Precision object handling and manipulation require the accurate positioning of industrial robots. A common practice for performing end effector positioning is to read joint angles and use industrial robot forward kinematics (FKs). However, industrial robot FKs rely on the robot Denavit–Hartenberg (DH) parameter values, which include uncertainties. Sources of uncertainty associated with industrial robot FKs include mechanical wear, manufacturing and assembly tolerances, and robot calibration errors. It is therefore necessary to increase the accuracy of DH parameter values to reduce the impact of uncertainties on industrial robot FKs. In this paper, we use differential evolution, particle swarm optimization, an artificial bee colony, and a gravitational search algorithm to calibrate industrial robot DH parameters. A laser tracker system, Leica AT960-MR, is utilized to register accurate positional measurements. The nominal accuracy of this non-contact metrology equipment is less than 3 μm/m. Metaheuristic optimization approaches such as differential evolution, particle swarm optimization, an artificial bee colony and a gravitational search algorithm are used as optimization methods to perform the calibration using laser tracker position data. It is observed that, using the proposed approach with an artificial bee colony optimization algorithm, the accuracy of industrial robot FKs in terms of mean absolute errors of static and near-static motion over all three dimensions for the test data decreases from its measured value of 75.4 μm to 60.1 μm (a 20.3% improvement).

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This paper proposes an industrial robot calibration methodology using an artificial bee colony algorithm. Open loop industrial robot positions are usually calculated using joint angle readings and industrial robot forward kinematics, where feedback control systems are then use iteratively to improve performance. This can often be time consuming and risks unstable control, so the preference is to enable as accurate open loop control as possible. Industrial robot forward kinematics include Denavit-Hartenberg (DH) parameters. However, assembly and manufacturing tolerances may result in differences between actual and nominal DH parameters. To improve industrial robot positional accuracies, it is required to better estimate its DH parameters. A highly accurate laser tracker system provides the positional measurement required to perform calibration of the DH parameters. For this purpose, a Leica AT960-MR, a laser tracker which works based on interferometry principles, is used to provide end effector 3D position measurements. An artificial Bee colony algorithm is then used to improve the cost function associated with the forward kinematic error by estimating more accurate industrial robot DH parameters. The implementation results demonstrate that using calibrated industrial robot DH parameters, it is possible to improve the open loop positional accuracies of the robot compared to uncalibrated forward kinematics mean absolute error for test data from 75.4 𝝁𝒎 to 60.1 𝝁𝒎 (20.3% improvement).

Static friction modelling is a critical task to have an accurate robot model. In this paper, a neural network separation approach to include nonlinear static friction in models of industrial robots is proposed. For this purpose, the terms corresponding to static friction within the overall robot mathematical model are separable terms treated independently from the rest of the model. The separation modelling process is accomplished by first determining the mathematical model for the system by excluding the friction terms and estimating its parameter values. This part of the model corresponds to gravitational terms only. Because persistency of excitation is required to maintain high accuracy and avoid singularity in the estimations, data with large variations across multiple joint angles are gathered for estimation purposes and a weighted least-squares approach is used. This estimation results in a highly accurate static mathematical model for industrial robots. Results from the weighted least-squares estimation are compared to the original least-squares estimation, ridge regression, a least absolute shrinkage and selection operator, and an elastic net to show superior performance. After modelling the gravitational terms of the model, a multilayer perceptron neural network is used to identify static friction forces in the model from experimental data. This is required in the case of a robot with multiple degrees of freedom because the friction of each joint is a function of several other joint angles acting upon it; making the solution complex and difficult to be obtained through other friction modelling methods. Experimental results obtained from a Universal Robots-UR5 demonstrate the high accuracy of the proposed modelling methodology under static conditions, and future work will consider the implementation of dynamic terms to integrate friction forces during movement.

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