Trajectory Method Research Articles

Analysis of observability and detectability for CSTR model of biochemical processes under uncertain system dynamics and various sets of measured outputs

An analysis of observability and detectability for continuous stirred tank reactor model of selected biochemical processes has been addressed in this paper. In particular, properties of observability or detectability of the considered system model have been proved under uncertain system dynamics in view of various sets of system measured outputs. It is related to considering system dynamics depending on initial conditions and the impact of inputs taking into account a given measured output. The method of indistinguishable state trajectories (indistinguishable dynamics) and tools based on the Lyapunov second method were used to investigate the observability and detectability properties. The analysis was performed for eight cases of different sets of measured outputs with association to the realistic features of measuring devices. The obtained research results are essential for system state estimation that involves the synthesis of state observers. The proposed approach may be successfully applied to the complex biochemical non-linear uncertain systems modelled as continuous stirred tank reactors.

Exploring systemic effects of the friendship paradox on social network participation

The friendship paradox states that, on average, people have fewer friends than their friends do. This can lead to social perception biases, such as the belief that one’s friends are more socially engaged than oneself. In a recent paper, we investigated the consequences of this type of social comparison for content sharing behavior in online social networks (Medhat and Iyer, The Friendship paradox and social network participation, international workshop on complex networks and their applications, pp 301–315, 2023). We simulated a scenario where people compare the feedback that their own content receives to the feedback that their friends’ content receives and adjust their sharing based on the comparison. If sharing and feedback rates are initially uniform over individuals, then feedback disparities initially depend solely upon the local structural friending paradox. These structurally induced disparities may then induce sharing disparities that further amplify (or potentially, reduce) feedback disparities, triggering cycles of updates of sharing rates and feedback disparities. In our previous work, we observed that monotonic responses to social comparisons, where larger disparities result in greater behavioral changes, led to an asymptotic decline in overall network sharing. In this paper, we extend our earlier work by studying fundamental properties of our friendship-paradox-induced sharing trajectories (FIT) method. We analyze how sharing rates trend when it is dictated by both observed feedback disparities and activity thresholds for collective behavior. We also evaluate the iterative impact of FIT on network nodes, as a measure of node centrality in a network, finding it to have the ability to identify central nodes at a community level and to do so at a lower computational complexity than community detection, a property not matched by commonly used node centrality methods such as betweeness, closeness and degree centrality.

A Fast Tracking Method for Frontal Volleyball Spike Trajectory Based on Bee Algorithm

A Fast Tracking Method for Frontal Volleyball Spike Trajectory Based on Bee Algorithm

Precision of meteor trajectory and orbital measurements by the MIOS

Abstract Measurement errors of meteors can substantially affect the accuracy of meteoroid trajectory and orbit determinations, potentially leading to spurious meteoroid orbits. Here, we evaluate the measurement errors associated with the meteor and ionospheric irregularity observation system (MIOS) developed at low latitude Ledong and Sanya, China, aimed at observing various meteors and their associated plasma density irregularity phenomena, and investigate how these errors affect the determination of meteor trajectories and orbits. The measurement error of meteor position is estimated to be ∼2 pixels, corresponding to 0.04○, which is sufficient to detect true radiant dispersion and structural characteristics in younger meteor showers. By simulating meteoroids from the Draconid, Geminid, and Perseid meteor showers with the ∼2 pixels measurement error and the Monte Carlo trajectory method, the precision of corresponding meteoroid trajectories is derived. The radiant accuracy is 1.09○, with right ascension and declination accuracies of 0.78○ and 0.77○, respectively. The velocity accuracy is 0.64 km/s. The comparison of estimated and true radiant uncertainties shows that the estimated errors of the MIOS are generally consistent with the true meteor trajectory errors. Finally, we estimate the orbital measurement errors, which include an eccentricity of 0.05, a perihelion distance of 0.0086 AU, an inclination of 1.4○, and an argument of the perihelion of 1.86○. Based on observations of eight representative meteor showers during 2019-2023, the accuracy of the MIOS in detecting meteor trajectories and orbits is further validated.

Optimized Trajectory Unraveling for Classical Simulation of Noisy Quantum Dynamics.

The dynamics of open quantum systems can be simulated by unraveling it into an ensemble of pure state trajectories undergoing nonunitary monitored evolution, which has recently been shown to undergo measurement-induced entanglement phase transition. Here, we show that, for an arbitrary decoherence channel, one can optimize the unraveling scheme to lower the threshold for entanglement phase transition, thereby enabling efficient classical simulation of the open dynamics for a broader range of decoherence rates. Taking noisy random unitary circuits as a paradigmatic example, we analytically derive the optimum unraveling basis that on average minimizes the threshold. Moreover, we present a heuristic algorithm that adaptively optimizes the unraveling basis for given noise channels, also significantly extending the simulatable regime. When applied to noisy Hamiltonian dynamics, the heuristic approach indeed extends the regime of efficient classical simulation based on matrix product states beyond conventional quantum trajectory methods. Finally, we assess the possibility of using a quasi-local unraveling, which involves multiple qubits and time steps, to efficiently simulate open systems with an arbitrarily small but finite decoherence rate.

Identification of health trajectories of patients with persistent spinal pain syndrome type 2 using latent class trajectory methods.

Persistent spinal pain syndrome Type 2 (PSPS-T2) is a long-lasting condition that consists of persistent pain following spinal surgery. Although this condition has long-term effects, it is currently studied at a given time point or over a limited period of time, which does not reflect the true impact of pain patients. To bridge this gap, we used latent class trajectory models to extract clusters with different trajectories of patients with PSPS-T2. Data from the PREDIBACK study, an observational, multicentric, and longitudinal investigation carried out prospectively, were used. This study focuses on patients with PSPS-T2, tracking their outcomes at 3-month intervals over a one-year period. Health status was evaluated using a novel multidimensional clinical response index (MCRI). The trajectories of patients' health status were extracted using mixture of mixed effect models. Two hundred (200) PSPS-T2 patients were included. Two clusters were identified, including 'persistent low health' trajectories (63.1%) and 'improving health' trajectories (36.9%). Regarding the factors associated with these trajectories, our results showed that lower age, lower body mass index, lower pain intensity, lower functional disability, lower anxiety and less extended pain surface were associated with improving health status. Clustering methods provide an opportunity to identify two distinct clusters of pain-related health trajectories of PSPS-T2 patients. Persistence of the symptoms was not observed in one third of the PSPS-T2 study patients, who belong to the improving pain-related health cluster, while the other two thirds did not achieve improved health over a 1-year follow-up. Our study findings suggest that the use of trajectory-based methods could improve patient evaluation and pain management as it allows for obtaining a global view of patients during their care pathway compared to conventional methods, which only focus on specific visits. Our study also advocates for multidimensional assessment and management of pain by targeting not only pain intensity but also the psychological distress, functional capacity and pain surface at an early stage of pain onset after spine surgery.

State-to-State Time-Dependent Quantum Dynamics Studies of the Si(3P) + OH(X 2Π) → OSi(X 1Σg+) + H(2S) Reaction Based on a New HOSi(X2A') Potential Energy Surface.

Quantum and quasi-classical dynamics calculations were conducted for the reaction of Si with OH on the latest potential energy surface (PES), which is obtained by fitting tens of thousands of ab initio energy points by using the many-body expansion formula. To obtain an accurate PES, all energy points calculated with aug-cc-pVQZ and aug-cc-pV5Z basis sets were extrapolated to the complete basis set limit. The accuracy of our new PES was verified by comparing the topographic characteristics and contour maps of potential energy with other works. In addition, the anharmonic vibrational frequencies of HOSi and HSiO based on the present ab initio and PES by means of quantum dynamics methods were calculated. Dynamics information such as reaction probability, integral cross sections (ICS), product distribution, and rate constants was obtained on the new HOSi(X2A') PES. The dynamic information calculated using the quasi-classical trajectory method and time-dependent wave packet method is generally in good agreement, except for the vibrational state-resolved ICSs of product. The calculated differential cross section and capture time reveal that the reaction is primarily governed by the complex formation mechanism.

A windowed mean trajectory approximation for condensed phase dynamics.

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

Study of a Companion Trajectory Kinematics Analysis Method for the Five-Blade Rotor Swing Scraper Pump

This paper proposes a five-blade rotor swing scraper pump (FRSSP) to overcome traditional volumetric pumps’ drawbacks, such as poor sealing performance, low volumetric efficiency, and complex structure. This pump employs a rotating cam-swing scraper mechanism to achieve fluid intake and discharge. The FRSSP is compact in structure, self-sealing, and highly efficient in volumetric utilization, offering promising applications. A companion trajectory kinematic analysis method of the FRSSP is proposed. The polar coordinate equation of the companion trajectory is derived from the profile equation of the five-blade rotor cam. Based on this trajectory, a kinematic model of the scraper pump is established, resulting in the kinematic equations for the swing angle of the scraper, the pressure angle of the scraper, the rotation angle of the rotor, the angular velocity of the scraper, and the angular acceleration of the scraper. The kinematics of the FRSSP were simulated and validated using ADAMS. Comparing the results of theoretical calculations and simulation reveals that the error in the scraper swing angle is 1.85%, the maximum error in the scraper angular velocity is 4.93%, and the maximum error in the scraper angular acceleration is 2.47%, confirming the accuracy of the kinematic analysis method. A sensitivity analysis was performed on the kinematic research method for companion trajectories. After modifying the dimensions of key components in the scraper pump, the discrepancies between theoretical calculations and simulation results were within 5%, confirming the accuracy and robustness of the method. Flow field simulation analysis and experimental tests on the scraper pump revealed that the deviation between the simulated and experimental outlet flow rates was less than 5%, validating the feasibility of the pump’s structural principles and the reliability of the simulations. Furthermore, these findings indirectly affirmed the correctness of the companion trajectory kinematic analysis method.

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.

Comparing Skill Transfer Between Full Demonstrations and Segmented Sub-Tasks for Neural Dynamic Motion Primitives

Programming by demonstration has shown potential in reducing the technical barriers to teaching complex skills to robots. Dynamic motion primitives (DMPs) are an efficient method of learning trajectories from individual demonstrations using second-order dynamic equations. They can be expanded using neural networks to learn longer and more complex skills. However, the length and complexity of a skill may come with trade-offs in terms of accuracy, the time required by experts, and task flexibility. This paper compares neural DMPs that learn from a full demonstration to those that learn from simpler sub-tasks for a pouring scenario in a framework that requires few demonstrations. While both methods were successful in completing the task, we find that the models trained using sub-tasks are more accurate and have more task flexibility but can require a larger investment from the human expert.

The impacts of socioeconomic development and climate change on long-term nutrient dynamics: A case study in Poyang Lake

The anthropogenic activities associated with rapid socioeconomic development affect global climate change and the water quality of lake ecosystems. However, the impacts of socioeconomic and climate changes on lake nutrient dynamics require additional study. In this study, we used a long-term dataset (1987–2021) of Poyang Lake to identify the nutrient dynamics and assess the impacts of social and climatic factors on nutrient concentrations. The filtering trajectory method (FTM) suggested that in Poyang Lake, nutrients first increased and then decreased, with TP reaching its highest value of 157 μg/L in 2015. The study employs a combination of structural equation modeling (SEM) and FTM to identify the complex interactions between socio-economic and climatic factors affecting nutrient concentrations in Poyang Lake. The SEM results revealed that socioeconomic factors rather than climate change determined the long-term changes in TN and TP. Additionally, FTM results verified that GDP, urbanization (Ur) and P-fertilizer (Pfer) were the key drivers of TN; Ur, population (P), and sewerage treatment rate (STR) were the primary factors of TP. Through generalized additive models (GAMs), we observed that GDP accounted for 86 % of the temporal variability in TN and 45.7 % of that in TP, exhibiting inverted U-shaped relationships with both TN and TP. Air temperature (AT), a climatic factor accounted for only 44.6 % and 14.8 % of the variation in TN and TP, respectively. In addition, Pfer explained 66.0 % of the variation in TN, and STR explained 50.4 % of the variation in TP with a peak TP at the STR threshold of approximately 80 %. Our findings highlight the importance of Pfer and STR as critical indicators for watershed nutrient management. The identification of key temporal drivers and nutrient trajectories provides a scientific basis for developing management strategies. The results highlight coordinated control strategies for water pollution and carbon reduction as essential measures for mitigating climate change.

MSR144 Group-Based Multivariate Trajectory Methods to Assess Patient-Reported Outcomes in Acute Myeloid Leukaemia: An Evaluation of Published Methods and Results

MSR144 Group-Based Multivariate Trajectory Methods to Assess Patient-Reported Outcomes in Acute Myeloid Leukaemia: An Evaluation of Published Methods and Results

Scheme and trajectory design of in-situ atmospheric sampling with multi-pass aeroassisted maneuvers

Planetary atmospheric detection is an important way to recognize the physical and chemical properties of planets that inform about their formation and evolution, and atmospheric in-situ sampling is an ideal way to obtain high-resolution information. In this paper, a scheme for in-situ sampling of planetary atmosphere based on multi-pass aeroassisted maneuvers is given, and the corresponding design method for multiple traversal trajectories through the atmosphere is proposed. The aeroassisted maneuvering scheme achieves target-area sampling by crossing the atmosphere circularly, and is able to flexibly adjust the sampling altitude, thus having the advantage of three-dimensional and wide-area sampling. The trajectory design method involves algorithms to determine key design parameters separately. Specifically, the minimum entry periapsis altitude is determined by building its mapping relationship with path constraints to satisfy the minimum flight altitude constraint. Besides, the pass number of atmospheric flights is calculated by giving the upper bound of the energy attenuation and mission-time constraints. Then, a rapid inclination correction method via bank angle reversal is given to satisfy the inclination constraint of the maneuver. In numerical simulations, three Martian atmospheric detection scenarios, designated as high-latitude region with superficial ice water, magnetic anomalies region, and the polar region enriched with atmospheric transport properties, are established, with corresponding maneuvering sampling trajectories and characteristic parameter distributions provided. This paper introduces for the first time the use of multi-pass aeroassisted maneuvers for in-situ atmospheric sampling. Simulation results demonstrate the effectiveness and general applicability of the proposed method.

A trajectory tracking control method for the discharge arm of the self-propelled forage harvester

The cooperative operation between the self-propelled forage harvester and the trailer aims to achieve precise and automatic forage unloading. The discharge arm serves as the core structure for conveying forage, and the precision and speed of its motion control are crucial factors influencing the efficiency of forage harvesting. In this context, we proposed a trajectory tracking control method for the discharge arm based on an improved particle swarm optimization (IPSO)-PID controller. Firstly, we utilized the Denavit-Hartenberg (D-H) model of the discharge arm for a positive kinematics solution and the geometric resolution and linear fitting method for the inverse kinematics solution. Secondly, we employed the polynomial interpolation method for trajectory planning on the joint space of the discharge arm, and the PSO algorithm for time-optimal trajectory planning. Then, we designed an IPSO-PID trajectory tracking control algorithm and built an Amesim-Simulink co-simulation model for multiple simulation experiments. Finally, we conducted several performance tests of the discharge arm automatic control system in the workstation and the field, respectively. The experiment results indicate that the performance of the IPSO-PID controller exceeds that of all other controllers, which can meet the discharge arm’s motion control accuracy and speed requirements. Our research results are of great significance for improving the productivity and automation process of the self-propelled forage harvester and provide valuable references for research on automatic and precise control of material loading in other agricultural cooperative harvesting.

Smooth and Time-Optimal Trajectory Planning for Robots Using Improved Carnivorous Plant Algorithm

To improve the safety and reliability of robotic manipulators during high-speed precision movements, this paper proposes a method for smooth and time-optimal trajectory planning incorporating kinodynamic constraints. The primary objective is to use an evolutionary algorithm to determine a trajectory by considering time and jerk within the feasible path-pseudo-velocity phase plane region. Firstly, the path parameterization theory extracted the maximum pseudo-velocity projection curve from the kinodynamic constraints. Subsequently, the feasible region in the phase plane was defined through reachability analysis of discrete linear systems. Thereafter, we constructed the trajectory function using a cubic B-spline curve, optimizing its control points with an improved carnivorous plant optimization algorithm. Finally, the effectiveness and practicality of this method were verified through simulations on a 6-DOF manipulator.

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.

Intelligent optimization of horizontal wellbore trajectory based on reinforcement learning

Ultra-long horizontal wells are crucial for improving the production and developmental benefits of shale oil and gas wells. Currently, advanced downhole semi-closed-loop steering drilling technology depends on a dual communication mechanism between the surface and downhole, as well as the empirical decisions of human experts. However, it is difficult to acutely control the trajectory of ultra-long horizontal open hole drilling in a reservoir owing to geological uncertainties related to shale oil and gas, the uncertainty of the drilling tool's building capacity, and the lag of measurement information while drilling. This report proposes an adaptive target detection and design method for ultra-long horizontal well trajectories based on reinforcement learning. The developed approach enables dynamic identification of reservoir sequences according to logging-while-drilling data and prediction of horizontal targets in real-time, with a recognition accuracy of 90.1%. Additionally, measurement-while-drilling data are used to accurately characterize the depth, inclination, and azimuth of the target-entering process. The dynamic interaction mechanism between the bit and the target environment is simulated by defining the bit action, reward function, and an update mechanism. The drilling engineering conditions restrict the interactions, such that the bit automatically decides the direction in which to drill the targets, demonstrating 100% accuracy for the wellbore trajectory toward the target. The experimental application results indicate that the developed method can be applied to determine the dynamic target area of a horizontal well in real time and make intelligent downhole decisions regarding ultra-long horizontal section borehole trajectory adjustments while drilling and measuring. The drilling rate of high-quality reservoirs is therefore significantly improved. The results discussed herein provide insights to support further developments of downhole full-closed-loop intelligent autonomous decision-making borehole trajectory control.

A fast calculation method for three-impulse contingency return trajectory during the near-moon phase based on differential algebra

Aimed at the demand of contingency return at any time during the near-moon phase in the manned lunar landing missions, a fast calculation method for three-impulse contingency return trajectories is proposed. Firstly, a three-impulse contingency return trajectory scheme is presented by combining the Lambert transfer and maneuver at the special point. Secondly, a calculation model of three-impulse contingency return trajectories is established. Then, fast calculation methods are proposed by adopting the high-order Taylor expansion of differential algebra in the two-body trajectory dynamics model and perturbed trajectory dynamics model. Finally, the performance of the proposed methods is verified by numerical simulation. The results indicate that the fast calculation method of two-body trajectory has higher calculation efficiency compared to the semi-analytical calculation method under a certain accuracy condition. Due to its high efficiency, the characteristics of the three-impulse contingency return trajectories under different contingency scenarios are further analyzed expeditiously. These findings can be used for the design of contingency return trajectories in future manned lunar landing missions.

Theoretical Investigation of Rate Coefficients and Dynamical Mechanisms for N + N + N Three-Body Recombination Based on Full-Dimensional Potential Energy Surfaces

Three-body recombination reactions, in which two particles form a bound state while a third one bounces off after the collision, play significant roles in many fields, such as cold and ultracold chemistry, astrochemistry, atmospheric physics, and plasma physics. In this work, the dynamics of the recombination reaction for the N3 system over a wide temperature range (5000–20,000 K) are investigated in detail using the quasi-classical trajectory (QCT) method based on recently developed full-dimensional potential energy surfaces. The recombination products are N2(X) + N(4S) in the 14A″ state, N2(A) + N(4S) in the 24A″ state, and N2(X) + N(2D) in both the 12A″ and 22A″ states. A three-body collision recombination model involving two sets of relative translational energies and collision parameters and a time-delay parameter is adopted in the QCT calculations. The recombination process occurs after forming an intermediate with a certain lifetime, which has a great influence on the recombination probability. Recombination processes occurring through a one-step three-body collision mechanism and two distinct two-step binary collision mechanisms are found in each state. And the two-step exchange mechanism is more dominant than the two-step transfer mechanism at higher temperatures. N2(X) formed in all three related states is always the major recombination product in the temperature range from 5000 K to 20,000 K, with the relative abundance of N2(A) increasing as temperature decreases. After hyperthermal collisions, the formed N2(X/A) molecules are distributed in highly excited rotational and vibrational states, with internal energies mainly distributed near the dissociation threshold. Additionally, the rate coefficients for this three-body recombination reaction in each state are determined and exhibit a negative correlation with temperature. The dynamic insights presented in this work might be very useful to further simulate non-equilibrium dynamic processes in plasma physics involving N3 systems.