Kinematics Of Serial Robots Research Articles

Closed-form solutions for the inverse kinematics of serial robots using conformal geometric algebra

This work addresses the inverse kinematics of serial robots using conformal geometric algebra. Classical approaches include either the use of homogeneous matrices, which entails high computational cost and execution time, or the development of particular geometric strategies that cannot be generalized to arbitrary serial robots. In this work, we present a compact, elegant and intuitive formulation of robot kinematics based on conformal geometric algebra that provides a suitable framework for the closed-form resolution of the inverse kinematic problem for manipulators with a spherical wrist. For serial robots of this kind, the inverse kinematics problem can be split in two subproblems: the position and orientation problems. The latter is solved by appropriately splitting the rotor that defines the target orientation in three simpler rotors, while the former is solved by developing a geometric strategy for each combination of prismatic and revolute joints that forms the position part of the robot. Finally, the inverse kinematics of 7 DoF redundant manipulators with a spherical wrist is solved by extending the geometric solutions obtained in the non-redundant case.

A branch-and-prune method to solve closure equations in dual quaternions

Using dual quaternions, the closure equations of a kinematic loop can be expressed as a system of multiaffine equations. In this paper, this property is leveraged to introduce a branch-and-prune method specially tailored for solving such systems of equations. The new method is objectively simpler (in the sense that it is easier to understand and to implement) than previous approaches relying on general techniques such as interval Newton methods or methods based on Bernstein polynomials or linear relaxations. Moreover, it relies on two basic operations — linear interpolation and projection onto coordinate planes— that can be efficiently computed. The generality of the proposed method is evaluated on position analysis problems with 0-, 1-, and 2-dimensional solution sets, including the inverse kinematics of serial robots and the forward kinematics of parallel ones. The results obtained on these problems show that the efficiency of the method compares favorably to state-of-the-art alternatives.

Hyper Dual Quaternions representation of rigid bodies kinematics

Hyper-Dual Quaternions, HDQ, are first introduced in this paper. Utilizing the Hyper-Dual Numbers, HDN, Dual Quaternions, DQ, and hyper-dual angle, the general expression of HDQ is obtained. Rigid single- and multi-body kinematics such as in a serial robot kinematics, are then expressed in HDQ form. Taking advantage of the dual numbers’ “automatic differentiation” feature, HDQ encompasses both body pose (translational and rotational) and body velocities in a compact form with no need for further pose differentiation.

Kinematic calibration of serial robot using dual quaternions

Purpose The purpose of this paper is to propose an error model for serial robot kinematic calibration based on dual quaternions. Design/methodology/approach The dual quaternions are the combination of dual-number theory and quaternion algebra, which means that they can represent spatial transformation. The dual quaternions can represent the screw displacement in a compact and efficient way, so that they are used for the kinematic analysis of serial robot. The error model proposed in this paper is derived from the forward kinematic equations via using dual quaternion algebra. The full pose measurements are considered to apply the error model to the serial robot by using Leica Geosystems Absolute Tracker (AT960) and tracker machine control (T-MAC) probe. Findings Two kinematic-parameter identification algorithms are derived from the proposed error model based on dual quaternions, and they can be used for serial robot calibration. The error model uses Denavit–Hartenberg (DH) notation in the kinematic analysis, so that it gives the intuitive geometrical meaning of the kinematic parameters. The absolute tracker system can measure the position and orientation of the end-effector (EE) simultaneously via using T-MAC. Originality/value The error model formulated by dual quaternion algebra contains all the basic geometrical parameters of serial robot during the kinematic calibration process. The vector of dual quaternion error can be used as an indicator to represent the trend of error change of robot’s EE between the nominal value and the actual value. The accuracy of the EE is improved after nearly 20 measurements in the experiment conduct on robot SDA5F. The simulation and experiment verify the effectiveness of the error model and the calibration algorithms.

An improved kinematic model for serial robot calibration based on local POE formula using position measurement

Purpose This paper aims to propose a calibration model for kinematic parameters identification of serial robot to improve its positioning accuracy, which only requires position measurement of the end-effector. Design/methodology/approach The proposed model is established based on local frame representation of the product of exponentials (local POE) formula, which integrates all kinematic errors into the twist coordinates errors; then they are identified with the tool frame’ position deviations simultaneously by an iterative least squares algorithm. Findings To verify the effectiveness of the proposed method, extensive simulations and calibration experiments have been conducted on a 4DOF SCARA robot and a 5DOF drilling machine, respectively. The results indicate that the proposed model outperforms the existing model in convergence, accuracy, robustness and efficiency; fewer measurements are needed to gain an acceptable identification result. Practical implications This calibration method has been applied to a variable-radius circumferential drilling machine. The machine’s positioning accuracy can be significantly improved from 11.153 initially to 0.301 mm, which is well in the tolerance (±0.5 mm) for fastener hole drilling in aircraft assembly. Originality/value An accurate and efficient kinematic calibration model has been proposed, which satisfies the completeness, continuity and minimality requirements. Due to generality, this model can be widely used for serial robot kinematic calibration with any combination of revolute and prismatic joints.

A mathematical model to systematically align superconducting radio frequency cavities employing the serial robot kinematic theory

In Superconducting Radio Frequency (SRF) cryomodules, precise alignment of cavities is necessary to ensure high beam quality and to increase the overall energetic efficiency. In the SSR1 (Single Spoke Resonator 1) cryomodule, the cavities are aligned using a system of seven screws which allows to control five Degree of Freedoms (DOFs). The relation between the rotation of each screw and the movement of the cavity is non-linear, thus the aligning process, currently based on a trial-and-error procedure, can be time consuming and affected by human error. In this paper the design of an alignment mathematical model, based on the serial robot kinematic, is described and tested on a SSR1 cavity. The goal of the proposed model is to give a step by step operational procedure that bring the SSR1 cavity to a desired location reducing the uncertainties related to the current operator-driven alignment process.

Machining of large scaled CFRP-Parts with mobile CNC-based robotic system in aerospace industry

Industrial robots have already demonstrated their advantages in smart and efficient production in a wide field of applications and industries. However, their use for machining of structural aircraft components is still impeded by the disadvantage of low absolute accuracy, sensitivity to process loads and limited workspace compared to large machining centers.A mobile robotic system is presented as a new approach for machining applications of large aircraft components. The system presented in this paper consists of a CNC-based serial robot kinematic with additional secondary encoder systems on every axis. The entire system is based on a Siemens CNC control, which evolves the robot to a full-featured machine tool. This setup enables additional possibilities for the implementation of extended control strategies and advanced calibration routines. Thus, high demands and challenging tolerances in aircraft manufacturing will be fulfilled, so that process times and investment cost can be reduced significantly.

The Research of Rapid Construction Method of Kinematics Coordinate System from a Kind of Mobile Robot

In order to study how to solve the serial robot kinematics quickly, so we transformed the kinematics coordinate system by Y axis, and the computed results show that transforming the kinematics coordinate system by Y axis could solve the kinematic model quickly and efficiently; the computed results suggest that constructing the redundant coordinate system and transforming the kinematics coordinate system by Y axis could solve the serial robotic kinematics efficiently.

Determination of the Identifiable Parameters in Robot Calibration Based on the POE Formula

This paper presents an analytical approach to determine and eliminate the redundant model parameters in serial-robot kinematic calibration based on the product of exponentials formula. According to the transformation principle of the Lie algebra se(3) between different frames, the connection between the joints' twist errors and the links' geometric ones is established. Identifiability analysis shows that the redundant errors are simply equivalent to the commutative elements of the robot's joint twists. Using the Lie bracket operation of se(3), a linear partitioning operator can be constructed to analytically separate the identifiable parameters from the system error vector. Then, error models satisfying the completeness, minimality, and model continuity requirements can be obtained for any serial robot with all combinations and configurations of revolute and prismatic joints. The conventional conclusion that the maximum number of independent parameters is 4r + 2p + 6 in a generic serial robot with r revolute and p prismatic joints is verified. Using the quotient manifold of the Lie group SE(3), the links' geometric errors and the joints' offset errors can be integrated as a whole, such that all these errors can be identified simultaneously. To verify the effectiveness of the proposed method, calibration simulations and experiments are conducted on an industrial six-degree-of-freedom (DoF) serial robot.

A Computational Algorithm for a Spatial Serial Robot

The inverse kinematics of serial robots is a central problem in the automatic control of robot manipulators. The aim of this paper is to obtain a computational algorithm to compute the inverse kinematics problem of a spatial serial robot. We use a series of algebraic and numeric transformations to reduce the problem to a univariate polynomial equation. The results can be directly applied to symbolic calculations and decreased considerably the calculation time.

Application of robot kinematics methods to the simulation and control of neutron beam line positioning systems

Neutron stress measurements require specimens of complex geometry to be speedily and accurately positioned and oriented with respect to the neutron beam. Recognition that a majority of the specimen positioning systems in use at strain scanning facilities are effectively serial robot manipulators, suggests that the methods of serial robot kinematic modelling may be applied to advantage. The adoption of robotics methods provides a simple and reliable framework for controlling positioning systems of arbitrary geometry and complexity. In addition the numerical solution of the inverse kinematic problem is facilitated, allowing specimens to be automatically positioned and orientated so that pre-determined strain components are measured. It is also shown that, given sufficient degrees of freedom, a secondary characteristic of the measurement position such as the measurement count time may be simultaneously optimised.

Solving algebraic systems using matrix computations

Finding zeros of algebraic sets is a fundamental problem in scientific and geometric computation. It arises in symbolic and numeric techniques used to manipulate sets of polynomial equations. In this paper, we outline algorithms and applications for solving zero and one dimensional algebraic sets using matrix computations. These algorithms make use of techniques from elimination theory and reduce the problem to finding singular sets of matrix polynomials. We make use of algorithms for eigen-decomposition, singular value decomposition and Gaussian elimination to compute the singular sets. These algorithms have been implemented and perform very well in practice. We describe their application to computing conformations of molecular chains, inverse kinematics of serial robots, solid modeling and manufacturing.