Body-fixed Reference Frame Research Articles

Adaptive fault-tolerant trajectory tracking control of twin-propeller non-rudder unmanned surface vehicles

This paper studies the fault-tolerant trajectory tracking control problem of twin-propeller non-rudder unmanned surface vehicles (TPNR USVs) subject to propeller faults. Firstly, a propeller model of TPNR USVs is constructed by decomposing propeller thrusts on the body-fixed reference frame. A propeller fault model is also established by taking into account floating and loss-of-effectiveness faults. Secondly, to ensure tracking errors stay in reasonable ranges, a novel guaranteed transient performance method is proposed. Meanwhile, corresponding error transformation functions are constructed. Thirdly, by utilizing the excellent nonlinearity approximation performance of neural networks (NNs), an adaptive fault-tolerant trajectory tracking control scheme, which can guarantee TPNR USVs track the desired trajectory quickly and accurately even in the event of propeller faults, is proposed. Finally, the fault-tolerant trajectory tracking performance analysis demonstrates the efficiency of the proposed control scheme.

GNSS-based precise orbit determination for maneuvering LEO satellites

Maneuverability is essential for low Earth orbit (LEO) satellites to fulfill various operational objectives. However, the precise orbit determination (POD) process might deteriorate due to imperfect satellite orbital dynamics modeling. This article develops a generic POD strategy with maneuver handling for LEO satellites equipped with high-performance spaceborne Global Navigation Satellite System (GNSS) receivers. Given the time span of an executed maneuver, a set of constant thrust accelerations in the satellite body-fixed reference frame is estimated without using a-priori maneuver accelerations. In addition, different numbers of velocity pulses are estimated at predefined epochs determined by the duration of a maneuver. POD experiments are done for the GRACE-FO and Sentinel-3 satellites, for which the orbit maneuvers vary significantly. The orbits are assessed via internal consistency checks and external orbit validations. Internally, in each direction, the agreement between the reduced-dynamic and kinematic orbits reaches a level of 1 cm, which is comparable with the reference day without maneuvers. Externally, comparisons with the official GRACE-FO products and orbits from the Sentinel-3 Copernicus POD Quality Working Group confirm the reliability of the new orbits with maneuver handling. Finally, satellite laser ranging and K-band ranging measurements indicate a 1-cm accuracy of the absolute orbits and a 2-mm accuracy of the GRACE-FO relative orbits. The maneuver handling strategy is tested in the Bernese GNSS Software, consistently developed at the Astronomical Institute of the University of Bern.

Quaternion-Based Adaptive Trajectory Tracking Control of a Rotor-Missile with Unknown Parameters Identification

This paper investigates the adaptive trajectory tracking control problem and the unknown parameter identification problem of a class of rotor-missiles with parametric system uncertainties. First, considering the uncertainty of structural and aerodynamic parameters, the six-degree-of-freedom (6DoF) nonlinear equations describing the position and attitude dynamics of the rotor-missile are established, respectively, in the inertial and body-fixed reference frames. Next, a hierarchical adaptive trajectory tracking controller that can guarantee closed-loop stability is proposed according to the cascade characteristics of the 6DoF dynamics. Then, a memory-augmented update rule of unknown parameters is proposed by integrating all historical data of the regression matrix. As long as the finitely excited condition is satisfied, the precise identification of unknown parameters can be achieved. Finally, the validity of the proposed trajectory tracking controller and the parameter identification method is proved through Lyapunov stability theory and numerical simulations.

Reciprocating Compressor Dynamics Modelling by a Bond Graph Approach

This research is dedicated to developing an analytical physics-based model of a reciprocating compressor based on a bond graph approach. At first, a mathematical model is developed for one-cylinder reciprocating compressor based on multi-body dynamics, particularly considering planar motion of the rigid bodies using body fixed reference frames. All the dynamical equations of motions are represented and linked altogether by the bond graph that simulates a complete system model. The model has unique capability to show forces at various joints, which enhances our understanding of complex system behavior. Moreover, the consequences of changing coefficients of those forces are accentuated. The utility of the model in fault diagnosis and condition monitoring are emphasized by highlighting the effects of a crack in a joint and a dent on cylinder wall. Nonlinear differential equations extracted from bond graph model are solved efficiently using a MATLAB stiff solver. Responses of the model parts are analyzed later by force analysis along with a comparison with a previous research to examine model validity.

Six degree-of-freedom body-fixed hovering over unmapped asteroids via LIDAR altimetry and reinforcement meta-learning

We optimize a six degrees of freedom hovering policy using reinforcement meta-learning. The policy maps flash LIDAR measurements directly to on/off spacecraft body-frame thrust commands, allowing hovering at a fixed position and attitude in the asteroid body-fixed reference frame. Importantly, the policy does not require position and velocity estimates, and can operate in environments with unknown dynamics, and without an asteroid shape model or navigation aids. Indeed, during optimization the agent is confronted with a new randomly generated asteroid for each episode, insuring that it does not learn an asteroid's shape, texture, or environmental dynamics. This allows the deployed policy to generalize well to novel asteroid characteristics, which we demonstrate in our experiments. Moreover, our experiments show that the optimized policy adapts to actuator failure and sensor noise. Although the policy is optimized using randomly generated synthetic asteroids, it is tested on two shape models from actual asteroids: Bennu and Itokawa. We find that the policy generalizes well to these shape models. The hovering controller has the potential to simplify mission planning by allowing asteroid body-fixed hovering immediately upon the spacecraft's arrival to an asteroid. This in turn simplifies shape model generation and allows resource mapping via remote sensing immediately upon arrival at the target asteroid.

Simulation of collision-induced absorption spectra based on classical trajectories and ab initio potential and induced dipole surfaces. I. Case study of N2-N2 rototranslational band.

This paper presents theoretical formalism and some results of the collision-induced absorption (CIA) spectral simulation based on the classical trajectory analysis. Our consideration relies on the use of ab initio potential energy and dipole moment surfaces for two interacting rigid monomers. Rigorous intermolecular Hamiltonian is represented and used in the body-fixed reference frame. The complete set of dynamical equations with Boltzmann-weighted initial conditions is solved to render a large number of classical trajectories. The spectral shape is calculated as an ensemble-averaged Fourier spectrum issued from the time-dependent induced dipole along individual scattering trajectories. Considering a pair of N2 molecules as an example, we have calculated the rototranslational CIA band profiles at T = 78, 89, 109, 129, 149, 179, 228, 300, and 343 K. The classical trajectory-based spectral shape was corrected to satisfy the quantum principle of detailed balance. Good accuracy of our semiclassical approach was demonstrated by comparison with available experimental data as well as with results of the previously published purely quantum simulation by Karman et al. [J. Chem. Phys. 142, 084306 (2015)] in which the same ab initio calculated N2-N2 potential energy and induced dipole moment surfaces were used.

Distributed Formation Control based on Orientation Alignment and Position Estimation

Formation control is studied for single-and double-integrators on the plane based on orientation alignment and position estimation. It is assumed that agents measure the relative positions of their neighbors with respect to their own local body-fixed reference frames without any common sense of orientation. The proposed control strategy consists of an orientation alignment, a position estimation, and a position control law. It is shown that the proposed control strategy allows the agents to achieve the desired formation if the interaction graph is uniformly connected and the orientation angles belong to an interval with arc length less than π.

Characterizing the astrophysical S factor for C12+C12 fusion with wave-packet dynamics

A quantitative study of the astrophysically important sub-barrier fusion of $^{12}$C+$^{12}$C is presented. Low-energy collisions are described in the body-fixed reference frame using wave-packet dynamics within a nuclear molecular picture. A collective Hamiltonian drives the time propagation of the wave-packet through the collective potential-energy landscape. The fusion imaginary potential for specific dinuclear configurations is crucial for understanding the appearance of resonances in the fusion cross section. The theoretical sub-barrier fusion cross sections explain some observed resonant structures in the astrophysical S-factor. These cross sections monotonically decline towards stellar energies. The structures in the data that are not explained are possibly due to cluster effects in the nuclear molecule, which are to be included in the present approach.

Horizontal path-following control for deep-sea work-class ROVs based on a fuzzy logic system

ABSTRACTA path-following control scheme for deep-sea work-class remotely operated vehicles (ROVs) subjected to disturbing forces and moments generated by parameter variations, ocean currents, umbilical cables and other unknown disturbances is designed in this paper. The disturbing forces and moments could be obtained based on a mathematical model of ROVs in a body-fixed reference frame. A fuzzy logic system (FLS) was used to approximate the forces and moments, and then an adaptive speed controller (used as an inner loop of the ROVs’ hover and path-following control) based on a force and moment compensator was designed. The results of numerical simulations and underwater experiments indicated that the disturbing forces and moments acting on ROVs can be approximated precisely by using the FLS, and the designed controller achieves strong anti-disturbance ability, tracking performance and robustness.

Screw and Lie group theory in multibody kinematics

After three decades of computational multibody system (MBS) dynamics, current research is centered at the development of compact and user-friendly yet computationally efficient formulations for the analysis of complex MBS. The key to this is a holistic geometric approach to the kinematics modeling observing that the general motion of rigid bodies and the relative motion due to technical joints are screw motions. Moreover, screw theory provides the geometric setting and Lie group theory the analytic foundation for an intuitive and compact MBS modeling. The inherent frame invariance of this modeling approach gives rise to very efficient recursive O ( n ) algorithms, for which the so-called “spatial operator algebra” is one example, and allows for use of readily available geometric data. In this paper, three variants for describing the configuration of tree-topology MBS in terms of relative coordinates, that is, joint variables, are presented: the standard formulation using body-fixed joint frames, a formulation without joint frames, and a formulation without either joint or body-fixed reference frames. This allows for describing the MBS kinematics without introducing joint reference frames and therewith rendering the use of restrictive modeling convention, such as Denavit–Hartenberg parameters, redundant. Four different definitions of twists are recalled, and the corresponding recursive expressions are derived. The corresponding Jacobians and their factorization are derived. The aim of this paper is to motivate the use of Lie group modeling and to provide a review of different formulations for the kinematics of tree-topology MBS in terms of relative (joint) coordinates from the unifying perspective of screw and Lie group theory.

Required coefficient of friction in the anteroposterior and mediolateral direction during turning at different walking speeds.

This study investigated the required coefficient of friction (RCOF) and the tangent of center of mass (COM)–center of pressure (COP) angle in the mediolateral (ML) and anteroposterior (AP) directions during turning at different walking speeds. Sixteen healthy young adults (8 males and 8 females) participated in this study. The participants were instructed to conduct trials of straight walking and 90° step and spin turns to the right at each of three self-selected speeds (slow, normal, and fast). The ML and AP directions during turning gait were defined using the orientation of the pelvis to construct a body-fixed reference frame. The RCOF values and COM–COP angle tangent in the ML direction during turning at weight acceptance phase were higher than those during straight walking, and those values increased with increasing walking speed. The ML component of the RCOF and COM–COP tangent values during weight acceptance for step turns were higher than those for spin turns. The mean centripetal force during turning tended to increase with an increase in walking speed and had a strong positive correlation with the RCOF values in the ML direction (R = 0.97 during the weight acceptance phase; R = 0.95 during the push-off phase). Therefore, turning, particularly step turn, is likely to cause lateral slip at weight acceptance because of the increased centripetal force compared with straight walking. Future work should test at-risk population and compare with the present results.

A computationally efficient safety assessment for collaborative robotics applications

Safety during interaction with unstructured and dynamic environments is now a well established requirement for complex robotic systems. A wide variety of approaches focus on the introduction of safety evaluation methods in order to shape a consequent safety-oriented control strategy, able to reactively prevent collisions between the robot and potential obstacles, including a human being. This paper presents a new safety assessment, named kinetostatic safety field, that captures the risk in the vicinity of an arbitrary rigid body “source of danger” (e.g. an obstacle, a human body part or a robot link) moving in R3. The safety field depends on the position and velocity of the body but it is also influenced by its real shape and size, exploiting its triangular mesh. The introduction of a body-fixed reference frame in the definition of the field provides closed form computability and an effective computation time reduction, that allows for real-time applications. In particular, intensive computations, connected to the specific body geometry, can be performed only once and off-line, ensuring a fast and constant on-line computation time, independently of the number of mesh elements. Furthermore, we combine the safety field concept with a safety-oriented reactive control strategy for redundant manipulators. Our approach allows to enhance safety in several real-time collision avoidance scenarios, including collision avoidance with potential obstacles, self-collision avoidance and safe human–robot coexistence. The proposed control strategy is validated through experiments performed on an ABB FRIDA dual arm robot.

Towards an Approach to 6 DOF Inertial Kinematics

Abstract: The interest of computer-aided investigations of structure motions in maritime applications has become more relevant during the last years. The present work deals with the 6DOF (six degrees of freedom) motion-simulation of a free floating vessel in a seaway. A comparison between the calculation of forces and moments in the body-fixed system using the Kirchhoff-Motion-Equations and the calculation within the inertial coordinate system is shown. For this purpose, the relevant equations are defined in the inertial reference frame. Special attention applies to the matrices of mass and moment of inertia. Due to hydrodynamic effects in maritime applications and the transformation from a moving body-fixed reference frame, these matrices are time varying in the inertial reference frame. Finally, a comparison of the registered ship motions in the body-fixed and the inertial reference frame is presented.

Shape model, reference system definition, and cartographic mapping standards for comet 67P/Churyumov-Gerasimenko – Stereo-photogrammetric analysis of Rosetta/OSIRIS image data

We analyzed more than 200 OSIRIS NAC images with a pixel scale of 0.9−2.4 m/pixel of comet 67P/Churyumov-Gerasimenko (67P) that have been acquired from onboard the Rosetta spacecraft in August and September 2014 using stereo-photogrammetric methods (SPG). We derived improved spacecraft position and pointing data for the OSIRIS images and a high-resolution shape model that consists of about 16 million facets (2 m horizontal sampling) and a typical vertical accuracy at the decimeter scale. From this model, we derive a volume for the northern hemisphere of 9.35 km3 ± 0.1 km3. With the assumption of a homogeneous density distribution and taking into account the current uncertainty of the position of the comet’s center-of-mass, we extrapolated this value to an overall volume of 18.7 km3 ± 1.2 km3, and, with a current best estimate of 1.0 × 1013 kg for the mass, we derive a bulk density of 535 kg/m3 ± 35 kg/m3. Furthermore, we used SPG methods to analyze the rotational elements of 67P. The rotational period for August and September 2014 was determined to be 12.4041 ± 0.0004 h. For the orientation of the rotational axis (z-axis of the body-fixed reference frame) we derived a precession model with a half-cone angle of 0.14◦, a cone center position at 69.54◦/64.11◦ (RA/Dec J2000 equatorial coordinates), and a precession period of 10.7 days. For the definition of zero longitude (x-axis orientation), we finally selected the boulder-like Cheops feature on the big lobe of 67P and fixed its spherical coordinates to 142.35◦ right-hand-rule eastern longitude and –0.28◦ latitude. This completes the definition of the new Cheops reference frame for 67P. Finally, we defined cartographic mapping standards for common use and combined analyses of scientific results that have been obtained not only within the OSIRIS team, but also within other groups of the Rosetta mission.

Rankine Source Method for Ship–Ship Interaction Problems

A Rankine source method is extended and applied to ship–ship interaction problems. The method covers the nonlinear steady flow and linear seakeeping in the frequency domain. The nonlinear steady flow solution accounts for the nonlinear free-surface conditions, ship wave, and dynamic trim and sinkage. Periodic flow due to waves is linearized with respect to the wave amplitude, taking into account interactions with the nonlinear steady flow following Hachmann approach, which considers the steady perturbation potential as constant in the body-fixed reference frame. This is advantageous for the prediction of ship motions at moderate to high Froude numbers. In this context, a new formulation of the boundary condition for the multibody case is derived. Two examples are considered, overtaking in calm water and replenishment at sea. For a feeder vessel overtaken by a container ship, horizontal forces and yaw moment are computed and compared with reference data. As an example of replenishment operation, interaction between a frigate and a supply vessel is studied. Ship motions are computed for two relative positions and three forward speeds and compared with model test data for the largest forward speed. The Rankine source method proves as more accurate compared with a zero-speed freesurface Green function method. [DOI: 10.1115/1.4029316]

Mixed quantum/classical theory for inelastic scattering of asymmetric-top-rotor + atom in the body-fixed reference frame and application to the H₂O + He system.

The mixed quantum/classical theory (MQCT) for inelastic molecule-atom scattering developed recently [A. Semenov and D. Babikov, J. Chem. Phys. 139, 174108 (2013)] is extended to treat a general case of an asymmetric-top-rotor molecule in the body-fixed reference frame. This complements a similar theory formulated in the space-fixed reference-frame [M. Ivanov, M.-L. Dubernet, and D. Babikov, J. Chem. Phys. 140, 134301 (2014)]. Here, the goal was to develop an approximate computationally affordable treatment of the rotationally inelastic scattering and apply it to H2O + He. We found that MQCT is somewhat less accurate at lower scattering energies. For example, below E = 1000 cm(-1) the typical errors in the values of inelastic scattering cross sections are on the order of 10%. However, at higher scattering energies MQCT method appears to be rather accurate. Thus, at scattering energies above 2000 cm(-1) the errors are consistently in the range of 1%-2%, which is basically our convergence criterion with respect to the number of trajectories. At these conditions our MQCT method remains computationally affordable. We found that computational cost of the fully-coupled MQCT calculations scales as n(2), where n is the number of channels. This is more favorable than the full-quantum inelastic scattering calculations that scale as n(3). Our conclusion is that for complex systems (heavy collision partners with many internal states) and at higher scattering energies MQCT may offer significant computational advantages.

Consistent Structural Linearization in Flexible Aircraft Dynamics with Large Rigid-Body Motion

This paper investigates the linearization, using perturbation methods, of the structural deformations in the nonlinear flight dynamic response of aircraft with slender, flexible wings. The starting point is the coupling of a displacement-based geometrically nonlinear flexible-body dynamics formulation with a three-dimensional unsteady vortex lattice method. This is followed by a linearization of the structural degrees of freedom, which are assumed to be small in a body-fixed reference frame. The translations and rotations of that reference frame and their time derivatives, which describe the vehicle flight dynamics, can still be arbitrarily large. The resulting system preserves all couplings between rigid and elastic motions and can be projected onto a few vibration modes of the unconstrained aircraft with geometrically nonlinear static deflections at a trim condition. Equally, the unsteady aerodynamics can be approximated on a fixed lattice defined by the deformed static geometry. Numerical studies on a representative high-altitude long-endurance aircraft are presented to illustrate the approach. The results show an improvement compared to those obtained using the mean-axes approximation.

Mixed quantum/classical theory of rotationally and vibrationally inelastic scattering in space-fixed and body-fixed reference frames

We formulated the mixed quantum/classical theory for rotationally and vibrationally inelastic scattering process in the diatomic molecule + atom system. Two versions of theory are presented, first in the space-fixed and second in the body-fixed reference frame. First version is easy to derive and the resultant equations of motion are transparent, but the state-to-state transition matrix is complex-valued and dense. Such calculations may be computationally demanding for heavier molecules and/or higher temperatures, when the number of accessible channels becomes large. In contrast, the second version of theory requires some tedious derivations and the final equations of motion are rather complicated (not particularly intuitive). However, the state-to-state transitions are driven by real-valued sparse matrixes of much smaller size. Thus, this formulation is the method of choice from the computational point of view, while the space-fixed formulation can serve as a test of the body-fixed equations of motion, and the code. Rigorous numerical tests were carried out for a model system to ensure that all equations, matrixes, and computer codes in both formulations are correct.

Semiclassical description of quantum rotator in terms of SU(2) coherent states

We introduce coordinates of the rigid body (rotator) using mutual positions between body-fixed and space-fixed reference frames. Wave functions that depend on such coordinates can be treated as scalar functions of the group SU(2). Irreducible representations of the group SU(2) × SU(2) in the space of such functions describe their possible transformations under independent rotations of the both reference frames. We construct sets of the corresponding group SU(2) × SU(2) Perelomov coherent states (CS) with a fixed angular momentum j of the rotator as special orbits of the latter group. Minimization of different uncertainty relations is discussed. The classical limit corresponds to the limit j → ∞. Considering Hamiltonians of rotators with different characteristics, we study the time evolution of the constructed CS. In some cases, the CS time evolution is completely or partially reduced to their parameter time evolution. If these parameters are chosen as Euler angles, then they obey the Euler equations in the classical limit. Quantum corrections to the motion of the quantum rotator can be found from exact equations on the CS parameters.

Body-fixed relativistic molecular Hamiltonian and its application to nuclear spin-rotation tensor: Linear molecules

The relativistic molecular Hamiltonian written in the body-fixed frame of reference is the basis for high-precision calculations of spectroscopic parameters involving nuclear vibrations and/or rotations. Such a Hamiltonian that describes electrons fully relativistically and nuclei quasi-relativistically is just developed for semi-rigid nonlinear molecules [Y. Xiao and W. Liu, J. Chem. Phys. 138, 134104 (2013)]. Yet, the formulation should somewhat be revised for linear molecules thanks to some unusual features arising from the redundancy of the rotation around the molecular axis. Nonetheless, the resulting isomorphic Hamiltonian is rather similar to that for nonlinear molecules. Consequently, the relativistic formulation of nuclear spin-rotation (NSR) tensor for linear molecules is very much the same as that for nonlinear molecules. So is the relativistic mapping between experimental NSR and NMR.