efficiency. Therefore, according to the propulsion characteristics of the oscillating paddle in the underwater environment, the hydrodynamic model and physical constraints of the oscillating paddle are established. Then, the oscillating gait trajectory of the paddle is optimized by the trajectory optimization method. The performance of the optimized trajectory was tested in the simulation environment and the actual underwater environment. Findings The prototype of the robot was built and tested in a small swimming pool. The research results confirm that the propulsion efficiency of the optimized trajectory is higher than that of the traditional trajectory under the condition of the same amplitude and period. Specifically, the maximum speed of the robot can reach 0.24 m/s when using the optimized trajectory, which is about 50% higher than that before optimization. Originality/value The optimized trajectory with the generated impulse as the optimization target is applied to the paddle oscillation, which can improve the thrust impulse generated by the fin-wheel underwater robot during underwater motion, thereby greatly improving the underwater propulsion efficiency and moving speed.

A trajectory optimization method for CAVs at intersections considering energy-efficiency balance

With the development of vehicle-to-everything (V2X) technology, connected automated vehicles (CAVs) will be an important part of urban road transportation. However, frequent acceleration, deceleration, and rapid stopping within intersections lead to increased energy consumption, reduced driving efficiency and balanced benefits. The study proposes an optimal control method for vehicle trajectories that considers energy-efficiency balance (OCM-EEB) based on the characteristics of V2X technology. The method first develops a vehicle trajectory control model based on the Intelligent Driver Model (IDM) by accounting for the features of V2X technology, and further, introduces the idea of balanced optimization, considering energy-efficiency balance, a vehicle trajectory optimal control model (OCM) is proposed. The proposed model was solved by design algorithms based on the non-dominated sorting genetic algorithm-II (NSGA-II). The experimental results showed that the vehicle trajectory optimization control method could increase the balanced driving efficiency of the vehicle within intersection, which is conducive to improving the robustness of the vehicle’s trajectory state, and then prove the effectiveness of the method proposed in this study. The method also provides an important technical basis for the vehicle trajectory optimization experiments under a real V2X environment in the future.

A train trajectory optimization method based on the safety reinforcement learning with a relaxed dynamic reward

Train trajectory optimization (TTO) is an effective way to address energy consumption in rail transit. Reinforcement learning (RL), an excellent optimization method, has been used to solve TTO problems. Although traditional RL algorithms use penalty functions to restrict the random exploration behavior of agents, they cannot fully guarantee the safety of the process and results. This paper proposes a proximal policy optimization based safety reinforcement learning framework (S-PPO) for the train trajectory optimization, including a safe action rechoosing mechanism (SARM) and a relaxed dynamic reward mechanism (RDRM) combining a relaxed sparse reward and a dynamic dense reward. SARM guarantees that the new states generated by the agent consistently adhere to the environmental security constraints, thereby enhancing sampling efficiency and facilitating algorithm convergence. RDRM makes it easier for agents to obtain successful samples by relaxing time constraints, which also offers a better balance between exploration and exploitation. The experimental results show that S-PPO can significantly improve performance and obtain better train operation trajectories than soft constraint methods, and the convergence process is smoother. Finally, it was demonstrated that S-PPO exhibits good adaptability across various speed limit tracks.

Research on real-time trajectory optimization methods for stratospheric airships based on deep learning

Research on real-time trajectory optimization methods for stratospheric airships based on deep learning