Search Results (54)

This work systematically addresses the dual challenges of non-inertial dynamic coupling and kinematic constraint redundancy encountered in dynamic modeling of serial–parallel–serial hybrid robotic mechanisms, and proposes an improved Newton–Euler modeling method with constraint compensation. Taking the Skiing Simulation Platform with 6-DOF as the research mechanism, the inverse kinematic model of the closed-chain mechanism is established through $G_F$ set theory, with explicit analytical expressions derived for the motion parameters of limb mass centers. Introducing a principal inertial coordinate system into the dynamics equations, a recursive algorithm incorporating force/moment coupling terms is developed. Numerical simulations reveal a 9.25% periodic deviation in joint moments using conventional methods. Through analysis of the mechanism’s intrinsic properties, it is identified that the lack of angular momentum conservation constraints on the end-effector in non-inertial frames leads to system controllability degradation. Accordingly, a constraint compensation strategy is proposed: establishing linearly independent differential algebraic equations supplemented with momentum/angular momentum balance equations for the end platform. Co-Simulation results demonstrate that the optimized model reduces the maximum relative error of actuator joint moments to 0.98%, and maintains numerical stability across the entire configuration space. The constraint compensation framework provides a universal solution for dynamics modeling of complex closed-chain mechanisms, validated through applications in flight simulators and automotive driving simulators. Full article

For unmanned aerial vehicles with long-duration autonomous missions, efficient energy management is critically important. One of the most promising solutions is solar power, the implementation of which requires the continuous orientation tracking of the Sun’s position. This study presents a three-axis active solar tracking system based on a gimbal mount, providing full kinematic control of the panel in space. A mathematical model of orientation is developed using the Earth-Centered Inertial, local geographic frame, and unmanned aerial vehicle body coordinate systems. An aerodynamic analysis is conducted, including a quantitative assessment of drag, lift, and torque on the panel. Based on the obtained characteristics, limiting conditions for the safe operation of the tracker are formulated. An adaptive control algorithm is introduced, minimizing a generalized objective function that accounts for angular deviation, aerodynamic loads, and current energy balance. Numerical simulations are described, demonstrating system stability under various scenarios: turbulence, maneuvers, power limitations, and sensor errors. The results confirm the effectiveness of the proposed approach under real-world operating conditions. Full article

Precision positioning in orchards relies on Global Navigation Satellite System and Inertial Navigation System (GNSS/INS) integration. However, dense foliage often causes GNSS blockages, degrading accuracy and robustness. This paper proposes an optimized GNSS/INS integrated navigation method based on a hybrid Gated Recurrent Unit (GRU)–Transformer model (GRU-T). The GRU–Transformer hybrid dynamically adjusts the process noise covariance matrix within an error-state Extended Kalman Filter (ES-EKF) framework to address non-stationary noise and signal outages. Forest field tests demonstrate that GRU-T significantly improves positioning accuracy. Compared with the conventional ES-EKF, the proposed method achieves reductions in position root mean square error (PRMSE) of 48.74% (East), 41.94% (North), and 61.59% (Up), and reductions in velocity root mean square error (VRMSE) of 71.5% (East), 39.31% (North), and 56.48% (Up) in the East–North–Up (ENU) coordinate frame. The GRU-T model effectively captures both short- and long-term temporal dependencies and meets real-time, high-frequency sampling requirements. These results indicate that the GRU–Transformer hybrid model enhances the accuracy and robustness of GNSS/INS navigation in complex orchard environments, offering technical support for high-precision positioning in intelligent agricultural machinery systems. Full article

The hybrid laser inertial navigation system (INS) is increasingly vital for high precision under high-dynamic, long-duration conditions, especially in complex aircraft environments. Key components like the base, platform, and inner/outer frames significantly impact system accuracy and stability through thseir static and dynamic characteristics. This study focuses on minimizing deviations in the INS body coordinate system caused by elastic deformation under high overload by developing a mechanical simulation model of a rotational modulation structure and a structural model of the outer frame assembly. A reliability analysis model is established, considering both functional and structural strength failures. To address uncertainties from manufacturing, technical conditions, material selection, and assembly errors, a global sensitivity analysis based on Bayesian inference evaluates parameter contributions to functional failure probability, using a sample size of N1 = 5 × 10⁵. Additionally, uncertainty analysis via Sobol sequence sampling (N2 = 10,000) examines the impact of mean design parameter variations on failure probability for ZL107 and SiCp/Al aluminum matrix composite frames. Experimental verification concludes the study. The results indicate that the SiCp/Al composite material demonstrates superior mechanical performance compared to traditional materials such as the ZL107 aluminum alloy. The uncertainties in the inner frame thickness, inner frame material strength, and outer frame thickness have the most significant impact on the probability of functional failure in the hybrid INS, with sensitivity indices of ${\delta }_6^{P\left\{F\right\}}$ = 0.01657, ${\delta }_2^{P\left\{F\right\}}$ = 0.00873, and ${\delta }_4^{P\left\{F\right\}}$ = 0.00818, respectively. The mechanical properties of the outer frame structure made from SiCp/Al are significantly enhanced, with failure probabilities across three failure modes markedly lower than those of the ZL107 frame, indicating high reliability. In an impact test conducted on the product, the laser gyroscope worked normally, the hybrid laser system function was normal, and the platform angular velocity change corresponding to each impact direction was less than 12 ″/s. The maximum angle change of the inner and outer frames was 0.107°, indicating that the system structure can withstand large overloads and multiple levels of mechanical environments and has good environmental adaptability and reliability. This analytical approach provides a valuable method for reliability evaluation and design of new hybrid INS structures. More importantly, it provides insights into the influence of design parameter uncertainties on navigation accuracy, offering critical support for the advancement of inertial technology. Full article

This paper offers new insights into gravitational interactions within a general non-inertial reference frame. By utilizing symbolic tensor calculus, the study establishes a unified framework that connects time derivatives in non-inertial frames to those in inertial frames. The research introduces new first integrals of motion for a system of many particles in arbitrary non-inertial and barycentric rotating reference frames. These first integrals provide a kinematic and geometric visualization of motion in non-inertial frames. Additionally, a generalized potential energy function is presented for broader applicability. For the gravitational two-body problem, the paper delivers a closed-form, coordinate-free solution for the motion of each body relative to the original frame. Consequently, sufficient conditions for stability against collisions are established within the context of the two-body problem in a non-inertial reference frame. Furthermore, the paper examines the relative orbital motion of spacecraft, presenting a closed-form and coordinate-free solution in the local vertical local horizontal (LVLH) non-inertial frame, which is centered on the center of mass of the main spacecraft. Full article

This study presents a multi-drone proof of concept for efficient forest mapping and autonomous operation, framed within the context of the OPENSWARM EU Project. The approach leverages state-of-the-art open-source simultaneous localisation and mapping (SLAM) frameworks, like LiDAR (Light Detection And Ranging) Inertial Odometry via Smoothing and Mapping (LIO-SAM), and Distributed Collaborative LiDAR SLAM Framework for a Robotic Swarm (DCL-SLAM), seamlessly integrated within the MRS UAV System and Swarm Formation packages. This integration is achieved through a series of procedures compliant with Robot Operating System middleware (ROS), including an auto-tuning particle swarm optimisation method for enhanced flight control and stabilisation, which is crucial for autonomous operation in challenging environments. Field experiments conducted in a forest with multiple drones demonstrate the system’s ability to navigate complex terrains as a coordinated swarm, accurately and collaboratively mapping forest areas. Results highlight the potential of this proof of concept, contributing to the development of scalable autonomous solutions for forestry management. The findings emphasise the significance of integrating multiple open-source technologies to advance sustainable forestry practices using swarms of drones. Full article

The use of inertial measurement units (IMUs) as an alternative to optical marker-based systems has the potential to make gait analysis part of the clinical standard of care. Previously, an IMU-based system leveraging Rauch–Tung–Striebel smoothing to estimate knee angles was assessed using a six-degrees-of-freedom joint simulator. In a clinical setting, however, accurately measuring abduction/adduction and external/internal rotation of the knee joint is particularly challenging, especially in the presence of soft tissue artefacts. In this study, the in vivo IMU-based joint angles of 40 asymptomatic knees were assessed during level walking, under two distinct sensor placement configurations: (1) IMUs fixed to a rigid harness, and (2) IMUs mounted on the skin using elastic hook-and-loop bands (from here on referred to as “skin-mounted IMUs”). Estimates were compared against values obtained from a harness-mounted optical marker-based system. The comparison of these three sets of kinematic signals (IMUs on harness, IMUs on skin, and optical markers on harness) was performed before and after implementation of a REference FRame Alignment MEthod (REFRAME) to account for the effects of differences in coordinate system orientations. Prior to the implementation of REFRAME, in comparison to optical estimates, skin-mounted IMU-based angles displayed mean root-mean-square errors (RMSEs) up to 6.5°, while mean RMSEs for angles based on harness-mounted IMUs peaked at 5.1°. After REFRAME implementation, peak mean RMSEs were reduced to 4.1°, and 1.5°, respectively. The negligible differences between harness-mounted IMUs and the optical system after REFRAME revealed that the IMU-based system was capable of capturing the same underlying motion pattern as the optical reference. In contrast, obvious differences between the skin-mounted IMUs and the optical reference indicated that the use of a harness led to fundamentally different joint motion being measured, even after accounting for reference frame misalignments. Fluctuations in the kinematic signals associated with harness use suggested the rigid device oscillated upon heel strike, likely due to inertial effects from its additional mass. Our study proposes that optical systems can be successfully replaced by more cost-effective IMUs with similar accuracy, but further investigation (especially in vivo and upon heel strike) against moving videofluoroscopy is recommended. Full article

Tripping is the largest cause of falls, and low swing foot ground clearance during the mid-swing phase, particularly at the critical gait event known as Minimum Foot Clearance (MFC), is the major risk factor for tripping-related falls. Intervention strategies to increase MFC height can be effective if applied in real-time based on feed-forward prediction. The current study investigated the capability of machine learning models to classify the MFC into various categories using toe-off kinematics data. Specifically, three MFC sub-categories (less than 1.5 cm, between 1.5 and 2.0 cm, and higher than 2.0 cm) were predicted to apply machine learning approaches. A total of 18,490 swing phase gait cycles’ data were extracted from six healthy young adults, each walking for 5 min at a constant speed of 4 km/h on a motorized treadmill. K-Nearest Neighbor (KNN), Random Forest, and XGBoost were utilized for prediction based on the data from toe-off for five consecutive frames (0.025 s duration). Foot kinematics data were obtained from an inertial measurement unit attached to the mid-foot, recording tri-axial linear accelerations and angular velocities of the local coordinate. KNN, Random Forest, and XGBoost achieved 84%, 86%, and 75% accuracy, respectively, in classifying MFC into the three sub-categories with run times of 0.39 s, 13.98 s, and 170.98 s, respectively. The KNN-based model was found to be more effective if incorporated into an active exoskeleton as the intelligent system to control MFC based on the preceding gait event, i.e., toe-off, due to its quicker computation time. The machine learning-based prediction model shows promise for the prediction of critical MFC data, indicating higher tripping risk. Full article

Installing multi-camera systems and inertial measurement units (IMUs) in self-driving cars, micro aerial vehicles, and robots is becoming increasingly common. An IMU provides the vertical direction, allowing coordinate frames to be aligned in a common direction. The degrees of freedom (DOFs) of the rotation matrix are reduced from 3 to 1. In this paper, we propose a globally optimal solver to calculate the relative poses and scale of generalized cameras with a known vertical direction. First, the cost function is established to minimize algebraic error in the least-squares sense. Then, the cost function is transformed into two polynomials with only two unknowns. Finally, the eigenvalue method is used to solve the relative rotation angle. The performance of the proposed method is verified on both simulated and KITTI datasets. Experiments show that our method is more accurate than the existing state-of-the-art solver in estimating the relative pose and scale. Compared to the best method among the comparison methods, the method proposed in this paper reduces the rotation matrix error, translation vector error, and scale error by 53%, 67%, and 90%, respectively. Full article

In this paper, the kinematic models of the Strapdown Inertial Navigation System (SINS) and its errors on the $\mathbb{SE}\left(3\right)$ group in the Earth-Centered Inertial frame (ECI) are established. On the one hand, with the ECI frame being regarded as the reference, based on the joint representation of attitude and velocity on the $\mathbb{SE}\left(3\right)$ group, the dynamic of the local geographic coordinate system (n-frame) and the body coordinate system (b-frame) evolve on the differentiable manifold, respectively, and the high-order expansion of the Baker–Campbell–Haussdorff equation compensates for the non-commutative motion errors stimulated by strong maneuverability. On the other hand, the kinematics of the left- and right-invariant errors of the n-frame and the b-frame on the $\mathbb{SE}\left(3\right)$ group are separately derived, where the errors of the b-frame completely depend on inertial sensor errors, while the errors of the n-frame rely on position errors and velocity errors. In this way, the errors brought by the inconsistency of the reference coordinate system are tackled, and a novel attitude error definition is introduced to separate and decouple the factors affecting the dynamic of the n-frame errors and the b-frame errors for better attitude estimation. Through a turntable experiment and a car-mounted field experiment, the effectiveness of the proposed kinematic models in estimating attitude has been verified, with a remarkable improvement in yaw angle accuracy in the case of large initial misalignment angles, and the models developed have better robustness compared to the traditional $\mathbb{SE}\left(3\right)$ group-based model. Full article

Recently, inertial measurement units have been gaining popularity as a potential alternative to optical motion capture systems in the analysis of joint kinematics. In a previous study, the accuracy of knee joint angles calculated from inertial data and an extended Kalman filter and smoother algorithm was tested using ground truth data originating from a joint simulator guided by fluoroscopy-based signals. Although high levels of accuracy were achieved, the experimental setup leveraged multiple iterations of the same movement pattern and an absence of soft tissue artefacts. Here, the algorithm is tested against an optical marker-based system in a more challenging setting, with single iterations of a loaded squat cycle simulated on seven cadaveric specimens on a force-controlled knee rig. Prior to the optimisation of local coordinate systems using the REference FRame Alignment MEthod (REFRAME) to account for the effect of differences in local reference frame orientation, root-mean-square errors between the kinematic signals of the inertial and optical systems were as high as 3.8° ± 3.5° for flexion/extension, 20.4° ± 10.0° for abduction/adduction and 8.6° ± 5.7° for external/internal rotation. After REFRAME implementation, however, average root-mean-square errors decreased to 0.9° ± 0.4° and to 1.5° ± 0.7° for abduction/adduction and for external/internal rotation, respectively, with a slight increase to 4.2° ± 3.6° for flexion/extension. While these results demonstrate promising potential in the approach’s ability to estimate knee joint angles during a single loaded squat cycle, they highlight the limiting effects that a reduced number of iterations and the lack of a reliable consistent reference pose inflicts on the sensor fusion algorithm’s performance. They similarly stress the importance of adapting underlying assumptions and correctly tuning filter parameters to ensure satisfactory performance. More importantly, our findings emphasise the notable impact that properly aligning reference-frame orientations before comparing joint kinematics can have on results and the conclusions derived from them. Full article

The main purpose of the present paper is to prove the existence of periodic solutions of the three-body problem in the 3D Kepler formulation. We have solved the same problem in the case when the three particles are considered in an external inertial system. We start with the three-body equations of motion, which are a subset of the equations of motion (previously derived by us) for any number of bodies. In the Minkowski space, there are 12 equations of motion. It is proved that three of them are consequences of the other nine, so their number becomes nine, as much as the unknown trajectories are. The Kepler formulation assumes that one particle (the nucleus) is placed at the coordinate origin. The motion of the other two particles is described by a neutral system with respect to the unknown velocities. The state-dependent delays arise as a consequence of the finite vacuum speed of light. We obtain the equations of motion in spherical coordinates and split them into two groups. In the first group all arguments of the unknown functions are delays. We take their solutions as initial functions. Then, the equations of motion for the remaining two particles must be solved to the right of the initial point. To prove the existence–uniqueness of a periodic solution, we choose a space consisting of periodic infinitely smooth functions satisfying some supplementary conditions. Then, we use a suitable operator which acts on these spaces and whose fixed points are periodic solutions. We apply the fixed point theorem for the operators acting on the spaces of periodic functions. In this manner, we show the stability of the He atom in the frame of classical electrodynamics. In a previous paper of ours, we proved the existence of spin functions for plane motion. Thus, we confirm the Bohr and Sommerfeld’s hypothesis for the He atom. Full article

Our starting point is the covariant coordinate transformation equation of a relativistic positioning system in Minkowski space–time that maps the receiver’s emission coordinates (proper times broadcast by the emitters) to its coordinates in some inertial reference frame. Bancroft’s analytical (closed-form) solution to the basic pseudorange navigation equations with four emitters is recovered, and the subjacent elements are geometrically interpreted. The case of four static beacons is analysed as a clarifying situation. Full article

In most cases, the dynamic investigation of vehicle collisions with stationary obstacles concerns solutions to complex tasks related to the identification of occupant position in the vehicle. The motion of the bodies in the car is determined by the intensity of the inertial coordinate system, also known as moving reference frame, invariably fixed to the vehicle’s center of mass. The focus of the study is on how forces of inertia change their magnitude and direction in the car’s motion. This requires specific analysis carried out by dividing the vehicle trajectory into separate stages according to certain indicators, such as free motion, impact process, and post-impact residual motion. Particular attention has been paid to the impact itself, in which the forces of inertia are the most intense, and their magnitude and direction change abruptly. A solution to a Cauchy problem has been found, in which initial kinematic parameters of the crash process are considered, satisfying the kinematic values at rest position. Full article

Multi-scale modeling of expanding plasmas is crucial for understanding the dynamics and evolution of various astrophysical plasma systems such as the solar and stellar winds. In this context, the Expanding Box Model (EBM) provides a valuable framework to mimic plasma expansion in a non-inertial reference frame, co-moving with the expansion but in a box with a fixed volume, which is especially useful for numerical simulations. Here, fundamentally based on the Vlasov equation for magnetized plasmas and the EBM formalism for coordinates transformations, for the first time, we develop a first principles description of radially expanding plasmas in the EB frame. From this approach, we aim to fill the gap between simulations and theory at microscopic scales to model plasma expansion at the kinetic level. Our results show that expansion introduces non-trivial changes in the Vlasov equation (in the EB frame), especially affecting its conservative form through non-inertial forces purely related to the expansion. In order to test the consistency of the equations, we also provide integral moments of the modified Vlasov equation, obtaining the related expanding moments (i.e., continuity, momentum, and energy equations). Comparing our results with the literature, we obtain the same fluids equations (ideal-MHD), but starting from a first principles approach. We also obtained the tensorial form of the energy/pressure equation in the EB frame. These results show the consistency between the kinetic and MHD descriptions. Thus, the expanding Vlasov kinetic theory provides a novel framework to explore plasma physics at both micro and macroscopic scales in complex astrophysical scenarios. Full article