In current robot calibration approaches, the error propagation and identification of serial and parallel robots fail to be solved intuitively and generically, resulting in an inefficient calibration implementation and a low accuracy improvement. In this article, we present a generic error modeling method of serial robots and extend to parallel robots by finite and instantaneous screw (FIS) theory. The differential map and the explicit description of FIS on the robot motions enable a concise error modeling of the serial robot. The identifiability of errors in serial robot is discussed. The maximum independent errors are proved to be 4r + 2p + 6, where r and p are the numbers of revolute and prismatic joints, respectively. Based on the error mapping of serial limbs, reciprocal twist and wrench are introduced to consider the interaction among limbs and reveal the error propagation of the parallel robot. Then, the identification algorithms with high robustness and efficiency are investigated for the serial and parallel robots. Specifically, the conventional ill-conditioning problems of parallel robots are addressed. Finally, the proposed kinematic calibration framework for both types of robots are compared with the existing methods, and verified by simulations and experiments. The results show that our calibration approach improves the robot accuracy in a robust and efficient manner.

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 article presents a robot calibration method using finite and instantaneous screw 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.

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 the presented study, geometric errors are described as parameter uncertainty because they are unknown in design stage. A 5 degree-of-freedom (DoF) PKM is taken to exemplify this method. Elasto-dynamic model is firstly 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 (MCS) and response surface method (RSM). Finally, elasto-dynamic 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 novel 5-axis hybrid reconfigurable robot named Tricept-IV, including one 4-degree-of-freedom (4DOF) hybrid module and one 2DOF end effector, is investigated. Compared with extensive research that has been pursued for the parallel kinematic machines such as Tricept, Sprint Z3 Head, and so on, the hybrid kinematic machines have not adequately been studied. This paper demonstrates a method of workspace decomposition applied in the dimensional synthesis of a 4DOF hybrid module, which is the underlying architecture of the newly invented robot. This paper starts with an introduction of the Tricept-IV robot. After dividing the 4DOF hybrid module into one position-orientation coupling (POC) subsystem and one position-feed (PF) subsystem, its workspace is decomposed into POC and PF subspaces accordingly, and then the inverse position problem may be solved by means of one prejudgment method. Furthermore, the Jacobian matrix of the POC subsystem is obtained by the screw theory so as to formulate its kinematic performance index. Finally, the dimensional synthesis based on workspace decomposition of the hybrid module is carried out by taking a global view of the dimensional synthesis of these two subsystems.

Driven by requirements of five-axis numerical control (NC) machine for its executive mechanism, this paper creatively proposes a flow path to synthesize a novel class of n-degree-of-freedom (n-DoF, 4 ≤ n ≤ 6) parallel manipulators (PMs) resorting to four steps, and takes a patented 5-DoF PM, named T5, for example to demonstrate the flow path in depth. Comparing with existing five-axis executive mechanisms, this novel class of the PMs has some advantages of light end-effector, good static, dynamic performance, and so on. Upon the underlying architecture of T5, the kinematic analysis and optimal design are carried out for the first time, in which two essential procedures are involved, one is the kinematic performance index by means of the reciprocal product associated with the wrench screw and twist screw with specific physical meaning, the other is the design method adopted to perform the multi-objective dimensional synthesis using an artificial intelligence approach, that is nondominated sorting genetic algorithm II (NSGA-II). This paper is aimed at laying a solid theoretical and technical foundation for the prototype design and manufacture of T5 PM.

Multi-objective optimization of a typical parallel tracking mechanism considering parameter uncertainty is carried out in this paper. Both dimensional and sectional parameters are regarded as design variables. Workspace, kinematic, stiffness, and dynamic performances are simultaneously considered in formulating optimal objectives and constraint conditions. Considering manufacturing and assembling errors, parameter uncertainty is modeled and evaluated to minimize their effects on the optimized performances. Analytical models between objectives and design variables are established to improve the efficiency of optimization while its accuracy is assured. The study of parameter uncertainty and analytical mapping model is incorporated in the optimization of the parallel tracking mechanism. With the aid of particle swarm algorithm, a cluster of solutions, called Pareto frontier, are obtained. By proposing an index, a cooperative equilibrium point representing the balance among objectives is selected and the optimized parameters are determined. The present study is expected to help designers build optimized parallel tracking mechanism in an effective and efficient manner.