Inverse kinematic of European Robotic Arm based on a new geometrical approach

Document Type : Research Article


Faculty of Mechanical Engineering, Shahrood University of Technology, Shahrood, Iran



In this study, inverse kinematics is solved for the European Robotic Arm. This robot is a type of space manipulator and has seven degrees of freedom. Forward and inverse kinematic is obtained by a new geometrical method. The limitations of robot workspace are calculated for robot joints and grippers. A geometrical inverse kinematic is presented for the first time, and the transferring process for various situations is developed to grasp the object at any position and orientation. Considering multiple missions, for robots in the transferring process, there isn’t a unit method to support all the situations and tasks in the inverse kinematic problem. To determine the workspace of robot, its geometry and object situation (orientation and position) are considered. To this end, using the suggested inverse kinematic algorithm, the target coordinate and orientations are obtained. In the presented inverse kinematic algorithm, an analytical method is used to derive the joint space variables in terms of workspace variables. The European Robotic Arm can move step by step from one target point to the next one. So, a general transferring algorithm is presented to realize the robot’s mission. In the presented algorithm, when the target is unreachable by the one-step operation, the transferring mission is utilized by the robot. Some simulation plans, to validate the proposed algorithms, indicate that the presented method works correctly.


Main Subjects

[1] H. Cruijssen, M. Ellenbroek, M. Henderson, H. Petersen, P. Verzijden, M. Visser, The European Robotic Arm: A High-Performance Mechanism Finally on its way to Space,  in 42nd Aerospace Mechanisms Symposium, NASA Goddard Space Flight Center, 2014
[2] P.J. Lambooy, W.M. Mandersloot, R.H. Bentall, Some mechanical design aspects of the European Robotic Arm,  Proceedings of the 29th Aerospace Mechanisms Symposium. Johnson Space Center, Houston, Texas, (1995) 17–29.
[3] R. Boumans, C. Heemskerk, The European robotic arm for the international space station, Robotics and Autonomous Systems, 23(1-2) (1998) 17-27.
[4] F. Feng, L. Tang, J. Xu, H. Liu, Y. Liu, A review of the end-effector of large space manipulator with capabilities of misalignment tolerance and soft capture, Science China Technological Sciences, 59(11) (2016) 1621-1638.
[5] F. Romanelli, Hybrid control techniques for static and dynamic environments: a step towards robot-environment interaction, in:  Robot Manipulators New Achievements, IntechOpen, 29  (2010) 551–576.
[6] F.A.A. Cheein, F. di Sciascio, J.M. Toibero, R. Carelli, Robot Manipulator Probabilistic Workspace Applied to Robotic Assistance,  Robot Manipulators New Achievements, IntechOpen, 1(1) (2011).
[7] W. Liu, D. Chen, J. Steil, Analytical inverse kinematics solver for anthropomorphic 7-DOF redundant manipulators with human-like configuration constraints, Journal of Intelligent & Robotic Systems, 86(1) (2017) 63-79.
[8] K.D. Kendricks, A kinematic analysis of the gmf a-510 robot: An introduction and application of groebner basis theory, Journal of Interdisciplinary Mathematics, 16(2-3) (2013) 147-169.
[9] K. Kendricks, Solving the inverse kinematic robotics problem: A comparison study of the Denavit-Hartenberg matrix and Groebner basis theory, PhD  Thesis, Auburn University Libraries, Auburn, Alabama, 2007
[10] J.F.A. Díaz, M.S. Dutra, F.A.d.N.C. Pinto, Kinematical and dynamical models of KR 6 KUKA robot, including the kinematic control in a parallel processing platform, Robot manipulators new achievements, IntechOpen, (2010) 601-620.
[11] C. Lee, M. Ziegler, Geometric approach in solving inverse kinematics of PUMA robots, IEEE Transactions on Aerospace and Electronic Systems, (6) (1984) 695-706.
[12] S.N. Nabavi, A. Akbarzadeh, J. Enferadi, A Study on Kinematics and Workspace Determination of a General 6-P US Robot, Journal of Intelligent & Robotic Systems, 91(3-4) (2018) 351-362.
[13] Z. Xie, Kinematic, dynamic and accuracy reliablity analysis of 6 degree-of-freedom robotic arm, PhD  Thesis, University of Missouri, Columbia,  2013
[14] M. Shahinpoor, M. Jamshidi, Y.T. Kim, Exact solution to the inverse kinematics problem of a standard 6‐axis robot manipulator, Journal of robotic systems, 3(3) (1986) 259-280.
[15] J.D. Sun, G.Z. Cao, W.B. Li, Y.X. Liang, S.-D. Huang, Analytical inverse kinematic solution using the DH method for a 6-DOF robot, in:  2017 14th International Conference on Ubiquitous Robots and Ambient Intelligence (URAI), IEEE, 2017, pp. 714-716.
[16] J. Xie, W. Qiang, B. Liang, C. Li, Inverse kinematics problem for 6-DOF space manipulator based on the theory of screws, in:  2007 IEEE International Conference on Robotics and Biomimetics (ROBIO), IEEE, 2007, pp. 1659-1663.
[17] S. Sagara, Y. Taira, Digital Control of Free Floating Space Robot Manipulators Using Transpose of Generalized Jacobian Matrix, in:  Robot Manipulators New Achievements, IntechOpen, (2010) 361.
[18] I. Duleba, Kinematic Models of Doubly Generalized N-trailer Systems, Journal of Intelligent & Robotic Systems, 94(1) (2019) 135-142.
[19] W. Xu, Z. Mu, T. Liu, B. Liang, A modified modal method for solving the mission-oriented inverse kinematics of hyper-redundant space manipulators for on-orbit servicing, Acta Astronautica, 139 (2017) 54-66.
[20] Z.Y. Li, D.J. Zhao, J.S. Zhao, Structure synthesis and workspace analysis of a telescopic spraying robot, Mechanism and Machine Theory, 133 (2019) 295-310.
[21] J. Oh, H. Bae, J.-H. Oh, Analytic inverse kinematics considering the joint constraints and self-collision for redundant 7DOF manipulator, in:  2017 First IEEE International Conference on Robotic Computing (IRC), IEEE, 2017, pp. 123-128.
[22] W. Xu, Z. Hu, L. Yan, H. Yuan, B. Liang, Modeling and planning of a space robot for capturing tumbling target by approaching the Dynamic Closest Point, Multibody System Dynamics, 47(3) (2019) 203-241.
[23] R. Ghaedrahmati, A. Raoofian, A. Kamali, A. Taghvaeipour, An enhanced inverse dynamic and joint force analysis of multibody systems using constraint matrices, Multibody System Dynamics, 46(4) (2019) 329-353.
[24] M. Ellenbroek, J. Schilder, On the use of absolute interface coordinates in the floating frame of reference formulation for flexible multibody dynamics, Multibody system dynamics, 43(3) (2018) 193-208.
[25] A. Müller, Screw and Lie group theory in multibody kinematics, Multibody System Dynamics, 43(1) (2018) 37-70.
[26] K. Komoda, H. Wagatsuma, Energy-efficacy comparisons and multibody dynamics analyses of legged robots with different closed-loop mechanisms, Multibody System Dynamics, 40(2) (2017) 123-153.
[27] J.H. Ginsberg, Advanced engineering dynamics, Cambridge University Press, 1998