Spherical Constraint Research Articles

A Self-Calibration Method for Robot End-Effector Using Spherical Constraints

A self-calibration method utilizing spherical constraints is proposed for calibration of robot end-effectors. The method establishes a mathematical model to account for both the geometric errors of the robot and the deformation errors of the end-effector. A nonlinear least-squares parameter identification technique based on spherical constraints is employed to achieve autonomous calibration of the end-effector. Contrasted with methodologies relying on point plane or distance constraints, this novel technique delivers superior positioning accuracy, streamlined operational procedures and enhanced efficiency. Both simulation and experimental validation confirm that the self-calibration method using spherical constraints improves the positioning accuracy of the robot end-effector from 3 mm to 0.3 mm, showing the effectiveness of the method.

An error compensation method for on-machine measuring blade with industrial robot

To achieve the seamless integration of precision grinding blade with timely measured data, an on-machine measurement system employing industrial robot is developed. The limitation to its widespread application lies in the accuracy of measurement, prompting the proposal of an error compensation method to address the measurement error within the implemented blade on-machine measurement system. To address the pre-travel error in the measuring device of the on-machine measurement system, an analysis of the factors influencing the pre-travel error of the contact probe is conducted. Subsequently, pre-travel error data is gathered utilizing the experimental calibration method involving a standard ball, and a prediction model employing the bilinear interpolation algorithm is established to facilitate error compensation. Employing pre-travel error compensation for the analysis of the operating body error in the on-machine measurement system, a spherical center distance constraint error model is derived through closed-loop kinematic calibration of the six-degrees-of-freedom industrial robot. Kinematic parameter error identification is conducted using a hybrid algorithm combining the L-M algorithm and the adaptive factor double-variable DE algorithm. This approach diminishes the spherical center distance measurement error, reducing it from 0.081 mm to 0.016 mm. Subsequently, experiment is conducted to measure blade machining allowances using an on-machine robotic measurement system, comparing the obtained data with measurement from a blue light scanner and a coordinate measuring machine (CMM). The results reveal average absolute deviations of 0.020 mm, 0.015 mm, and 0.016 mm in the three blade cross sections for the on-machine robotic measurement system and the blue light scanner, respectively. Correspondingly, the average absolute deviations for the on-machine robotic measurement system and the CMM in the three blade sections are 0.028 mm, 0.029 mm, and 0.029 mm. Moreover, the on-machine measurement system demonstrates commendable measurement repeatability, with a standard deviation of 0.003 mm.

A lung biopsy path planning algorithm based on the double spherical constraint Pareto and indicators’ importance-correlation degree

Lung cancer has the highest mortality rate among cancers. The commonly used clinical method for diagnosing lung cancer is the CT-guided percutaneous transthoracic lung biopsy (CT-PTLB), but this method requires a high level of clinical experience from doctors. In this work, an automatic path planning method for CT-PTLB is proposed to provide doctors with auxiliary advice on puncture paths. The proposed method comprises three steps: preprocessing, initial path selection, and path evaluation. During preprocessing, the chest organs required for subsequent path planning are segmented. During the initial path selection, a target point selection method for selecting biopsy samples according to biopsy sampling requirements is proposed, which includes a down-sampling algorithm suitable for different nodule shapes. Entry points are selected according to the selected target points and clinical constraints. During the path evaluation, the clinical needs of lung biopsy surgery are first quantified as path evaluation indicators and then divided according to their evaluation perspective into risk and execution indicators. Then, considering the impact of the correlation between indicators, a path scoring system based on the double spherical constraint Pareto and the importance-correlation degree of the indicators is proposed to evaluate the comprehensive performance of the planned paths. The proposed method is retrospectively tested on 6 CT images and prospectively tested on 25 CT images. The experimental results indicate that the method proposed in this work can be used to plan feasible puncture paths for different cases and can serve as an auxiliary tool for lung biopsy surgery.

Research on motion planning system for wall-climbing mobile manipulator for large steel structures welding operation

Purpose The purpose of this study is to address the welding demands within large steel structures by presenting a global spatial motion planning algorithm for a mobile manipulator. This algorithm is based on an independently developed wall-climbing robot, which comprises a four-wheeled climbing mobile platform and a six-degree-of-freedom robotic manipulator, ensuring high mobility and operational flexibility. Design/methodology/approach A convex hull feasible domain constraint is developed for motion planning in the mobile manipulator. For extensive spatial movements, connected sequences of convex polyhedra are established between the composite robot’s initial and target states. The composite robot’s path and obstacle avoidance optimization problem are solved by constraining the control points on B-spline curves. A dynamic spatial constraint rapidlye-xploring random trees-connect (RRTC) motion planning algorithm is proposed for the manipulator, which quickly generates reference paths using spherical spatial constraints at the manipulator’s end, eliminating the need for complex nonconvex constraint modeling. Findings Experimental results show that the proposed motion planning algorithm achieves optimal paths that meet task constraints, significantly reducing computation times in task conditions and shortening operation times in non-task conditions. Originality/value The algorithm proposed in this paper holds certain application value for the realization of automated welding operations within large steel structures using mobile manipulator.

A closed-loop calibration method for serial robots based on position constraints and local area measurement

This paper presents a cost-effective and efficient closed-loop calibration method to enhance the absolute positioning accuracy of industrial robots. The method utilizes an economical and highly accurate set of simple measurement devices, including a device mounted on the robot's end effector and a spherical constraint device positioned within the robot's workspace. A novel local area measurement method is employed for the spherical constraint device, effectively converting position errors into the errors in the sphere center position of the constraint device. Furthermore, the error model considers both kinematic parameter deviations of the robot itself as well as those of the measurement device, along with non-kinematic errors caused by link self-weight. The closed-loop calibration model relies on position constraints, enabling identification and compensation of all error parameters using Levenberg Marquardt method after substituting measured data. The effectiveness of this proposed method is demonstrated through simulation and experimentation. In simulations, average position error reduces from 8.249 mm to 0.8384 mm, while absolute mean difference in sphere center positions obtained using our measurement equipment decreases from 1.206 mm to 0.1027 mm. Significant reductions in both position error and difference in sphere center position are indicated after calibration. This proves that the absolute mean value of the sphere center position difference can be used as the basis for judging the size of the robot's end position error. Experimental results show that absolute mean difference in sphere center position decreases from 0.4319 mm to 0.02869 mm, leading to substantial improvement in overall positioning accuracy.

A novel pose calibration method for laser displacement sensor in the five-axis on-machine measurement system

The five-axis on-machine measurement system, equipped with a laser displacement sensor, offers an effective approach for conducting on-site inspections of freeform surface parts. It is crucial to address the calibration error pertaining to the sensor’s pose, encompassing both the beam direction and the zero position, as it directly impacts the measurement accuracy. This paper presents a new approach for the calibration of a laser displacement sensor’s pose, which is mounted on the spindle of a five-axis gantry machine tool. The proposed method utilizes measurements taken from multiple angles of a standard ball. Through the utilization of spherical constraints and coordinate translation transformation, the Levenberg-Marquardt iteration method is employed to derive the sensor’s beam direction, while the least square method is used to determine the sensor’s zero position. Applying this proposed method, the maximum error in the distance between the centers of the standard double ball is below 0.008 mm, which can meet the precision requirements of on-site inspection of freeform surface parts.

A Lagrange–Newton algorithm for tensor sparse principal component analysis

This paper is concerned with the tensor sparse principal component analysis (TSPCA) by obtaining principal components which are linear combinations of a small subset of the original features for tensorial data. The core mathematical model can be formulated as a nonsmooth nonconvex optimization problem with a polynomial objective function, and with the sparsity constraint and the unit Euclidean spherical constraint. By employing the tools in tensor analysis, along with the variational properties for the involved ℓ 0 -norm, the optimality condition of TSPCA is analysed in terms of stationary points. To well resolve the problem, we reformulate the stationary conditions into the Lagrange stationary equation system via the property of the projection operator onto the sparsity constraint set. With special emphasis on the Jacobian nonsingularity of the corresponding nonlinear system, we propose the Lagrange–Newton algorithm for pursuing the stationary point, which serves as a promising approximation of the optimal solution to TSPCA. The locally quadratic convergence rate is also established under mild conditions. Numerical experiments illustrate the effectiveness of our proposed TSPCA approach in terms of the solution accuracy as well as the computation time.

Universality class of the mode-locked glassy random laser

By means of enhanced Monte Carlo numerical simulations parallelized on GPUs we study the critical properties of the spin-glass-like model for the mode-locked glassy random laser, a 44-spin model with complex spins with a global spherical constraint and quenched random interactions. Implementing two different boundary conditions for the mode frequencies we identify the critical points and the critical indices of the random lasing phase transition with finite size scaling techniques. The outcome of the scaling analysis is that the mode-locked random laser universality class is compatible with a mean-field one, though different from the mean-field class of the Random Energy Model and of the glassy random laser in the narrow band approximation, that is, the fully connected version of the present model. The low temperature (high pumping) phase is finally characterized by means of the overlap distribution and evidence for the onset of replica symmetry breaking in the lasing regime is provided.

An adaptive cubic regularization algorithm for computing H- and Z-eigenvalues of real even-order supersymmetric tensors

In this paper, we compute the H- and Z-eigenvalues of real even-order supersymmetric tensors by using the adaptive cubic regularization algorithm. First, the equation of eigenvalues of the tensor is represented by a spherically constrained optimization problem. Owing to the nice geometry of the spherical constraint, we minimize the objective function and preserve the constraint in an alternating way. The objective function of the optimization model is approximated by a cubic function with a tunable parameter, which is solved inexactly to obtain a trial step. Then the Cayley transform is applied to the trial step. Based on the ratio of actual and predicted reductions, a parameter is regulated to make sure that the cubic function is a good estimation of the original objective function. Finally we obtain an adaptive cubic regularization algorithm for computing an eigenvalue of a tensor (ACRCET). Furthermore, we prove that the sequence of iterations generated by ACRCET converges to an eigenvalue of a given tensor globally. In order to improve the computational efficiency, we propose a fast computing skill for Txr−2 which is the matrix-valued product of a hypergraph related tensor T and a vector x. Numerical experiments illustrate that the fast computing skill for Txr−2 is efficient and ACRCET is effective when computing H- and Z-eigenvalues of real even-order supersymmetric tensors.

Modeling and Parameter Identification of a 3D Measurement System Based on Redundant Laser Range Sensors for Industrial Robots.

The low absolute positioning accuracy of industrial robots is one of the bottlenecks preventing industrial robots from precision applications. Kinematic calibration is the main way to improve the absolute positioning accuracy of industrial robots, which greatly relies on three-dimensional (3D) measurement instruments, including laser trackers and pull rope mechanisms. These instruments are costly, and their required intervisibility space is large. In this paper, a precision 3D measurement instrument integrating multiple laser range sensors is designed, which fuses the information of multiple redundant laser range sensors to obtain the coordinates of a 3D position. An identification model of laser beam position and orientation parameters based on redundant distance information and standard spherical constraint is then developed to reduce the requirement for the assembly accuracy of laser range sensors. A hybrid identification algorithm of PSO-LM (particle swarm optimization Levenberg Marquardt) is designed to solve the high-order nonlinear problem of the identification model, where PSO is used for initial value identification, and LM is used for final value identification. Experiments of identification of position and orientation, verifications of the measuring accuracy, and the calibration of industrial robots are conducted, which show the effectiveness of the proposed 3D measurement instrument and identification methods. Moreover, the proposed instrument is small in size and can be used in narrow industrial sites.

Infinite Volume Gibbs States and Metastates of the Random Field Mean-Field Spherical Model

For the discrete random field Curie–Weiss models, the infinite volume Gibbs states and metastates have been investigated and determined for specific instances of random external fields. In general, there are not many examples in the literature of non-trivial limiting metastates for discrete or continuous spin systems. We analyze the infinite volume Gibbs states of the mean-field spherical model, a model of continuous spins, in a general random external field with independent identically distributed components with finite moments of some order larger than four and non-vanishing variances of the second moments. Depending on the parameters of the model, we show that there exist three distinct phases: ordered ferromagnetic, ordered paramagnetic, and spin glass. In the ordered ferromagnetic and ordered paramagnetic phases, we show that there exists a unique infinite volume Gibbs state almost surely. In the spin glass phase, we show the existence of chaotic size dependence, provide a construction of the Aizenman–Wehr metastate, and consider both the convergence in distribution and almost sure convergence of the Newman–Stein metastates. The limiting metastates are non-trivial and their structure is universal due to the presence of Gaussian fluctuations and the spherical constraint.

An efficient PGM-based algorithm with backtracking strategy for solving quadratic optimization problems with spherical constraint

We utilize projected gradient method (PGM for short) to solve quadratic optimization problem with spherical constraint. Based on the global convergence of simple first order conic method for trust region subproblem, we show that under some conditions, the global convergence of the PGM is guaranteed if the initial point is chosen specially. With only the multiplication of matrix and vector involved, a good approximation solution can be obtained in a low computation cost for large scale applications.

Synthesis of Multi-position 3-PRS Manipulator Based on Spherical Constraints by Eliminating the Parasitic Motion

Synthesis of Multi-position 3-PRS Manipulator Based on Spherical Constraints by Eliminating the Parasitic Motion

Extrinsic calibration method for 3D scanning system with four coplanar laser profilers

3D scanning is a crucial step to ensuring the machining quality of the workpiece and is an essential part of intelligent manufacturing. However, existing scanning systems usually have only one profiler, which must be combined with a dynamic tracking system to achieve a complete scan of a workpiece. This scanning method has low efficiency and complicated path planning for ring-shaped workpieces. Therefore, in this article, an efficient and high-accuracy 3D scanning system composed of a linear translation stage and four uniformly distributed laser profilers is built, and its extrinsic calibration method is studied. At first, based on the working parameters and spatial layout of multiple profilers, a stereoscopic calibrator composed of three non-collinear target balls (TBs) is designed. Then, a multi-profiler data fusion method is proposed, which utilizes a linear encoder to trigger the four profilers synchronously. Finally, by simultaneously using all data from the multiple profilers and the spherical constraint of each TB, all extrinsic parameters are accurately calibrated at the same time. Experimental results show that the average probing size error of the TB with a 38.1 mm diameter is stable at about 0.007 mm, and its extended uncertainty is about 0.100 mm (k = 2). In addition, standard cylinders and bend tubes are scanned. The results show that the proposed method can meet the high-accuracy calibration requirements of the tube-bending deformation detection system.

Fully Automated Generation of Prebiotically Relevant Reaction Networks from Optimized Nanoreactor Simulations.

The nanoreactor approach first introduced by the group of Martı́nez [Wang et al. Nat. Chem. 2014, 6, 1044-1048] has recently attracted much attention because of its ability to accelerate the discovery of reaction pathways. Here, we provide a comprehensive study of various simulation parameters and present an alternative implementation for the reactivity-enhancing spherical constraint function, as well as for the detection of reaction events. In this context, a fully automated postsimulation evaluation procedure based on RDKit and NetworkX analysis is introduced. The chemical and physical robustness of the procedure is examined by investigating the reactivity of selected homogeneous systems. The optimized procedure is applied at the GFN2-xTB level of theory to a system composed of HCN molecules and argon atoms, acting as a buffer, yielding prebiotically plausible primary and secondary precursors for the synthesis of RNA. Furthermore, the formose reaction network is explored leading to numerous sugar precursors. The discovered compounds reflect experimental findings; however, new synthetic routes and a large collection of exotic, highly reactive molecules are observed, highlighting the predictive power of the nanoreactor approach for unraveling the reactive manifold.

Generalised Gibbs Ensemble for spherically constrained harmonic models

We build and analytically calculate the Generalised Gibbs Ensemble partition function of the integrable Soft Neumann Model. This is the model of a classical particle which is constrained to move, on average over the initial conditions, on an NN dimensional sphere, and feels the effect of anisotropic harmonic potentials. We derive all relevant averaged static observables in the (thermodynamic) N\to\inftyN→∞ limit. We compare them to their long-term dynamic averages finding excellent agreement in all phases of a non-trivial phase diagram determined by the characteristics of the initial conditions and the amount of energy injected or extracted in an instantaneous quench. We discuss the implications of our results for the proper Neumann model in which the spherical constraint is imposed strictly.

Relative motion guidance for near-rectilinear lunar orbits with path constraints via actor-critic reinforcement learning

This paper presents a feedback guidance algorithm for proximity operation in cislunar environment based on actor-critic reinforcement learning. The algorithm is lightweight, closed-loop, and capable of taking path constraints into account. The method relies on reinforcement learning to make the well known Zero-Effort-Miss/Zero-Effort-Velocity guidance state dependent and allow for path constraints to be directly embedded. The algorithm is tested in the circular restricted three-body problem (CRTBP) framework for Near Rectilinear Orbits (NRO) in the Earth-Moon system. It shows promising results in terminal guidance error and satisfies path constraints in constraint scenarios comprising spherical constraints and keep-out-spheres with approach corridors. Furthermore, this approach indicates that reinforcement learning can be effectively used to solve constrained relative spacecraft guidance problems in complex environments and thus can be effective for autonomous relative motion operations in the Earth-Moon dynamical environment.

Activity-induced polar patterns of filaments gliding on a sphere

Active matter systems feature the ability to form collective patterns as observed in a plethora of living systems, from schools of fish to swimming bacteria. While many of these systems move in a wide, three-dimensional environment, several biological systems are confined by a curved topology. The role played by a non-Euclidean geometry on the self-organization of active systems is not yet fully understood, and few experimental systems are available to study it. Here, we introduce an experimental setup in which actin filaments glide on the inner surface of a spherical lipid vesicle, thus embedding them in a curved geometry. We show that filaments self-assemble into polar, elongated structures and that, when these match the size of the spherical geometry, both confinement and topological constraints become relevant for the emergent patterns, leading to the formation of polar vortices and jammed states. These results experimentally demonstrate that activity-induced complex patterns can be shaped by spherical confinement and topology.

An exact penalty approach for optimization with nonnegative orthogonality constraints

Optimization with nonnegative orthogonality constraints has wide applications in machine learning and data sciences. It is NP-hard due to some combinatorial properties of the constraints. We first propose an equivalent optimization formulation with nonnegative and multiple spherical constraints and an additional single nonlinear constraint. Various constraint qualifications, the first- and second-order optimality conditions of the equivalent formulation are discussed. By establishing a local error bound of the feasible set, we design a class of (smooth) exact penalty models via keeping the nonnegative and multiple spherical constraints. The penalty models are exact if the penalty parameter is sufficiently large but finite. A practical penalty algorithm with postprocessing is then developed to approximately solve a series of subproblems with nonnegative and multiple spherical constraints. We study the asymptotic convergence and establish that any limit point is a weakly stationary point of the original problem and becomes a stationary point under some additional mild conditions. Extensive numerical results on the problem of computing the orthogonal projection onto nonnegative orthogonality constraints, the orthogonal nonnegative matrix factorization problems and the K-indicators model show the effectiveness of our proposed approach.

Finding the global optimum of a class of quartic minimization problem

We consider a special nonconvex quartic minimization problem over a single spherical constraint, which includes the discretized energy functional minimization problem of non-rotating Bose-Einstein condensates (BECs) as one of the important applications. Such a problem is studied by exploiting its characterization as a nonlinear eigenvalue problem with eigenvector nonlinearity (NEPv). Firstly, we show that the NEPv has a unique nonnegative eigenvector, corresponding to the smallest nonlinear eigenvalue of NEPv, which is exactly the global minimizer to the optimization problem. Secondly, with these properties, we obtain that any algorithm converging to the nonnegative stationary point of this optimization problem finds its global optimum, such as the regularized Newton method. In particular, we obtain the convergence to the global optimum of the inexact alternating direction method of multipliers for this problem. Numerical experiments for applications in non-rotating BECs validate our theories.