Angle Parameterization Research Articles

Follower’s guide rail slope angle parameterization research for special high-speed cylinder cam mechanism

Follower’s guide rail slope angle parameterization research for special high-speed cylinder cam mechanism

An adaptive grouping sonar-inertial odometry for underwater navigation

This paper presents a sonar-inertial navigation system with an adaptive grouping optimization framework, which tightly couples inertial measurements with acoustic data from forward-looking sonar (FLS). The system’s front-end uses the sonar-inertial constraint-based feature matching (SICFM) to increase the accuracy and robustness of data association. SICFM is designed by incorporating two novel measures. Firstly, it combines prior motion information to refine the feature search region. Then, a Gaussian-gamma mixture model is formulated to reduce the impact of speckle noise on the selection of matching points. In the back-end, an adaptive grouping factor graph optimization framework is established. A frame manager is designed using the solvability of motion estimation to dynamically group sonar frames, thereby ensuring stable feature tracking for factor graph optimization. Pre-integration-based inertial measurement factor and reprojection-based sonar measurement factor are constructed as constraints in the optimization, which reduces the dependence on prior knowledge of the scene. Furthermore, an elevation angle parameterization is introduced, aiming at the nonlinear projection of sonar features. The evaluation is presented in simulation and real-world experiments, which validate our proposed algorithm in terms of robust localization with high accuracy.

Explorations of the holonomy of a rolling sphere

Consider a rigid body rolling with one point in contact with a fixed surface. Now suppose that the instantaneous point of contact traces out a closed path. As a demonstration of a phenomenon known as holonomy, the body will typically not return to its original orientation. The simplest demonstration of this phenomenon in rigid body dynamics occurs in the motion of a rolling sphere and finds application to path planning and reorientation of spherical robots. Motivated by earlier works of Bryant and Johnson, we establish expressions for the change in orientation of a rolling sphere after completing a rectangular path. We use numerical methods to show that all possible changes in orientation are possible using a single rectangular path. Based on the Euler angle parameterization of a rotation, we develop a more intuitive method to achieve a desired orientation using three rectangular paths. With regards to applications, the paths we discuss can be employed to achieve any desired reorientation of a spherical robot.

Collaborative optimization for variable stiffness composite laminates using a fiber angle description method based on Archimedean spiral function

When optimizing the fiber orientation of multilayer composite laminates, with the increasing number of layers, the number of design variables increases sharply, resulting in a large amount of computational cost. To address this challenge, this paper proposes a novel discrete fiber angle optimization method based on the Archimedean spiral function and applies it to a collaborative design framework of topology and fiber orientation. The proposed method uses the normal distribution function as the angle selection function in every layer. To prevent convergence issues in optimizing the fiber angle, a new candidate angle weighting formula is proposed. Further, a discrete fiber angle parameterization method based on the Archimedean spiral function for the thickness direction of laminates is presented, which requires only one variable to represent the fiber angle of any two layers in the element. To circumvent the issue of local optima and expand the design space, a collaborative optimization strategy is employed to improve the discrete fiber angle optimization results. Finally, the numerical examples indicate that in comparison to conventional approaches, the correlation of the proposed method with initial values is significantly reduced (σ2=0.00188). Under identical initial conditions, this method can improve the structural stiffness by over 20% at maximum.

Inverse kinematics and workspace analysis of a novel SSRMS-type reconfigurable space manipulator with two lockable passive telescopic links

This study proposes a novel space station remote manipulator system (SSRMS)-type reconfigurable space manipulator to enhance the adaptability of the traditional SSRMS-type manipulators in complex on-orbit tasks. The proposed manipulator has two lockable passive telescopic links (LPTLs) and allows changing their lengths to achieve reconfigurability. The inverse kinematics (IK) and the workspace for this manipulator are minutely analyzed. We develop a new CCDJAP-IK method to solve the IK problem by combining the cyclic coordinate descent (CCD) and joint angle parameterization (JAP) methods. This new method addresses the CCD method's convergence instability and the JAP method's high dependence on the pre-set value of the redundancy parameter. In particular, our approach is insensitive to the initial and singular configurations and can generate multiple exact solutions that satisfy the joint limit constraints. A reachability sphere map captures the proposed manipulator's kinematic capability for the workspace analysis. Then the effects of the two LPTLs on this capability are deeply explored. Based on the results, we propose an information-driven optimal configuration search method. Several typical simulations validate the proposed methods’ effectiveness.

General inverse kinematics method for 7-DOF offset manipulators based on arm angle parameterization

This paper proposes a general numerical methodology of inverse kinematics computation for 7-degree-of-freedom offset manipulators based on arm angle parameterization. First, analytical inverse kinematics solutions for two types of Spherical-Revolute-Spherical manipulators are derived based on arm angle parameterization. Then, the inverse kinematics of the offset manipulator is solved using a simplified manipulator. In each iteration of the algorithm, the inverse solution of the simplified manipulator is used to calculate the position and arm angle error between the actual manipulator and desired value. The error is utilized to compensate the position and arm angle of the simplified manipulator so that the inverse solution of the simplified manipulator gradually approaches the desired solution of the actual manipulator. Moreover, the problems of workspace reduction due to structure simplification and the placement of the iteration point outside of the workspace of the simplified manipulator are optimized. Additionally, the algorithm singularity problem of the offset manipulator is solved via the dual arm angle parameterization method. Finally, the method is validated by numerical simulation and physical experiments.

Human-like redundancy resolution: An integrated inverse kinematics scheme for anthropomorphic manipulators with radial elbow offset

As a mimic of the human arm structure, anthropomorphic manipulators with radial elbow offset (AMREO) are often deployed on humanoid service robots. However, the unique offset leads to difficulties in solving the analytical inverse kinematics (IK), which poses a challenge for further anthropomorphic control. This paper presents an integrated scheme for solving the path-wise IK problem of a 7-DoF AMREO in the position domain. Unlike other approaches, special attention is paid to the naturalness of the arm configuration, with the aim of making AMREO exhibit human-like behavior in human-centered environments. First, an analytical IK solution of AMREO for a single end-effector pose is derived based on the arm angle parameterization. Then, inspired by the habitual arm configurations in human reaching movements, the natural arm configuration mapped to wrist position is proposed for AMREO. To learn the patterns implied therein, a LSTM-based natural arm angle prediction network (NAPN) is designed and trained based on a human demonstration dataset. Finally, a redundancy resolution framework embedded with NAPN is built to generate smooth and natural joint configurations in the path-wise IK tasks. Comparative experiments show that the proposed analytical IK algorithm has better computational efficiency and precision than conventional methods, and can give complete results for one IK call within 4 μs. In addition, continuous path tracking experiments on a real robot validate the effectiveness and anthropomorphism of the redundancy resolution scheme based on NAPN.

Changes in the Local Conformational States Caused by Simple Na+ and K+ Ions in Polyelectrolyte Simulations: Comparison of Seven Force Fields with and without NBFIX and ECC Corrections.

Electrostatic interactions have a determining role in the conformational and dynamic behavior of polyelectrolyte molecules. In this study, anionic polyelectrolyte molecules, poly(glutamic acid) (PGA) and poly(aspartic acid) (PASA), in a water solution with the most commonly used K+ or Na+ counterions, were investigated using atomistic molecular dynamics (MD) simulations. We performed a comparison of seven popular force fields, namely AMBER99SB-ILDN, AMBER14SB, AMBER-FB15, CHARMM22*, CHARMM27, CHARMM36m and OPLS-AA/L, both with their native parameters and using two common corrections for overbinding of ions, the non-bonded fix (NBFIX), and electronic continuum corrections (ECC). These corrections were originally introduced to correct for the often-reported problem concerning the overbinding of ions to the charged groups of polyelectrolytes. In this work, a comparison of the simulation results with existing experimental data revealed several differences between the investigated force fields. The data from these simulations and comparisons with previous experimental data were then used to determine the limitations and strengths of these force fields in the context of the structural and dynamic properties of anionic polyamino acids. Physical properties, such as molecular sizes, local structure, and dynamics, were studied using two types of common counterions, namely potassium and sodium. The results show that, in some cases, both the macroion size and dynamics depend strongly on the models (parameters) for the counterions due to strong overbinding of the ions and charged side chain groups. The local structures and dynamics are more sensitive to dihedral angle parameterization, resulting in a preference for defined monomer conformations and the type of correction used. We also provide recommendations based on the results.

Analysis of Singular Configuration of Robotic Manipulators

Robotic manipulators inevitably encounter singular configurations in the process of movement, which seriously affects their performance. Therefore, the identification of singular configurations is extremely important. However, serial manipulators that do not meet the Pieper criterion cannot obtain singular configurations through analytical methods. A joint angle parameterization method, used to obtain singular configurations, is here creatively proposed. First, an analytical method based on the Jacobian determinant and the proposed method were utilized to obtain their respective singular configurations of the Stanford manipulator. The singular configurations obtained through the two methods were consistent, which suggests that the proposed method can obtain singular configurations correctly. Then, the proposed method was applied to a seven-degree-of-freedom (7-DOF) serial manipulator and a planar 5R parallel manipulator. Finally, the correctness of the singular configurations of the 7-DOF serial manipulator was verified through the shape of the end-effector velocity ellipsoid, the value of the determinant, the value of the condition number, and the value of the manipulability measure. The correctness of singular configurations of the planar 5R parallel manipulator was verified through the value of the determinant, the value of the condition number, and the value of the manipulability measure.

Precise semi-analytical inverse kinematic solution for 7-DOF offset manipulator with arm angle optimization

Seven-degree-of-freedom redundant manipulators with link offset have many advantages, including obvious geometric significance and suitability for configuration control. Their configuration is similar to that of the experimental module manipulator (EMM) in the Chinese Space Station Remote Manipulator System. However, finding the analytical solution of an EMM on the basis of arm angle parameterization is difficult. This study proposes a high-precision, semi-analytical inverse method for EMMs. Firstly, the analytical inverse kinematic solution is established based on joint angle parameterization. Secondly, the analytical inverse kinematic solution for a non-offset spherical-roll-spherical (SRS) redundant manipulator is derived based on arm angle parameterization. The approximate solution of the EMM is calculated in accordance with the relationship between the joint angles of the EMM and the SRS manipulator. Thirdly, the error is corrected using a numerical method through the analytical inverse solution based on joint angle parameterization. After selecting the stride and termination condition, the precise inverse solution is computed for the EMM based on arm angle parameterization. Lastly, case solutions confirm that this method has high precision, and the arm angle parameterization method is superior to the joint angle parameterization method in terms of parameter selection.

The Dynamics Characteristics of Flexible Spacecraft and its Closed-Loop Stability with Passive Control

Passive control is the most popular methodology for flexible spacecraft while it remains an open problem whether the closed-loop performance can be achieved only with passive control subject to the coupling modes of rigid and flexibility. Also, the closed-loop performance of passive PD control based on the dynamics of the Euler angle parameterization of spacecraft, which has been widely used in practice, is yet to be addressed. Towards these challenges, by introducing the input-output exact linearization theory and Lyapunov theory, the authors show that the closed-loop performance for flexible spacecraft with rigid and flexible modes can be achieved by adjusting the parameters of the passive controllers sufficiently large. This is done by firstly transforming the flexible spacecraft dynamics into an exact feedback linearization standard form, and then analyzing the closed-loop performance of flexible spacecraft.

Probing the concept of line tension down to the nanoscale

A novel mechanical approach is developed to explore by means of atom-scale simulation the concept of line tension at a solid-liquid-vapor contact line as well as its dependence on temperature, confinement, and solid/fluid interactions. More precisely, by estimating the stresses exerted along and normal to a straight contact line formed within a partially wet pore, the line tension can be estimated while avoiding the pitfalls inherent to the geometrical scaling methodology based on hemispherical drops. The line tension for Lennard-Jones fluids is found to follow a generic behavior with temperature and chemical potential effects that are all included in a simple contact angle parameterization. Former discrepancies between theoretical modeling and molecular simulation are resolved, and the line tension concept is shown to be robust down to molecular confinements. The same qualitative behavior is observed for water, but the line tension at the wetting transition diverges or converges toward a finite value depending on the range of solid/fluid interactions at play.

Bounded motion design in the Earth zonal problem using differential algebra based normal form methods

Establishing long-term relative bounded motion between orbits in perturbed dynamics is a key challenge in astrodynamics to enable cluster flight with minimum propellant expenditure. In this work, we present an approach that allows for the design of long-term relative bounded motion considering a zonal gravitational model. Entire sets of orbits are obtained via high-order Taylor expansions of Poincare return maps about reference fixed points. The high-order normal form algorithm is used to determine a change in expansion variables of the map into normal form space, in which the phase space behavior is circular and can be easily parameterized by action–angle coordinates. The action–angle representation of the normal form coordinates is then used to parameterize the original Poincare return map and average it over a full phase space revolution by a path integral along the angle parameterization. As a result, the averaged nodal period and drift in the ascending node are obtained, for which the bounded motion conditions are straightforwardly imposed. Sets of highly accurate bounded orbits are obtained, extending over several thousand kilometers, and valid for decades.

Total Least-Squares Iterative Closest Point Algorithm Based on Lie Algebra

In geodetic surveying, input data from two coordinates are needed to compute rigid transformations. A common solution is a least-squares algorithm based on a Gauss–Markov model, called iterative closest point (ICP). However, the error in the ICP algorithm only exists in target coordinates, and the algorithm does not consider the source model’s error. A total least-squares (TLS) algorithm based on an errors-in-variables (EIV) model is proposed to solve this problem. Previous total least-squares ICP algorithms used a Euler angle parameterization method, which is easily affected by a gimbal lock problem. Lie algebra is more suitable than the Euler angle for interpolation during an iterative optimization process. In this paper, Lie algebra is used to parameterize the rotation matrix, and we re-derive the TLS algorithm based on a GHM (Gauss–Helmert model) using Lie algebra. We present two TLS-ICP models based on Lie algebra. Our method is more robust than previous TLS algorithms, and it suits all kinds of transformation matrices.

RELATIVE CAMERA POSE ESTIMATION METHOD USING OPTIMIZATION ON THE MANIFOLD

Abstract. To solve the problem of relative camera pose estimation, a method using optimization with respect to the manifold is proposed. Firstly from maximum-a-posteriori (MAP) model to nonlinear least squares (NLS) model, the general state estimation model using optimization is derived. Then the camera pose estimation model is applied to the general state estimation model, while the parameterization of rigid body transformation is represented by Lie group/algebra. The jacobian of point-pose model with respect to Lie group/algebra is derived in detail and thus the optimization model of rigid body transformation is established. Experimental results show that compared with the original algorithms, the approaches with optimization can obtain higher accuracy both in rotation and translation, while avoiding the singularity of Euler angle parameterization of rotation. Thus the proposed method can estimate relative camera pose with high accuracy and robustness.

A new temperature- and humidity-dependent surface site density approach for deposition ice nucleation

Abstract. Deposition nucleation experiments with Arizona Test Dust (ATD) as a surrogate for mineral dusts were conducted at the AIDA cloud chamber at temperatures between 220 and 250 K. The influence of the aerosol size distribution and the cooling rate on the ice nucleation efficiencies was investigated. Ice nucleation active surface site (INAS) densities were calculated to quantify the ice nucleation efficiency as a function of temperature, humidity and the aerosol surface area concentration. Additionally, a contact angle parameterization according to classical nucleation theory was fitted to the experimental data in order to relate the ice nucleation efficiencies to contact angle distributions. From this study it can be concluded that the INAS density formulation is a very useful tool to describe the temperature- and humidity-dependent ice nucleation efficiency of ATD particles. Deposition nucleation on ATD particles can be described by a temperature- and relative-humidity-dependent INAS density function ns(T, Sice) with ns(xtherm) = 1.88 ×105 · exp(0.2659 · xtherm) [m−2] , (1) where the temperature- and saturation-dependent function xtherm is defined as xtherm = −(T−273.2)+(Sice−1) ×100, (2) with the saturation ratio with respect to ice Sice >1 and within a temperature range between 226 and 250 K. For lower temperatures, xtherm deviates from a linear behavior with temperature and relative humidity over ice. Also, two different approaches for describing the time dependence of deposition nucleation initiated by ATD particles are proposed. Box model estimates suggest that the time-dependent contribution is only relevant for small cooling rates and low number fractions of ice-active particles.

Saturated proportional derivative control of flexible-joint manipulators

In this paper, the control of flexible-joint robotic manipulators while avoiding actuator saturation is investigated. Several proportional derivative controllers are developed, all of which disallow actuator saturation by guaranteeing that the applied torque is less than a specified maximum value. In particular, a Gibbs parameterization of the joint angles is included in the control laws, which allows for an increased control torque as compared to an Euler angle parameterization. An equilibrium point of the closed-loop system is proven to be asymptotically stable using the Lyapunov stability analysis. Moreover, the proposed control laws do not require any knowledge of the [email protected]?s mass, stiffness, or dissipation properties, and as such, are robust to modelling errors. The proposed controllers are tested on a single-link flexible-joint manipulator experimentally and on a two-link flexible-joint manipulator in simulation, and are compared to the performance of controllers found in the literature.

Kinematic design of an anthropomimetic 7-DOF cable-driven robotic arm

In this paper, an anthropomimetic design of a 7-DOF dexterous robotic arm is proposed. Similar to the human arm, the arm consists of three sequentially connected modules, i.e., a 3-DOF shoulder module, a 1-DOF elbow module, and a 3-DOF wrist module. All three arm modules are also driven by cables in order to mimic the driving scheme and functionality of the human muscles. This paper addresses three critical design analysis issues, i.e., the displacement analysis, the tension-closure analysis, and the workspace analysis. A closed-form solution approach is presented for the forward displacement analysis, while the inverse displacement solution is obtained through an efficient optimization algorithm, in which both task-decomposition and dimension-reduction techniques are employed. An effective tension-closure analysis algorithm is also formulated based on the theory of convex analysis. The orientation workspace for the 3- DOF shoulder and wrist modules are then analyzed using a new equi-volumetric partition scheme based on the intuitive Tilt-and-Torsion angle parameterization. An optimization approach is then investigated for the kinematic design of the three joint modules, in which the design objective is to maximize the matched workspace of the robotic arm joints with that of the human arm joints. A research prototype of the 7-DOF cable-driven robotic arm has also been developed in order to demonstrate the anthropomimetic design concept. With a lightweight structure of 1 kg, the cable-driven robotic arm can carry a payload of 5 kg and has motion repeatability of ±2.5mm.

On Cartesian stiffness matrices in rigid body dynamics: an energetic perspective

Several Cartesian stiffness matrices for a single rigid body subject to a conservative force field are developed in this paper. The treatment is based on energetic arguments and an Euler angle parameterization of the rotation of the rigid body is employed. Several new representations for the stiffness matrix are obtained and the relation to other works on Cartesian stiffness matrices and Hessians is illuminated. Additional details are presented with respect to determining the Cartesian stiffness matrix for a pair of rigid bodies, as well as for a system of rigid bodies constrained to a plane.

The relationship of the hyperspherical harmonics toSO(3),SO(4) and orientation distribution functions

The expansion of an orientation distribution function as a linear combination of the hyperspherical harmonics suggests that the analysis of crystallographic orientation information may be performed entirely in the axis-angle parameterization. Practical implementation of this requires an understanding of the properties of the hyperspherical harmonics. An addition theorem for the hyperspherical harmonics and an explicit formula for the relevant irreducible representatives of SO(4) are provided. The addition theorem is useful for performing convolutions of orientation distribution functions, while the irreducible representatives enable the construction of symmetric hyperspherical harmonics consistent with the crystal and sample symmetries.