Trajectory Method Research Articles

A Learnable Image-Based Load Signature Construction Approach in NILM for Appliances Identification

One of the tasks of Non-Intrusive Load Monitoring (NILM) is load identification, which aims to extract and classify altered electrical signals after switching events are detected. In this subtask, representative and distinguishable load signatures are es-sential. At present, the literature approach to characterize electri-cal appliances is mainly based on manual feature engineering. However, the performance of signatures obtained by this way is limited. In this paper, we propose a novel load signature construc-tion method utilizing deep learning techniques. Specifically, three learnable load signatures are presented such as Learnable Recur-rent Graph (LRG), Learnable Gramian Matrix (LGM) and Gen-erative Graph (GG). Furthermore, we test different frameworks for learning these signatures and conclude that Temporal Convo-lutional Networks (TCN) based on residual learning are more suit-able for this work than the other schemes mentioned. The results of experiment on the PLAID datasets with submetered and aggre-gated, WHITED dataset and LILAC dataset confirm that our method outperforms the voltage-current trajectory, Recursive Graph and Gramian Angular Field methods in multiple evalua-tion metrics.

High-Energy Quantum Dynamics of the 15N + o-14N14N Rovibrational Activation and Isotope Exchange Processes.

We report full quantum reaction probabilities, computed within the framework of time-independent quantum mechanics using hyperspherical coordinates, for the 15N + 14N14N inelastic and reactive collision processes, restricted to total angular momentum J = 0, for kinetic energies up to 4.5 eV. We take advantage of the nonzero (i = 1) nuclear spin of 14N, leading to the existence of two nuclear spin isomers of 14N14N, namely, ortho- and para-14N14N, to restrict the study to the ortho molecular nitrogen species, with even rotational quantum number j = 0, 2, ... states. Specifically, we start with diatomic reagents ortho-14N14N in the initial rotational state j = 0. A comparison with similar works previously published by other groups using time-dependent wave packet and quasi-classical trajectory methods for the 14N + 14N14N fully symmetric collision is given. We find that reactive processes 15N + 14N14N involving atom exchange do not happen for collision energies less than 2.2 eV. Collisions at energies of around 2.0 eV are most effective for populating reactants' rovibrational states, that is, for inelastic scattering, whereas those at energies close to 5.0 eV yield a newly formed 14N15N isotopologue in a wide variety of excited vibrational levels.

SiS formation in the interstellar medium via SiH + S collisions

ABSTRACT One of the most important Si-bearing species in the intersellar medium is the SiS molecule. Thermal rate coefficients and other collisional properties are calculated for its formation via the title reaction using the quasi-classical trajectory method. An accurate representation of the HSiS potential energy surface is employed, which has been modelled from high-level ab initio calculations and a reliable description of long-range interactions as implied by the underlying double many-body expansion method. The calculated rate coefficients for the $\rm SiH + S \rightarrow SiS + H$ reaction can be modelled with k(T) = α(T/300)βe−γ/T where $\alpha =0.63\times 10^{-10}\, \rm cm^3\, s^{-1}$, β = -0.11, and $\gamma = 11.6\, \rm K$. This result is only slightly lower than that for SiS formation via Si + SH collisions. The contribution of each reaction mechanism and the rovibrational energy distributions of the nascent SiS molecule are also calculated. The title collision can also yield SH ($\rm SiH + S \rightarrow SH + Si$), but the corresponding rate coefficient is 20 to 27 times smaller than for SiS formation ($\alpha =0.025\times 10^{-10}\rm cm^3\, s^{-1}$, β =-0.13, and $\gamma = 9.38\, \rm K$). The role of intersections between excited electronic states is also discussed, based on novel calculations including eight electronic states.

Vibrational Mode-Specific Dynamics of the OH + C2H6 Reaction.

We investigate the effects of the initial vibrational excitations on the dynamics of the OH + C2H6 → H2O + C2H5 reaction using the quasi-classical trajectory method and a full-dimensional analytical ab initio potential energy surface. Excitation of the initial CH, CC, and OH stretching modes enhances, slightly inhibits, and does not affect the reactivity, respectively. Translational energy activates the early-barrier title reaction more efficiently than OH and CC stretching excitations, in accord with the Polanyi rules whereas CH stretching modes have similar or higher efficacy than translation, showing that these rules are not always valid in polyatomic processes. Scattering angle, initial attack angle, and product translational energy distributions show the dominance of direct stripping with increasing collision energy, side-on OH and isotropic C2H6 attack preferences, and substantial reactant-product translational energy transfer without any significant mode specificity. The reactant vibrational excitation energy of OH and C2H6 flows into the H2O and C2H5 product vibrations, respectively, whereas product rotations are not affected. The computed mode-specific H2O vibrational distributions show that initial OH excitation appears in the asymmetric stretching vibration of the H2O product and allow comparison with experiments.

Multi-UAV Cooperative and Continuous Path Planning for High-Resolution 3D Scene Reconstruction

Unmanned aerial vehicles (UAVs) are extensively employed for urban image captures and the reconstruction of large-scale 3D models due to their affordability and versatility. However, most commercial flight software lack support for the adaptive capture of multi-view images. Furthermore, the limited performance and battery capacity of a single UAV hinder efficient image capturing of large-scale scenes. To address these challenges, this paper presents a novel method for multi-UAV continuous trajectory planning aimed at the image captures and reconstructions of a scene. Our primary contribution lies in the development of a path planning framework rooted in task and search principles. Within this framework, we initially ascertain optimal task locations for capturing images by assessing scene reconstructability, thereby enhancing the overall quality of reconstructions. Furthermore, we curtail energy costs of trajectories by allocating task sequences, characterized by minimal corners and lengths, among multiple UAVs. Ultimately, we integrate considerations of energy costs, safety, and reconstructability into a unified optimization process, facilitating the search for optimal paths for multiple UAVs. Empirical evaluations demonstrate the efficacy of our approach in facilitating collaborative full-scene image captures by multiple UAVs, achieving low energy costs while attaining high-quality 3D reconstructions.

Semi-Analytical Midcourse Guidance for Coordinated Interception of Multiple Exo-Atmospheric Targets

The simultaneous interception of multiple exo-atmospheric threat targets can leave no buffer time for the targets and greatly reduces targets’ penetration probability. This paper proposes centralized and decentralized two midcourse guidance methods to solve the coordinated interception of multiple exo-atmospheric targets. First, the free-time cooperative interception problem minimizing the total impulses is established, where the nonlinear dynamics of the interceptors and targets, the initial impulse constraints, and the terminal interception constraints are considered. Second, the necessary conditions for the optimal cooperative interception problem are derived and then approximated using higher-order Taylor expansions, which result in a series of analytical nonlinear equations. Then, the semi-analytical centralized guidance mode is designed to achieve simultaneous interception of targets by directly solving the analytical nonlinear equations. To improve computational efficiency, the decentralized cooperative guidance mode is further proposed by using the developed iterative freezing trajectory method, where each interceptor uses information from other interceptors in the previous iteration for prediction and distributed computation. Numerical examples verify the effectiveness and robustness of the proposed two guidance methods. Results show that the computational efficiency of the decentralized guidance mode is more efficient compared with the centralized midcourse guidance mode.

Experimental and Theoretical Study of the Kinetics of the CH3 + HBr → CH4 + Br Reaction and the Temperature Dependence of the Activation Energy of CH4 + Br → CH3 + HBr.

The rate coefficient of the reaction of CH3 with HBr was measured and calculated in the temperature range 225-960 K. The results of the measurements performed in a flow apparatus with mass spectrometric detection agree very well with the quasiclassical trajectory calculations performed on a previously developed potential energy surface. The experimental rate coefficients are described well with a double-exponential fit, k1(exp) = [1.44 × 10-12 exp(219/T) + 6.18 × 10-11 exp(-3730/T)] cm3 molecule-1 s-1. The individual rate coefficients below 500 K accord with the available experimental data as does the slightly negative activation energy in this temperature range, -1.82 kJ/mol. At higher temperatures, the activation energy was found to switch sign and it rises up to about an order of magnitude larger positive value than that below 500 K, and the rate coefficient is about 50% larger at 960 K than that around room temperature. The rate coefficients calculated with the quasiclassical trajectory method display the same tendencies and are within about 8% of the experimental data between 960 and 300 K and within 25% below that temperature. The significant variation of the magnitude of the activation energy can be reconciled with the tabulated heats of formation only if the activation energy of the reverse CH4 + Br reaction also significantly increases with the temperature.

Analysis of O3 Pollution Characteristics, Formation Sensitivity, and Transport Impact in Southern Nanjing

As one of the most important city clusters in China, surface ozone (O3) pollution in the Yangtze River Delta (YRD) Region has become a prominent air quality problem in recent years. Online observations of ambient O3, nitrogen oxides (NOx), and volatile organic compounds (VOCs) were conducted in southern Nanjing from July-September 2020 and April-May 2021. On this basis, the pollution characteristics of O3 were analyzed. The O3-VOCs-NOx sensitivity and the transport influence of its precursors were further discussed using models. The frequency statistics of the daily maximum 8-hour moving average (DMA-8h O3) and hourly concentration (O3-1h) showed that O3 pollution in southern Nanjing was more serious than that in urban areas. Three typical O3 pollution episodes were selected during the whole observation period, which included August 16th-27th, 2020; September 3rd-11th, 2020; and May 17th-25th, 2021. The O3-VOCs-NOx sensitivities in these three pollution episodes were analyzed using the observation-based model (OBM). The results of the relative incremental reactivity (RIR) and empirical kinetics modeling approach (EKMA) showed that the sensitivities of O3 formation in the three pollution episodes were in the NOx-limited regime, the transition regime, and the VOCs-limited regime, respectively. This difference in O3-VOCs-NOx sensitivity reflects that the site may have been influenced by transport. Therefore, the potential source contribution function (PSCF) and the concentration weighted trajectory (CWT) method were further used to analyze the potential source areas of NOx, VOCs, and O3 in these three pollution episodes. The results showed that there were obvious regional transport effects of NOx, VOCs, and O3 in these three pollution episodes. The location of potential sources differed in these three pollution episodes, which were affected by the eastern cities of the Lishui site; the urban area of Nanjing and eastern area of Anhui Province; and the urban area of Nanjing and the middle of the YRD Region, respectively. The impact of transport on O3 and its precursors also indicated the necessity of regional joint prevention and control of O3 pollution in the YRD Region.

Transient Stability Analysis for Grid-Forming VSCs Based on Nonlinear Decoupling Method

With the increasing integration of renewable energy into the power grid, there is a growing demand for converters that not only provide stable power, but also support auxiliary functions such as grid-voltage regulation. Consequently, grid-forming strategies have attracted significant attention. However, due to the complexities of analyzing nonlinear coupling systems, a comprehensive transient stability analysis of grid-forming converters is still being explored. Conventional analysis methods rely on a simplified quasi-steady-state model for grid-forming voltage source converters (VSCs) and focus on analyzing the transient instability phenomenon caused by the outer power loop. However, this oversimplified model may yield incorrect conclusions. To address this limitation, this paper develops a full-order model that includes quadratic nonlinear terms to accurately represent the system’s nonlinear characteristics. The developed model is then decoupled into multiple low-order modes using a nonlinear decoupling method. These low-order modes can be analyzed using the mature inversing trajectory method, indirectly reflecting the transient stability of grid-forming VSCs under large disturbances. Through varying the inner and outer parameters, the transient stability of grid-forming VSCs is analyzed in detail. Furthermore, the analysis results are verified through hardware-in-loop (HIL) experiments.

A novel privacy protection method of residents' travel trajectories based on federated blockchain and InterPlanetary file systems in smart cities.

The government does have to record and analyze the travel trajectories of urban residents aiming to effectively control the epidemic during COVID-19. However, these privacy-related data are usually stored in centralized cloud databases, which are prone to be vulnerable to cyber attacks leading to personal trajectory information leakage. In this article, we proposed a novel secure sharing and storing method of personal travel trajectory data based on BC and InterPlanetary File System (IPFS). We adopt the Hyperledger Fabric, the representative of Federated BC framework, combined with the IPFS storage to form a novel mode of querying on-chain and storing off-chain aiming to both achieve the effectiveness of data processing and protect personal privacy-related information. This method firstly solves the efficiency problem of traditional public BC and ensures the security of stored data by storing the ciphertext of complete personal travel trajectory data in decentralized IPFS storage. Secondly, considering the huge amount of information of residents' travel trajectories, the method proposed in this article can obtain the complete information under the chain stored in IPFS by querying the index on the chain, which significantly improves the data processing efficiency of residents' travel trajectories and thus promotes the effective control of the new crown pneumonia epidemic. Finally, the feasibility of the proposed solution is verified through performance evaluation and security analysis.

Calculation method of the build-up rate of the internal push point-the-bit rotary steering tool

The internal push point-the-bit rotary steering tool is a new type of dynamic point-the-bit rotary steerable system. This paper comprehensively uses the mechanical and trajectory method to calculate the build-up rate of the tool to evaluate its build-up ability and realize accurate control of the wellbore trajectory during the directional drilling process. The influence of tool structure, wellbore geometric parameters, drilling process parameters, bit-cutting anisotropy, and formation characteristics on the build-up ability are considered. The tool deflection force, the structural lateral force on the bit, and the formation deflection force were calculated respectively, and the calculation model for the build-up rate of the internal push point-the-bit rotary steering tool is established according to the relationship between force and cutting displacement. In order to study the variation of the build-up rate of the tool in different well slope sections under the conditions of fixed bottom hole assembly and formation parameters, the build-up rate simulation calculation was carried out. The calculation results show that the maximum build-up rate of the tool under stable and controlled conditions increases with the increase of the well inclination, which means the internal push point-the-bit rotary steering tool is suitable for extended reach wells and horizontal wells. The research results provide a theoretical basis for the design of bottom hole assembly and the optimization of drilling process parameters when using the internal push point-the-bit rotary steering tool for directional drilling.

Investigation on reachable domain of contingency return trajectories in the circumlunar flight phase based on interval analysis

The investigation on reachable domain based on interval analysis is performed, which is aimed for the contingency return trajectories during the circumlunar flight stage in manned lunar landing engineering. First, the issue of contingency return trajectory, which adopts a non-coplanar maneuver during the circumlunar flight phase, is expounded upon. The mathematical model of the reachable domain of contingency return trajectories is established. Second, the contingency return trajectory is designed. An improved interval branch and bound algorithm is introduced and a reachable domain calculation method of the contingency return trajectories is proposed. Third, in numerical simulations, by comparing the reachable domain obtained by the traditional brute force method, the accuracy of the method presented in this paper is verified. It also indicates that this method has a higher calculation efficiency. Finally, numerous simulations are conducted to discuss the parameter characteristic of reachable domain by adopting this method. The study conclusions can serve as an important reference for the selection and decision of contingency return trajectory plans in the future manned lunar landing engineering.

Mixed model-based deconvolution of cell-state abundances (MeDuSA) along a one-dimensional trajectory.

Deconvoluting cell-state abundances from bulk RNA-sequencing data can add considerable value to existing data, but achieving fine-resolution and high-accuracy deconvolution remains a challenge. Here we introduce MeDuSA, a mixed model-based method that leverages single-cell RNA-sequencing data as a reference to estimate cell-state abundances along a one-dimensional trajectory in bulk RNA-sequencing data. The advantage of MeDuSA lies primarily in estimating cell abundance in each state while fitting the remaining cells of the same type individually as random effects. Extensive simulations and real-data benchmark analyses demonstrate that MeDuSA greatly improves the estimation accuracy over existing methods for one-dimensional trajectories. Applying MeDuSA to cohort-level RNA-sequencing datasets reveals associations of cell-state abundances with disease or treatment conditions and cell-state-dependent genetic control of transcription. Our study provides a high-accuracy and fine-resolution method for cell-state deconvolution along a one-dimensional trajectory and demonstrates its utility in characterizing the dynamics of cell states in various biological processes.

Solving non-linear optimization problems by a trajectory approach

Abstract Accepted by: Konstantinos Nikolopoulos We propose solving non-linear optimization problems by a trajectory method. A parameter is introduced into the optimization problem. For example, a variable in the original formulation is replaced by its squared value. The parameter is the power at which the variable is raised. For a particular value of the parameter (power of 2), the optimal solution is easily obtained. The original optimization problem is defined for another value of the parameter (power of 1). As another example, the means and standard deviations of a function based on a set of variables can be calculated. We multiply the standard deviations by a factor (the parameter) between 0 and 1. Suppose that the problem is easily solvable for zero standard deviations (factor of 0). If we ‘slowly’ increase the factor, the solution moves to the desired solution for a factor of 1. A trajectory connects the easily obtained solution to the desired solution. We trace the trajectory and the solution for the optimization problem is at the end of the trajectory. The procedure is applied for solving the single facility Weber location problem, and a competitive location problem with good results.

Robust interpolation for dispersed gas‐droplet flows using statistical learning with the fully Lagrangian approach

SummaryA novel methodology is presented for reconstructing the Eulerian number density field of dispersed gas‐droplet flows modelled using the fully Lagrangian approach (FLA). In this work, the nonparametric framework of kernel regression is used to accumulate the FLA number density contributions of individual droplets in accordance with the spatial structure of the dispersed phase. The high variation which is observed in the droplet number density field for unsteady flows is accounted for by using the Eulerian‐Lagrangian transformation tensor, which is central to the FLA, to specify the size and shape of the kernel associated with each droplet. This procedure enables a high level of structural detail to be retained, and it is demonstrated that far fewer droplets have to be tracked in order to reconstruct a faithful Eulerian representation of the dispersed phase. Furthermore, the kernel regression procedure is easily extended to higher dimensions, and inclusion of the droplet radius within the phase space description using the generalised fully Lagrangian approach (gFLA) additionally enables statistics of the droplet size distribution to be determined for polydisperse flows. The developed methodology is applied to a range of one‐dimensional and two‐dimensional steady‐state and transient flows, for both monodisperse and polydisperse droplets, and it is shown that kernel regression performs well across this variety of cases. A comparison is made against conventional direct trajectory methods to determine the saving in computational expense which can be gained, and it is found that times fewer droplet realisations are needed to reconstruct a qualitatively similar representation of the number density field.

Discovering spatiotemporal characteristics of the trans-regional harvesting operation using big data of GNSS trajectories in China

Trans-regional operation of agricultural machinery is an essential socialized service that can enhance the utilization rate of agricultural machinery and accelerate the progress of grain harvesting. In this paper, we quantitatively analyze the trans-regional operations of the harvesters using massive GNSS (Global Navigation Satellite System) data in China and reveal their spatiotemporal characteristics from the province, city and district perspectives. Trajectory data were collected from 25,763 harvesters during wheat harvesting season between May and June 2021 using the agricultural machinery operation big data system. Using the field road segmentation method for GNSS trajectory and the trans-regional operation judgment method, we calculated the quantity, driving distance, harvesting duration, and harvested area. Following this, we obtained the corresponding figures for each region, including the quantity, harvested area, harvesting duration, and distance of harvesters. To further analyze the flow and reliance on harvesters, we examined these factors at the province, city, and district scales for each respective region.. Our analysis revealed that approximately 57.1% of the harvesters were involved in trans-district operation, covering approximately 80.09 % of the total harvested area by all harvesters. Furthermore, we identified 6 provinces, 82 cities and 588 districts with a significant reliance on nonlocal harvesters. The findings provide valuable insights for the government, agricultural machinery enterprises, and agricultural machinery operators to optimize decision-making and configuration schemes to enhance the overall operational efficiency of harvesters.

Revealing the effect of changing the operating parameters of a double hydrostatic bearing on its characteristics

The object of research is hydrostatic processes in sliding bearings with several layers of lubricant. The task addressed was the influence of the structural and operational parameters of dual hydrostatic plain bearings on their static and dynamic characteristics. As a static characteristic, the bearing capacities of dual and conventional sleeve hydrostatic bearings were considered. When analyzing the dynamic characteristics, the amplitude-frequency characteristics were determined. They were obtained by calculation and as a result of experimental studies. When calculating the amplitude-frequency characteristics, the trajectory method was used. As external forces in the equations of motion of the rotor, hydrodynamic forces, the weight of the rotor, and its unbalance were considered. Experimental determination of the trajectories of the rotor was carried out on a special bench. It has been established that the bearing capacity of a double type bearing is approximately 1.75–1.85 times higher than the bearing capacity of a conventional sleeve bearing. The range of stable operation of the rotor on double-type bearings is approximately 1.4 times greater in comparison with the range of stable operation of the rotor on sleeve hydrostatic bearings. The vibration amplitudes in the resonance region for double bearings were approximately 1.5 times less than the rotor vibration amplitudes for sleeve bearings. The results make it possible to recommend dual-type hydrostatic bearings for rotor bearings of nuclear power plants, in powerful aircraft engines with a gearbox, various types of pumps, and other power plant units. The derived theoretical dependences make it possible to carry out practical calculation of hydrostatic bearings of a double type

A Safety Control Method of Car-Following Trajectory Planning Based on LSTM

This paper focuses on the potential safety hazards of collision in car-following behaviour generated by deep learning models. Based on an intelligent LSTM model, combined with a Gipps model of safe collision avoidance, a new, Gipps-LSTM model is constructed, which can not only learn the intelligent behaviour of people but also ensure the safety of vehicles. The idea of the Gipps-LSTM model combination is as follows: the concept of a potential collision point (PCP) is introduced, and the LSTM model or Gipps model is controlled and started through a risk judgment algorithm. Dataset 1 and dataset 2 are used to train and simulate the LSTM model and Gipps-LSTM model. The simulation results show that the Gipps-LSTM can solve the problem of partial trajectory collision in the LSTM model simulation. Moreover, the risk level of all trajectories is lower than that of the LSTM model. The safety and stability of the model are verified by multi-vehicle loop simulation and multi-vehicle linear simulation. Compared with the LSTM model, the safety of the Gipps-LSTM model is improved by 42.02%, and the convergence time is reduced by 25 seconds.

Conservative semi-Lagrangian method for continuity equation with various time steps in different parts of computational domain

The system of Navier Stokes differential equations describes gas flow near rocket nozzle. To find solution of this system in general case, scientists and engineers use numerical methods. Modern numerical methods do not allow engineers to model all features of gas flow. It happened because of sophisticated physical processes and limitations of computational hardware. So, at least where are two ways to improve it: to enlarge hardware or reduce computational complicacy. The global aim of many science investigations is to develop numerical approach with reduced computational complicacy and at the same time without loss of computational accuracy. In 1959, Aksel C. Wiin-Nielsen proposed a new and effective trajectories method for problem of numerical forecasting. In 1966, K. M. Magomedov developed similar approach (method of characteristics) for numerical modelling of space (three dimensional on space) gas flow. In 1982, O. Pironneau showed a new and effective approach for two dimensional approximation of the Navier Stokes problem. It was based on method of characteristics also. Nowadays, these methods are called semi-Lagrangian or Eulerian Lagrangian methods. They use Lagrangian nature of the transport process. To apply this advantage, scientists decompose each equation of Navier Stokes system into three parts: convective part (hyperbolic type), elliptic part and part of right-hand side. Scientists use semi-Lagrangian approach to approximate the convective parts of equations. To develop and test modern algorithms from family of semi-Lagrangian methods, we use continuity equation from the system of Navier Stokes equations. Conservative versions of semi-Lagrangian approach are based on Gauss Ostrogradsky (divergence) theorem. It allows scientists to get conservation low (balance equation) for numerical solution in norm of L1 space. Aim of our investigation is to use different time steps in different parts of computation domain. It enables us to obtain at the same time three advantages: convergence of numerical solution to exact solution, reduction of computational complicacy, implementation of conservation low (balance equation) without weight coefficients. For this purpose we decompose computational domain into two parts (subdomains) and use different time steps in them. Main complication is design algorithm in the boundaries of computational subdomains. We use one dimensional (on space) problem to demonstrate ability of developing numerical method with described advantages. Generalization of considered approach for two- or even three-dimensional cases allows engineers to model gas flow more accurately and without artificial viscosity. It is essentially important in the parts of computational domain with high level of solution gradient.

Trajectory planning method for docking of large aircraft components

PurposeIn the digital assembly system of large aircraft components (LAC), the docking trajectory of LAC is an important factor affecting the docking accuracy and stability of the LAC. The main content of docking trajectory planning is how to move the LAC from the initial posture and position to the target posture and position (TPP). This paper aims to propose a trajectory planning method of LAC based on measured data.Design/methodology/approachFirst, the posture and position error model of the wing is constructed according to the measured data of the measurement points (MPs) and the fork lug joints. Second, the particle swarm optimization algorithm based on the dynamic inertia factor is used to optimize the TPP of the wing. Third, to ensure the efficiency and stability of posture adjustment, the S-shaped curve is used as the motion trajectory of LAC, and the parameters of the trajectory are solved by the generalized multiplier method. Finally, a series of docking experiments are carried out.FindingsDuring the process of posture adjustment, the motion of the numerical control locator (NCL) is stable, and the interaction force between the NCLs is always within a reasonable range. After the docking, the MPs are all within the tolerance range, and the coaxiality error of the fork lug hole is less than 0.2 mm.Originality/valueIn this paper, the measured data rather than the theoretical design model is used to solve the TPP, which improves the docking accuracy of LAC. Experiment results show that the proposed trajectory method can complete the LAC docking effectively and improve the docking accuracy.