Model Based Robot Calibration Technique with Consideration of Joint Compliance
Robot accuracy plays an important role for robot based application in advanced industry.
Especially, robot accuracy decreases because of structural deformation when robot carries heavy load. Identification of physical robot parameters improves its accuracy by updating robot model parameters which are used in robot controller. This research presents identification technique of robot geometric parameters and its joint deformation joint angle.
The target of the paper is comparison of two cases 1) only geometric calibration and 2) geometric and joint deformation angles calibration. Simulation calibration is performed on a Hyundai 800 robot which is designed for carrying heavy loads. The robot position accuracy after calibration demonstrates the effectiveness and correctness of the method.
1. Introduction
Movement programming of robot can be performed on-site or off-site. On site programing shows weak points of only using in cases of a small number of robots. While off-site programing can transfer controlling program for a big number of robots at a time.
However, actual robot parameters normally differ from the robot model parameters which are installed in robot controller (supplied by robot manufacturer). This difference leads a physical robot come to a wrong targets. So, it is necessary to update robot parameters by robot calibration process.
Previous studies concentrated on modeling robot geometric error sources for purposes of calibration (Whitney et al., 1986; Schröer et al., 1997; Alici and Shirinzadeh, 2005). These errors are composed of two types: geometric and non-geometric errors. Geometric errors are link twist angle, link length errors, link and joint angle offsets. Non-geometric errors can be listed as gear backlash, joint deflection, link compliance, etc.
Some researchers assumed that only geometric errors exist on robots kinematic model (Benjamin et al., 1991; Hayati et al., 1988; Veitschegger and Wu, 1986; Khalil et al., 1990; Park et al., 2011). Other researchers (To and Webb, 2012; Gong et al., 2000) considered both link geometric and non-geometric errors (only joint deflection) robot models. The deformation of robot joints and links are caused by its weights and carried payloads; and it really affects robot position accuracy Duelen and Schroer, 1991; Hudgens et al., 1991).
To solve the problem of existence of robot physical deformation, Dulen et al. applied a theory of flexible beams to study the effects of link compliance. The research of Hudgen et al. identified general robot deflection characteristics by applied torques and forces. Both works should include other non-geometric errors to obtain more accurate robot model.
Acilli et al. utilized Fourier polynomial for predicting the position error caused by the non-geometric error (Alici and Shirinzadeh, 2005). By applying the method, a huge number of training date need to be collected, non-liner relationship of joint input and position output is not guarantee for all robot poses.
Artificial Neural Network (ANN) has more advantageous characters: learning ability, adaptation, and flexibility. Some studies have using the ANN to compensate for robot position errors (Joon et al., 2001; Aoyagi et al., 2010; Wang et al., 2012; Takanashi, 1990; Zhong et al., 1996). Jang et al. used a Radial Basis Function Network (RBFN) to form a relation input is joint positions and output is joint offset.
The works have utilized an ANN to make the relationship of end-effector positions and corresponding position errors. However, each robot configurations produce different error even the same end-point position (Meggiolaro et al., ; Zhong and Lewis, 1995). However, application of ANN for robot error compensation still has some drawback because unknowing the robot error sources, difficult to embed the algorithm into the robot controller.
In this paper, we present a technique for the calibration of industrial robots by considering both source of errors such as geometric and non-geometric error to obtain the robot model so closes to the physical robot. The proposed method models the robot joint compliance errors as a rotational spring.
Because of small deflection of robot joint shaft, functional stiffness relationship is assumed linear. Simulation calibration for the Hyundai HH800 robot was carried out to demonstrate the effectiveness and correctness of the proposed method. The simulation results show the more accuracy if we include joint deflection value to robot model.
2. Kinematic model of the HH800 robot
2.1 Kinematic model of HH800 robot
HH800 robot (Fig. 1) has 6 degree of freedom (dof), consists of a main open kinematic chain (6 dof) and a closed loop mechanism (2 dof). The open chain is form by the revolute joints 1, 2, 3p, 4, 5, and 6 and corresponding links. The closed mechanism PQRS is connected by the joints 2, 3, Q, R and S. The frames are attached at links by using Danevit-Hartenberg (D-H) convention (Hartenberg et al., 1955).
2.2 Robot joint compliance model
In a robot static pose, a robot joint torque causes a rotational deformation about a joint shaft. Then a joint shaft is considered as a torsional spring. In this section, we propose a torsional spring model to represent rotational joint compliance. The relation of input moment M and deformation angle δθ of torsional springs, for instance M = k(δθ)3. For small δθ, the relation can be assumed linear as follows: where Mi [Nm]: joint torque at joint axis i, ki [Nm/rad] stiffness coefficient of joint i, si [rad/Nm] compliance coefficient, δθi [º] is the deformation angle of joint i, i = 1, …, 6.
The active joint torques are computed by the methods presented in the studies (Luh et al., 1985; Nakamura et al., 1989). By applying a virtual work principle and an open tree-structure (joint R of the closed loop PQRS (Figs.1 and 2) is cut open). The first chain is connected. The second is connected by the joints 𝜃1, 𝜃3, Q, and R. As a result, the active robot joint torques are M1, M2, M3, M4, M5, and M6. Static joint torques calculation requires data of the robot dynamic parameters, such as link weights, link mass centers’ positions, and payload.
3. Formulation for parameter identification
Differential transformation of the open kinematic chain can be obtained by differentiating equations (2) in term of its kinematic parameters. Robot consists of a main open chain and a closed loop mechanism (Fig.1). Robot identification equations are formed by including the differential output variable the closed loop 𝜃3𝑝 into differential transformation of the open kinematic chain at according variable.
4. Simulation and Results
A robot calibration system consists of a Hyundai HH800 robot; an assumed 3D point measurement device (measurement accuracy of 0.01 mm/m, repeatability of +/-0.006 mm/m). Measurement position is defined at a point E on robot tool. The three-dimensional coordinates of the end points are measured by the assumed measuring device and saved in a computer; the associated robot joint readings also are recorded.
In the identification process, we identify the robot link geometric errors and joint compliance parameters by using the above measurement. The total number of identifiable parameters is 29 (25 geometric and 4 joint compliance parameters, s2, s3, s4, s5). Because the first joint axis is vertical, the s1 torsional deformation about the first axis is so small compared with other joint, s1 deformation does not effects much and can be neglected.
The simulation results show that before calibration the mean end-point deviation of robot is 29,74 [mm], this number decrease to 0.453 mm for case geometric parameter calibration, the number is reduced to 0.1 mm for case geometric and stiffness parameter calibration. The stiffness parameters of joints 2, 3, 4, 5 are s2 = 1.792×107 [rad/Nm], s3 = 1.915 ×107 [rad/Nm], s4 = 1.959 ×107 [rad/Nm], and s5 = 1.820 ×107 [rad/Nm], respectively. Maximum values of robot end-point deviation are shown in the third column of Table 2 accordingly.
5. Conclusions
This paper suggested a model based calibration method for increasing robot position accuracy. The method has many advantages such as less computing time, fast convergence, and accurate knowledge of error sources. The simulation was performed on the Hyundai HH800 robot show that robot average accuracy is increased significantly to 0.1 [mm] (from 29, 74 [mm] before calibration). The simulation calibration results show that the including joint deformation into robot model for case of robot carrying load is necessary.
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Author: Hoai-Nhan Nguyen *, Trong-Hai Nguyen, Dinh-Tung Vo, Quoc-Phuong Pham
* HUTECH Institute of Engineering, Ho Chi Minh City University of Technology (HUTECH), Ho Chi Minh City, Vietnam.
Keywords: kinematic identification; joint stiffness; robot calibration.
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