Kinematic Constraints Research Articles

Angular Momentum in a Special Nonlinear Elastic Rod

In the constrained Cosserat theory of a rod with a rigid cross-section, the balance of angular momentum is satisfied by a restriction on the constitutive equations that requires a second order tensor to be symmetric. The kinematics of the rod are determined by satisfying the balances of linear and director momentum and kinematic constraints. In contrast, the Antman model for a special Cosserat theory of rods proposes constitutive equations directly for the force and mechanical moment applied to the rod and the kinematics are determined by the balances of linear and angular momentum. These two models differ by their treatment of angular momentum. This note poses and answers the question: Are the solutions of these two models identical for the same strain energy?

Impact of the continuum Coulomb interaction in quantum-orbit-based treatments of high-order above-threshold ionization

We perform a systematic comparison between photoelectron momentum distributions computed with the rescattered quantum-orbit strong-field approximation (RQSFA) and the Coulomb quantum-orbit strong-field approximation (CQSFA). We exclude direct, hybrid, and multiply scattered CQSFA trajectories and focus on the contributions of trajectories that undergo a single act of rescattering. For this orbit subset, one may establish a one-to-one correspondence between the RQSFA and CQSFA contributions for backscattered and forward-scattered trajectory pairs. We assess the influence of the Coulomb potential on the ionization and rescattering times of specific trajectory pairs, kinematic constraints determined by rescattering, and quantum interference between specific pairs of trajectories. We analyze how the Coulomb potential alters their ionization and return times, and their interference in photoelectron momentum distributions. We show that Coulomb effects are not significant for high or medium photoelectron energies and shorter orbits, while for lower momentum ranges or longer electron excursion times in the continuum, the residual Coulomb potential is more important. We also assess the agreement of both theories for different field parameters and show that it improves with the increase of the wavelength. Published by the American Physical Society 2024

Machine learning-based modelling, feature importance and Shapley additive explanations analysis of variable-stiffness composite beam structures

In the current work, the displacement and inner stress state of orthotropic, composite, variable-stiffness beam structures is investigated, combining the extended Kantorovich method (EKM) with machine learning (ML) modeling and explainable artificial intelligence (AI) techniques. The complete displacement and inner stress fields of variable stiffness (VS) composite beams with a through-thickness variation of their material properties are computed for different orthotropy, material gradation and slenderness attributes. Both deep learning and tree-based machine learning architectures are considered, identifying high accuracy and low computational cost modeling architectures. Thereupon, the significance of underlying fundamental design features is assessed, classifying their importance for the first time. In particular, material orthotropy, stiffness gradation and slenderness are analyzed for different boundary conditions, elucidating their interdependence and relative significance. It is shown that reduced end kinematic constraints overall favor the importance of stiffness gradation. Differences in the importance of each design feature for the transverse displacement and inner normal and shear stress fields are identified and quantified using Shapley additive explanations (SHAP) analysis. It is found that material orthotropy is more important than stiffness gradation for the transverse displacement rather than for the normal or shear stress fields developed, for which their relative importance is inverted. What is more, evidence is provided that increased gradation and orthotropy values have opposite signed contributions to the stress fields developed at critical positions of the VS composite, while they uniquely yield equal-signed contributions to the transverse displacement field.

Air–Ground Collaborative Multi-Target Detection Task Assignment and Path Planning Optimization

Collaborative exploration in environments involving multiple unmanned aerial vehicles (UAVs) and unmanned ground vehicles (UGVs) represents a crucial research direction in multi-agent systems. However, there is still a lack of research in the areas of multi-target detection task assignment and swarm path planning, both of which play a vital role in enhancing the efficiency of environment exploration and reducing energy consumption. In this paper, we propose an air–ground collaborative multi-target detection task model based on Mixed Integer Linear Programming (MILP). In order to make the model more suitable for real situations, kinematic constraints of the UAVs and UGVs, dynamic collision avoidance constraints, task allocation constraints, and obstacle avoidance constraints are added to the model. We also establish an objective function that comprehensively considers time consumption, energy consumption, and trajectory smoothness to improve the authenticity of the model and achieve a more realistic purpose. Meanwhile, a Branch-and-Bound method combined with the Improved Genetic Algorithm (IGA-B&B) is proposed to solve the objective function, and the optimal task assignment and optimal path of air–ground collaborative multi-target detection can be obtained. A simulation environment with multi-agents, multi-obstacles, and multi-task points is established. The simulation results show that the proposed IGA-B&B algorithm can reduce the computation time cost by 30% compared to the traditional Branch-and-Bound (B&B) method. In addition, an experiment is carried out in an outdoor environment, which further validates the effectiveness and feasibility of the proposed method.

A Lie group variational integrator in a closed-loop vector space without a multiplier

Abstract. As a non-tree multi-body system, the dynamics model of four-bar mechanism is a differential algebraic equation. The constraints breach problem leads to many problems for computation accuracy and efficiency. With the traditional method, constructing an ODE-type dynamics equation for it is difficult or impossible. In this exploration, the dynamics model is built with geometry mechanic theory. The kinematic constraint variation relation of a closed-loop system is built in matrix and vector space with Lie group and Lie algebra theory respectively. The results indicate that the attitude variation between the driven body and the follower body has a linear recursion relation, which is the basis for dynamics modelling. With the Lie group variational integrator method, the closed-loop system Lagrangian dynamics model is built in vector space, with Legendre transformation. The dynamics model is reduced to be the Hamilton type. The kinematic model and dynamics model are solved using Newton iteration and the Runge–Kutta method respectively. As a special case of a crank and rocker mechanism, the dynamics character of a parallelogram mechanism is presented to verify the good structure conservation character of the closed-loop geometry dynamics model.

Improved Collision Avoidance Algorithm of Autonomous Rice Transplanter Based on Virtual Goal Point

To ensure the operation safety and efficiency of an autonomous rice transplanter, a path planning method of obstacle avoidance based on the improved artificial potential field is proposed. Firstly, the obstacles are divided into circular or elliptic obstacles according to the difference between the length and width of an obstacle as well as the angle between the vehicle’s forward direction and the length direction of the obstacle. Secondly, improved repulsive fields for circular and elliptic models are developed. To escape the local minimum and goal inaccessibility of the traditional artificial potential field as well as meet the requirements of agronomy and vehicle kinematics constraints, the adaptive setting and adjusting strategy for virtual goal points is proposed according to relative azimuth between obstacle and vehicle. The path smoothing method based on the B-spline interpolation method is presented. Finally, the intelligent obstacle avoidance algorithm is designed, and the path evaluation rule is given to obtain the low-cost, non-collision, smooth and shortest obstacle avoidance path. To verify the effectiveness of the proposed obstacle avoidance algorithm, simulation and field experiments are conducted. Simulation and experimental results demonstrate that the proposed improved collision avoidance algorithm is highly effective and realizable.

An Efficient Linear Programming-Based Time-Optimal Feedrate Planning Considering Kinematic and Dynamics Constraints of Robots

An Efficient Linear Programming-Based Time-Optimal Feedrate Planning Considering Kinematic and Dynamics Constraints of Robots

Musculoskeletal model degrees of Freedom: Frontal plane constraints are hindering our understanding of human movement

Induced acceleration analyses have expanded our understanding on the contributions of muscle forces to center of mass and segmental kinematics during a myriad of tasks. While these techniques have identified a subset of major muscle that contribute to locomotion, most analyses have included models with only one frontal plane degree of freedom (dof) actuated by the hip joint. The purpose of this study was to define the impact of including knee and subtalar joint frontal plane dof on model superposition accuracy and muscle specific contributions to mediolateral accelerations. Induced acceleration analyses were performed using OpenSim with the Lai model on a freely available dataset of one subject running at 4 m/s. Analyses were performed on four models (standard, with subtalar joint, with frontal plane knee, and combined frontal plane knee with subtalar) with the kinematic constraint and perturbation analyses. Root mean square error and correlations were computed against experimental kinematics. Adding frontal plane dofs improved mediolateral acceleration correlations on average by > 0.25 while only minimally impacting errors. The constraints method performed better than the perturbation method for mediolateral accelerations. Including frontal plane knee dof resulted in muscle and method specific responses. All muscles presented with a complete flip of polarity for constraint method, imparted by allowing the medial/lateral muscles to contribute according to their anatomical function. Only the gluteus medius flipped for the perturbation method. This study provides significant support for the inclusion of frontal plane knee and subtalar dof and the need for reevaluation of muscle contributions via induced acceleration.

Simultaneous Trajectory and Speed Planning for Autonomous Vehicles Considering Maneuver Variants

The paper presents a technique of motion planning for autonomous vehicles (AV) based on simultaneous trajectory and speed optimization. The method includes representing the trajectory by a finite element (FE), determining trajectory parameters in Frenet coordinates, composing a model of vehicle kinematics, defining optimization criteria and a cost function, forming a set of constraints, and adapting the Gaussian N-point scheme for quadrature numerical integration. The study also defines a set of minimum optimization parameters sufficient for making motion predictions with smooth functions of the trajectory and speed. For this, piecewise functions with three degrees of freedom (DOF) in FE’s nodes are implemented. Therefore, the high differentiability of the trajectory and speed functions is ensured to obtain motion criteria such as linear and angular speeds, acceleration, and jerks used in the cost function and constraints. To form the AV roadway position, the Frenet coordinate system and two variable parameters are used: the reference path length and the lateral displacement perpendicular to reference line’s tangent. The trajectory shape, then, depends only on the final position of the AV’s mass center and the final reference’s curvature. The method uses geometric, kinematic, dynamic, and physical constraints, some of which are related to hard restrictions and some to soft restrictions. The planning technique involves parallel forecasting for several variants of the AV maneuver followed by selecting the one corresponding to a specified criterion. The sequential quadratic programming (SQP) technique is used to find the optimal solution. Graphs of trajectories, speeds, accelerations, jerks, and other parameters are presented based on the simulation results. Finally, the efficiency, rapidity, and prognosis quality are evaluated.

Vision-based UAV adaptive tracking control for moving targets with velocity observation

An adaptive image-based visual servoing (IBVS) controller is designed for a quadrotor unmanned aerial vehicle (UAV) to achieve robust tracking for moving targets, under underactuation and tight coupling constraints of UAV kinematics. Specifically, image features are selected from perspective image moments of a planar target to obtain virtual feature dynamics regarding UAV kinematics and dynamics. By constructing an auxiliary variable, a translational velocity observer for moving target is constructed by using virtual image features. An IBVS tracking controller is designed without target geometric information by combining UAV and visual feature dynamics. Designed controller and observer make the UAV robustly reach desired height and track the moving target, despite uncertainty of target movement. The controller has asymptotical convergence performance, and the target velocity is observed according to Lyapunov stability analysis. Simulation and experimental results show that the proposed method has smoother and more accurate performance in motion tracking and target velocity prediction under system uncertainty.

Cooperative navigation of unmanned aerial vehicle formation with delayed measurement

Abstract This paper focused on the problem of positioning accuracy degradation caused by delayed measurement information in Unmanned Aerial Vehicle (UAV) formation cooperative navigation under complex environments such as cities and hills, and presented a non-synchronous compensation algorithm based on kinematic constraints and constructed a distributed cooperative navigation filter based on the analysis of the basic operating characteristics of inertial devices, satellite receivers, and ranging sensors. In the UAV formation, the leader-UAV is equipped with Real-Time Kinematic (RTK) differential equipment and airborne data link to construct the airborne reference beacons and provide cooperative navigation services for the wingmen-UAV. Firstly, the navigation filtering framework with inertial sensors as the core is established. Secondly, the non-synchronous compensation filter is constructed by using the kinematic constraint model, which compensates and corrects the non-synchronous air-based position of the leader-UAV, and reduces the effect of delayed measurement on the positioning error of the system. Then the fault diagnosis algorithm is utilized to complete the identification and rejection of abnormal range values in the case of Non-Line-of-Sight (NOLS). Finally, the navigation parameters are solved by the Kalman filter. Simulation results show that the non-synchronous compensated filtering proposed in this paper can improve the absolute positioning accuracy by 55%, which effectively improves the cooperative navigation performance and robustness under the presence of random time delay in the measurement information.

Withdrawal model for fiber motions in the tuft disentanglement

Tuft disentanglement involves the principal actions of opening and carding, which are essential processing in textile technology. In this article, tuft disentanglement is modeled as fiber withdrawal considering the fiber interactions within the tuft. Based on the reasonable tuft model, the kinematic constraints were constructed in the disentanglement considering the carding essence and fiber interactions. Combined with the dynamic equation, the state of the fibers can be solved as a linear complementarity problem due to the complementarity in the fiber interactions. The withdrawal forces verified the simulations, which capture the qualitative features of experiments. Also, the effect of the withdrawal parameters on disentanglement was studied. The simulation results showed that the withdrawal forces increased with increasing withdrawal velocities and decreasing gauge lengths. The simulation results are consistent with the experiments. The proposed computational framework can be extended for predicting the mechanical behaviors of other random fibrous materials involving fiber interactions.

Improving Vehicle Heading Angle Accuracy Based on Dual-Antenna GNSS/INS/Barometer Integration Using Adaptive Kalman Filter

High-accuracy heading angle is significant for estimating autonomous vehicle attitude. By integrating GNSS (Global Navigation Satellite System) dual antennas, INS (Inertial Navigation System), and a barometer, a GNSS/INS/Barometer fusion method is proposed to improve vehicle heading angle accuracy. An adaptive Kalman filter (AKF) is designed to fuse the INS error and the GNSS measurement. A random sample consensus (RANSAC) method is proposed to improve the initial heading angle accuracy applied to the INS update. The GNSS heading angle obtained by a dual-antenna orientation algorithm is additionally augmented to the measurement variable. Furthermore, the kinematic constraint of zero velocity in the lateral and vertical directions of vehicle movement is used to enhance the accuracy of the measurement model. The heading errors in the open and occluded environment are 0.5418° (RMS) and 0.636° (RMS), which represent reductions of 37.62% and 47.37% compared to the extended Kalman filter (EKF) method, respectively. The experimental results demonstrate that the proposed method effectively improves the vehicle heading angle accuracy.

An improved methodology to restrict the range of motion of mechanical joints

Joints with rotational degrees of freedom, for instance, revolute, spherical, or universal joints, are commonly utilized in real-world scenarios. In the multibody systems methodology, mechanical joints usually are formulated as classical kinematic constraints such that there is no restriction of the range of motion (RoM) of the joint. Thus, the formulation must include additional restrictions to prevent the joints from performing unacceptable movements and to avoid unrealistic configurations of the connected bodies. Therefore, the aim of this work is to propose a methodology to restrict the RoM of mechanical joints. Joint resistance moments are applied to the bodies connected by the joint to mimic the dissipative behavior of the materials constituent of joints and to prevent unacceptable configurations of those bodies. The proposed methodology aims to extend and improve a previously published study, specifically in the definition of the RoM limits, calculation of the penalty moments, and establishment of their direction of application. Enhanced methods to deal with the detection of unacceptable joint configurations, namely the elliptical and polynomial approaches, are proposed. A parametrization procedure is described to correctly calculate the direction of the penalty moments to apply to the connected bodies. The methodology is investigated in the dynamic modeling and simulation of one demonstrative example of application, namely a simple pendulum. A parametric analysis is performed to assess the influence of the methodology parameters in the response of the model. The methodology allows the correct restriction of the RoM of joints, while preserving the mechanical energy of the system.

Online Multi-Agent Task Assignment and Path Finding With Kinematic Constraint in the Federated Internet of Things

Online Multi-Agent Task Assignment and Path Finding With Kinematic Constraint in the Federated Internet of Things

Design And Analysis of Flapping Wing Aircraft Based on Crank Mechanism

This paper is proposed a flapping wing aircraft based on the crank slider mechanism to solve the problems of the two flapping wing structures, such as synchronization and excessive local stress common to existing ornithopters. MATLAB is used to solve the equations to determine the dimensions of the individual components, and the 3D model is designed by SolidWorks software. The static analysis on flapping wings, the static stress, and the static strain distribution map of flapping wings are carried out. Moreover, the mechanism of flapping wing aircraft is modeled in Adams software, which simulates the actual structure by designing the kinematic constraint relationships between the components. It was concluded that the flapping wing could achieve a flapping angle of 30 degrees in one cycle, which was consistent with the simulation results by MATLAB. Furthermore, it was found that the first principal stress of the danger point was less than the yield strength of the material to determine the rationality of material selection. Finally, the fluid trace distribution on the upper and lower sides of the flapping wings was analyzed, which was consistent with the actual situation.

A yarn-scale woven fabric model including significant slippage formulated within the Arbitrary Lagrangian Eulerian framework

A numerical model is proposed to simulate significant yarn slippage and unweaving in woven fabrics using the Arbitrary Lagrangian Eulerian (ALE) method. Woven fabrics were modeled at the yarn scale using 1D ALE elements with additional slip displacement degrees of freedom (DOF). The relatively weak bending stiffness of the yarn was included using a rotation-free approach. A weave kinematic constraint between crossing yarns allowed an efficient description of the deformation modes due to the yarn assembly such as in-plane shear. In particular, normal compaction at weave points was taken into account using an additional crimp amplitude DOF and couplings of the fabric’s cohesion with the normal and lateral compaction were considered. To deal with yarn unweaving, a specific void-ALE 1D element was developed in order to avoid remeshing, time-step reduction (explicit scheme) and early deactivation of the weave kinematic constraint. To demonstrate the capabilities of this numerical model, common characterization tests such as in-plane and out-of-plane pullouts, which induced unweaving were simulated. Finally, a first forming simulation on a hemisphere was performed to verify whether the cohesion of the fabric remained well represented in situations without loss of cohesion before simulating forming on a prismatic punch involving significant yarn slippage.

KinFit: A Kinematic Fitting Package for Hadron Physics Experiments

A kinematic fitting package, KinFit, based on the Lagrange multiplier technique has been implemented for generic hadron physics experiments. It is particularly suitable for experiments where the interaction point is unknown, such as experiments with extended target volumes. The KinFit package includes vertex finding tools and fitting with kinematic constraints, such as mass hypothesis and four-momentum conservation, as well as combinations of these constraints. The new package is distributed as an open source software via GitHub. This paper presents a comprehensive description of the KinFit package and its features, as well as a benchmark study using Monte Carlo simulations of the pprightarrow pK^+Lambda rightarrow pK^+ppi ^- reaction. The results show that KinFit improves the parameter resolution and provides an excellent basis for event selection.

Automated guided vehicle dispatching and routing integration via digital twin with deep reinforcement learning

The manufacturing industry has witnessed a significant shift towards high flexibility and adaptability, driven by personalized demands. However, automated guided vehicle (AGV) dispatching optimization is still challenging when considering AGV routing with the spatial-temporal and kinematics constraints in intelligent production logistics systems, limiting the evolving industry applications. Against this backdrop, this paper presents a digital twin (DT)-enhanced deep reinforcement learning-based optimization framework to integrate AGV dispatching and routing at both horizontal and vertical levels. First, the proposed framework leverages a digital twin model of the shop floor to provide a simulation environment that closely mimics the actual manufacturing process, enabling the AGV dispatching agent to be trained in a realistic setting, thus reducing the risk of finding unrealistic solutions under specific shop-floor settings and preventing time-consuming trial-and-error processes. Then, the AGV dispatching with the routing problem is modeled as a Markov Decision Process to optimize tardiness and energy consumption. An improved dueling double deep Q network algorithm with count-based exploration is developed to learn a better-dispatching policy by interacting with the high-fidelity DT model that integrates a static path planning agent using A* and a dynamic collision avoidance agent using a deep deterministic policy gradient to prevent the congestion and deadlock. Experimental results show that our method outperforms four state-of-the-art methods with shorter tardiness, lower energy consumption, and better stability. The proposed method provides significant potential to utilize the digital twin and reinforcement learning in the decision-making and optimization of manufacturing processes.

Real-time interpolation with low-pass filtering for five-axis hybrid machining robots

This paper proposes a new interpolation approach for five-axis hybrid robots to enhance the surface quality and efficiency of machining processes. Hybrid robots have the potential to manufacture large, complex structural parts with high flexibility and a favorable load-to-weight ratio. To interpolate G01 commands, the proposed method implements finite impulse response (FIR) filters rather than splines. These filters smoothly synchronize the motions of tool center points (TCPs) and tool orientation vectors (TOVs), and are designed for each linear segment online with geometric programming while considering joint constraints. Additionally, the adjacent linear segments are locally blended with bounded geometric errors under kinematic constraints. The proposed method generates time-optimal trajectories with jerk-limited joint motions in real-time, making it more effective than current interpolation methods. The effectiveness of the proposed method is verified through the flank milling operation on aluminum alloy.