Robot calibration to provide an accurate kinematic model is widely adopted in the advanced controller development of articulated serial robot performing complicated tasks. Conventional calibration methods mainly focus on the complete, continuous and minimal error modeling. The generation and accumulation of errors have not been explicitly explained. In addition, the error identification and compensation sometimes are not practical for controller establishment. This paper presents a robot calibration method using finite and instantaneous screw (FIS) theory. From the differentiation of finite screw, the errors are defined by the deviations of instantaneous screws at initial pose. The error modeling is explicit. We also propose an advanced optimization algorithm based identification method and regard the geometry of redundant errors as constraints. The identified instantaneous screw errors are then converted to the joint actuation errors. Without modifying existing motion controller, errors are compensated by modified inputs. A UR3 robot is taken as an example to illustrate the calibration method. Simulation and experiment are implemented for verification. Comparing with the accuracy before calibration, the position and orientation accuracy of UR3 robot after calibration has improved by 94.75% and 89.29%. The results also show that modified inputs can be conveniently connected to controller development. 

This paper deals with the elastodynamic modeling and parameter sensitivity analysis of a parallel manipulator with articulated traveling plate (PM-ATP) for assembling large components in aviation and aerospace. In the elastodynamic modeling, the PM-ATP is divided into four levels, i.e., element, part, substructure, and the whole mechanism. Herein, three substructures, including translation, bar, and ATP, are categorized according to the composition of the PM-ATP. Based on the kineto-elastodynamic (KED) method, differential motion equations of lower levels are formulated and assembled to build the elastodynamic model of the upper level. Degrees of freedom (DoFs) at connecting nodes of parts and deformation compatibility conditions of substructures are considered in the assembling. The proposed layer-by-layer method makes the modeling process more explicit, especially for the ATP having complex structures and multiple joints. Simulations by finite element software and experiments by dynamic testing system are carried out to verify the natural frequencies of the PM-ATP, which show consistency with the results from the analytical model. In the parameter sensitivity analysis, response surface method (RSM) is applied to formulate the surrogate model between the elastic dynamic performances and parameters. On this basis, differentiation of performance reliability to the parameter mean value and standard variance are adopted as the sensitivity indices, from which the main parameters that greatly affect the elastic dynamic performances can be selected as the design variables. The present works are necessary preparations for future optimal design. They can also provide reference for the analysis and evaluation of other PM-ATPs.

Geometric errors, vibration, and elastic deformation are the main causes for inaccuracy of parallel kinematic machines (PKMs). Instead of tackling these inaccuracies after the prototype has been built, this paper proposes a design optimization method to minimize vibration and deformation considering the effects of geometric errors before constructing the PKM. In this paper, geometric errors are described as parameter uncertainty because they are unknown in design stage. A five degree-of-freedom (DoF) PKM is taken to exemplify this method. Elastodynamic model is first formulated by a step-by-step strategy. On this basis, dynamic performances, including natural frequency, elastic deformation, and maximum stress, are analyzed. These analytical results are verified by finite-element simulation and experiment. Then, the necessity of concerning parameter uncertainty in optimization is addressed. Next, parameter uncertainty is added to the formulation of objectives and constraints by Monte Carlo simulation and response surface method. Finally, elastodynamic optimization of the 5-DoF PKM is implemented to rebuild a prototype which is robust to geometric errors and has minimal vibration and deformation. The proposed method can also be applied to accuracy improvement of any machines in practical applications.

A parameterized inverse kinematic model is the theoretical basis for performance analysis, design and control of parallel mechanism (PM). Current methods are either computationally expensive or difficult to get analytical form. To deal with this problem, this paper proposes a parameterized method by conformal geometric algebra (CGA). Based on the description and computation of screw motions in CGA, closure equations about successive screw displacements of any PM can be formulated. Joint displacements of each limb and screw parameters of end-effector are then solved in an analytical manner. The proposed method is exemplified by a 3 degree-of-freedom (DoF) PM, which shows high efficiency in deriving the analytical inverse kinematic model.

Having potentially high stiffness and good dynamic response, a parallel pose adjusting mechanism was proposed for being an attachment to a big serial robot of a macro-micro robotic system. This paper addresses its design optimization problem mainly concerning arrangements of design variables and objectives. Parameter changes during construction are added to the design variables in order to prevent the negative effects to the physical prototype. These parameter changes are interpreted as parameter uncertainty and modeled by probabilistic theory. For the objectives, both static and dynamic performances are simultaneously optimized by Pareto-based method. The involved performance indices are instantaneous energy based stiffness index, first natural frequency and execution mass. The optimization procedure is implemented as: (1) carrying out performance modeling and defining performance indices, (2) reformulating statistical objectives and probabilistic constraints considering parameter uncertainty, (3) conducting Pareto-based optimization with the aid of response surface method (RSM) and particle swarm optimization (PSO), (4) selecting optimal solution by searching for cooperative equilibrium point (CEP). By addressing parameter uncertainty and the best compromise among multiple objectives, the presented optimization procedure provides more reliable optimal parameters that would not be affected by minor parameter changes during construction, and less biased optimum between static and dynamic performances comparing with the conventional optimization methods. The proposed optimization method can also be applied to the other similar mechanisms.

The demands for advanced and flexible docking equipment are increasing in the fields of aerospace, shipbuilding and construction machinery. Position and orientation accuracy is one of the most important criteria, which would directly affect the docking quality. Taking a novel one-translational and three-rotational docking equipment, referred to as PaQuad parallel mechanism as example, this article proposed an accuracy improvement strategy by geometric accuracy design and error compensation. Drawing mainly on screw theory, geometric error modeling of PaQuad parallel mechanism was first carried out via four independent routes. Joint perturbations and geometric errors were included in each route error twist. Wrenches due to articulated traveling plate were applied to eliminate joint perturbations. Then, geometric accuracy design was implemented at component and substructure levels. The basic principle was to transfer geometric errors into dimensional or geometric tolerance. High-precision machining/assembling techniques were applied to satisfy the tolerance. Finally, error compensation resorting to kinematic calibration was implemented at mechanism level. It can be summarized as identification modeling, measurement planning, and parameter identification and modification. Maximum deviations of PaQuad parallel mechanism before calibration experiment were 0.01mm, 0.027 after kinematic calibration. Orientation accuracy of PaQuad parallel mechanism has improved one order of magnitude. It proves the effectiveness of accuracy improvement in terms of geometric accuracy design and error compensation.

An approach for geometric error modeling of parallel manipulators (PMs) based on the visual representation and direct calculation of conformal geometric algebra is introduced in this paper. In this method, the finite motion of an open-loop chain is firstly formulated. Through linearization of the finite motion, error propagation of the open-loop chain is analyzed. Then the error sources are separated in terms of joint perturbations and geometric errors. Next, motions and constraints of PMs are analyzed visually by their reciprocal property. Finally geometric error model of PMs are formulated considering the actuations and constraints. The merits of this new approach are twofold: (1) complete and continuous geometric error modeling can be achieved since finite motions are considered, (2) visual and analytical computation of motions and constraints are applied for transferring geometric errors from the open-loop chain to the PM. A 2-DoF rotational PM is applied to demonstrate the geometric error modeling process. Comparisons between simulation and analytical models show that this approach is highly effective.

It has long been a challenge to carry out the optimal design of parallel kinematic machine (PKM) simultaneously considering stiffness and mass performances. This paper proposes the stiffness and mass optimization of PKM by settling performance indices, constraint conditions based on parameter uncertainty and cooperative equilibrium among performances. Firstly, instantaneous energy-based stiffness indices and mass in motion are defined as objectives. Instead of computationally expensive numerical analysis, analytical mapping models between objectives and parameters are investigated to improve optimization efficiency. Then, considering the effects of parameter uncertainty resulted from manufacturing errors during construction, constraint conditions are formulated by probabilistic method. Based on particle swarm optimization (PSO), a multi-objective optimization is implemented. A group of solutions are obtained to flag as Pareto frontier that reflects the competitive features between stiffness and mass performances. A cooperative equilibrium searching method is proposed to find out the final solution. Finally, this optimization approach is exemplified and validated by a five degree-of-freedom (DoF) PKM. Although its mass increases 17.17%, the stiffness is nearly 3 times better than before optimization.