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Complicated workpiece, such as an engine block, has special rough locating datum features (i.e. six independent datum features) due to its complex structure. This locating datum error cannot be handled by current variation propagation model based on differential motion vectors. To extend variation prediction fields, this paper aims to solve the unaddressed variation sources to modify current model for multistage machining processes.

To overcome the limitation of current variation propagation model based on differential motion vectors caused by the unaddressed variation sources, this paper will extend the current model by handling the unaddressed datum-induced variation and its corresponding fixture variation.

The measurement results of the rear face with respect to the rough datum W and the pan face with respect to the hole Q by coordinate measuring machine (CMM) are −0.006 mm and 0.031 mm. The variation results for rear face and pan face predicted by the modified model are −0.009 mm and 0.025 mm, respectively. The discrepancy of model prediction and measurement is very small.

This paper modifies the variation propagation model based on differential motion vectors by solving the unaddressed variation sources, which can extend the variation prediction fields for some complicated workpiece and is useful in the future work for many fields, such as process monitoring, fault diagnosis, quality-assured setup planning and process-oriented tolerancing.

Assembly variations, which will propagate along the assembly process, are inevitable and difficult to analyze in Aeronautical Thin‐Walled Structures (ATWS) assembly. The purpose of this paper is to present a new method for analyzing the variation propagation of ATWS with automated riveting.

The paper addresses the variation propagation model and method by first, forming a novel Stage‐State model to represent the process of automated riveting. Second, the effect of positioning error on assembly variation is defined as propagation variation (PV), and propagation matrix of key characteristic points (KCP) is discussed. Third, the effect between the variations in each stage is defined as expansion variation (EV). According to the analysis of mismatch error and the reference transformation, the expansion matrix is formed.

The model can solve the variation propagation problem of ATWS with automated riveting efficiently, which is shown as an example of this paper.

The variation obtained by the model and method presented in this paper is in conformity with the variation measured in experiments.

The propagation variation and expansion variation is proposed for the first time, and variations are studied according to novel propagation matrix and expansion matrix.

This study aims to present a model and analysis of automotive body outer cover panels (OCPs) assembly systems to predict assembly variation. In the automotive industry, the OCPs assembly process directly influences the quality of the automobile body appearance. However, suitable models to describe variation propagation of OCPs assembly systems remain unknown.

An adaptive state space model for OCPs assembly systems is introduced to accurately express variation propagation, including variation accumulation and transition, where two compliant deviations make impacts on key product characteristics (KPCs) of OCP, and the impacts are accumulated from welding process to threaded connection process. Another new source of variation from threaded connection is included in this model. To quantify the influence of variation from threaded connection on variation propagation, the threaded connection sensitivity matrix is introduced to build up a linear relationship between deviation from threaded connection and output deviation in KPCs. This matrix is solved by homogeneous coordinate transformation. The final deviation of KPCs will be transferred to ensure gaps and flushes between two OCPs, and the transition matrix is considered as a unit matrix to build up the transition relationship between different states.

A practical case on the left side body structure is described, where simulation result of variation propagation reveals the basic rule of variation propagation and the significant effect of variation from threaded connection on variation propagation of OCPs assembly system.

The model can be used to predict assembly variation or potential dimension problems at a preliminary assembly phase. The calculated results of assembly variation guide designers or technicians on tolerance allocation, fixture layout design and process planning.

Modeling and analysis of dimensional variation propagation is a crucial support technology for variation reduction, product/process design evaluation and recognition of variation source. However, owing to the multi-deviation (i.e. part deviations and fixture deviations) and multi-interaction (i.e. part-to-part interaction, part-to-fixture interaction and station-to-station interaction) in assembly processes, it is difficult for designers to describe or understand the variation propagation (or accumulation) mechanism clearly. The purpose of this paper is to propose a variation propagation modeling and analysis (VPMA) method based on multiple constraints aiming at a single station.

Initially, part-to-part constraints (PPCs) and part-to-fixture constraints (PFCs) are applied for the multi-interaction of assembly, and multiple constraints graph (MCG) model is proposed for expressing PPCs, PFCs, parts, as well as the variation propagation relation among them. Then, locating points (LPs) are adopted for representing the deviations in constraints, and formulas for calculating the deviations of LPs are derived. On that basis, a linearized relation between LPs’ deviations and part’s locating deviations is derived. Finally, a wing box is presented to validate the proposed method, and the results indicate the methodology’s feasibility.

MCG is an effective tool for dimensional VPMA, which is shown as an example of this paper.

Functions of geometric constraints in dimensional variation propagation are revealed, and MCG is proposed to formulize dimensional variation propagation.

Manufacturing errors, which will propagate along the assembly process, are inevitable and difficult to analyze for complex products, such as aircraft. To realize the goal of precise assembly for an aircraft, with revealing the nonlinear transfer mechanism of assembly error, a set of analytical methods with response to the assembly error propagation process are developed. The purpose of this study is to solve the error problems by modeling and constructing the coordination dimension chain to control the consistency of accumulated assembly errors for different assemblies.

First, with the modeling of basic error sources, mutual interaction relationship of matting error and deformation error is analyzed, and influence matrix is formed. Second, by defining coordination datum transformation process, practical establishing error of assembly coordinate system is studied, and the position of assembly features is modified with actual relocation error considering datum changing. Third, considering the progressive assembly process, error propagation for a single assembly station and multi assembly stations is precisely modeled to gain coordination error chain for different assemblies, and the final coordination error is optimized by controlling the direction and value of accumulated error range.

Based on the proposed methodology, coordination error chain, which has a direct influence on the property of stealthy and reliability for modern aircrafts, is successfully constructed for the assembly work of the jointing between leading edge flap component and wing component at different assembly stations.

Precise assembly work at different assembly stations is completed to verify methodology’s feasibility. With analyzing the main comprised error items and some optimized solutions, benefit results for the practical engineering application showing that the maximum value of the practical flush of the profiles between the two components is only 0.681 mm, the minimum value is only 0.021 mm, and the average flush of the entire wing component is 0.358 mm, which are in accordance with theoretical calculation results and can successfully fit the assembly requirement. The potential user can be the engineers for manufacturing the complex products.

The motion of a disk spinning on a horizontal surface has drawn a great deal of interest recently. The objectives of the researches are to find out what produces an increasing rattling sound and why the spinning ends so abruptly. In order to understand the behaviour of the spinning disk better, we derived a mathematical model of the rolling/sliding motion of a thin, rigid disk on a rigid, rough horizontal plane, and found the numerical solution of the related initial value problem. Then we studied the motion of the commercially available Tangent Toy disk [3]. The results show that the normal contact force becomes very large whenever the inclination of the disk becomes small. As the inclination of the disk oscillates with time, the time‐graph of the normal contact force exhibits periodical peaks, which correlate well with the peaks in the recorded sound response. They could well be responsible for the rattling sound heard during the motion.

Permanent magnet synchronous spherical motors can have wide use in robotics and industrial automation. They enable three-DOF omnidirectional motion of their rotor. They are suitable for several applications, such as actuation in robotics, traction in electric vehicles and use in several automation systems. Unlike conventional synchronous motors, permanent magnet synchronous spherical motors consist of a fixed inner shell, which is the stator, and a rotating outer shell, which is the rotor. Their dynamic model is multivariable and strongly nonlinear. The treatment of the associated control problem is important.

In this paper, the multivariable dynamic model of permanent magnet synchronous spherical motors is analysed, and a nonlinear optimal (H-infinity) control method is developed for it. Differential flatness properties are proven for the spherical motors’ state-space model. Next, the motors’ state-space description undergoes approximate linearization with the use of first-order Taylor series expansion and through the computation of the associated Jacobian matrices. The linearization process takes place at each sampling instance around a time-varying operating point, which is defined by the present value of the motors’ state vector and by the last sampled value of the control input vector. For the approximately linearized model of the permanent magnet synchronous spherical motors, a stabilizing H-infinity feedback controller is designed. To compute the controller’s gains, an algebraic Riccati equation has to be repetitively solved at each time-step of the control algorithm. The global stability properties of the control scheme are proven through Lyapunov analysis. Finally, the performance of the nonlinear optimal control method is compared against a flatness-based control approach implemented in successive loops.

Due to the nonlinear and multivariable structure of the state-space model of spherical motors, the solution of the associated nonlinear control problem is a nontrivial task. In this paper, a novel nonlinear optimal (H-infinity) control approach is proposed for the dynamic model of permanent magnet synchronous spherical motors. The method is based on approximate linearization of the motor’s state-space model with the use of first-order Taylor series expansion and the computation of the associated Jacobian matrices. Furthermore, the paper has introduced a different solution to the nonlinear control problem of the permanent magnet synchronous spherical motor, which is based on flatness-based control implemented in successive loops.

The presented control approaches do not exhibit any limitations, but on the contrary, they have specific advantages. In comparison to global linearization-based control schemes (such as Lie-algebra-based control), they do not make use of complicated changes of state variables (diffeomorphisms) and transformations of the system's state-space description. The computed control inputs are applied directly to the initial nonlinear state-space model of the permanent magnet spherical motor without the intervention of inverse transformations and thus without coming against the risk of singularities.

The motion control problem of spherical motors is nontrivial because of the complicated nonlinear and multivariable dynamics of these electric machines. So far, there have been several attempts to apply nonlinear feedback control to permanent magnet-synchronous spherical motors. However, due to the model’s complexity, few results exist about the associated nonlinear optimal control problem. The proposed nonlinear control methods for permanent magnet synchronous spherical motors make more efficient, precise and reliable the use of such motors in robotics, electric traction and several automation systems.

The treated research topic is central for robotic and industrial automation. Permanent magnet synchronous spherical motors are suitable for several applications, such as actuation in robotics, traction in electric vehicles and use in several automation systems. The solution of the control problem for the nonlinear dynamic model of permanent magnet synchronous spherical motors has many industrial applications and therefore contributes to economic growth and development.

The proposed nonlinear optimal control method is novel compared to past attempts to solve the optimal control problem for nonlinear dynamical systems. Unlike past approaches, in the new nonlinear optimal control method, linearization is performed around a temporary operating point, which is defined by the present value of the system's state vector and by the last sampled value of the control inputs vector and not at points that belong to the desirable trajectory (setpoints). Besides, the Riccati equation which is used for computing the feedback gains of the controller is new, and so is the global stability proof for this control method. Compared to nonlinear model predictive control, which is a popular approach for treating the optimal control problem in industry, the new nonlinear optimal (H-infinity) control scheme is of proven global stability, and the convergence of its iterative search for the optimum does not depend on initial conditions and trials with multiple sets of controller parameters. It is also noteworthy that the nonlinear optimal control method is applicable to a wider class of dynamical systems than approaches based on the solution of state dependent Riccati equations (SDRE). The SDRE approaches can be applied only to dynamical systems which can be transformed into the linear parameter varying form. Besides, the nonlinear optimal control method performs better than nonlinear optimal control schemes, which use approximation of the solution of the Hamilton–Jacobi–Bellman equation by Galerkin series expansions. Furthermore, the second control method proposed in this paper, which is flatness-based control in successive loops, is also novel and demonstrates substantial contribution to nonlinear control for robotics and industrial automation.

An optimal solution method based on 2-norm is proposed in this study to solve the inverse kinematics multiple-solution problem caused by a high redundancy. The current research also presents a motion optimization based on the 2-Norm of high-redundant mobile humanoid robots, in which a kinematic model is designed through the entire modeling.

The current study designs a highly redundant humanoid mobile robot with a differential mobile platform. The high-redundancy mobile humanoid robot consists of three modular parts (differential driving platform with two degrees of freedom (DOF), namely, left and right arms with seven DOF, respectively) and has total of 14 DOFs. Given the high redundancy of humanoid mobile robot, a kinematic model is designed through the entire modeling and an optimal solution extraction method based on 2-norm is proposed to solve the inverse kinematics multiple solutions problem. That is, the 2-norm of the angle difference before and after rotation is used as the shortest stroke index to select the optimal solution. The optimal solution of the inverse kinematics equation in the step is obtained by solving the minimum value of the objective function of a step. Through the step-by-step cycle in the entire tracking process, the kinematic optimization of the highly redundant humanoid robot in the entire tracking process is realized.

Compared with the before and after motion optimizations based on the 2-norm algorithm of the robot, its motion after optimization shows minimal fluctuation, improved smoothness, limited energy consumption and short path during the entire mobile tracking and operating process.

In this paper, the whole kinematics model of the highly redundant humanoid mobile robot is established and its motion is optimized based on 2-norm, which provides a theoretical basis for the follow-up research of the service robot.

In this paper, the whole kinematics model of the highly redundant humanoid mobile robot is established and its motion is optimized based on 2-norm, which provides a theoretical basis for the follow-up research of the service robot.

In this paper, the whole kinematics model of the highly redundant humanoid mobile robot is established and its motion is optimized based on 2-norm, which provides a theoretical basis for the follow-up research of the service robot.

Motion optimization based on the 2-norm of a highly redundant humanoid mobile robot with the entire modeling is performed on the basis of the entire modeling. This motion optimization can make the highly redundant humanoid mobile robot’s motion path considerably short, minimize energy loss and shorten time. These researches provide a theoretical basis for the follow-up research of the service robot, including tracking and operating target, etc. Finally, the motion optimization algorithm is verified by the tracking and operating behaviors of the robot and an example.

Gives introductory remarks about chapter 1 of this group of 31 papers, from ISEF 1999 Proceedings, in the methodologies for field analysis, in the electromagnetic community. Observes that computer package implementation theory contributes to clarification. Discusses the areas covered by some of the papers ‐ such as artificial intelligence using fuzzy logic. Includes applications such as permanent magnets and looks at eddy current problems. States the finite element method is currently the most popular method used for field computation. Closes by pointing out the amalgam of topics.

The purpose of this paper is to present a follow-the-leader motion strategy for multi-section continuum robots, which aims to make the robot have the motion ability in a confined environment and avoid a collision.

First, the mechanical design of a multi-section continuum robot is introduced and the forward kinematic model is built. After that, the follow-the-leader motion strategy is proposed and the differential evolution (DE) algorithm for calculating optimal posture parameters is presented. Then simulations and experiments are carried out on a series of predefined paths to analyze the performance of the follow-the-leader motion.

The follow-the-leader motion can be well performed on the continuum robots this study proposes in this research. The experimental results show that the deviation from the path is less than 9.7% and the tip error is no more than 15.6%.

Currently, the follow-the-leader motion is affected by the following factors such as gravity and continuum robot design. Furthermore, the position error is not compensated under open-loop control. In future work, this paper will improve the accuracy of the robot and introduce a closed-loop control strategy to improve the motion accuracy.

The main contribution of this paper is to present an algorithm to generate follow-the-leader motion of the continuum robot based on DE. This method is suitable for solving new arrangements in the process of following a nonlinear path. Then, it is expected to promote the engineering application of the continuum robot.