Inverse kinematics solution for humanoid robot minimizing gravity-related joint torques

Journal title

Archive of Mechanical Engineering




vol. 69


No 3


Mikołajczyk, Kacper : Faculty of Power and Aeronautical Engineering, Warsaw University of Technology, Warsaw, Poland ; Szumowski, Maksymilian : Faculty of Power and Aeronautical Engineering, Warsaw University of Technology, Warsaw, Poland ; Woliński, Łukasz : Faculty of Power and Aeronautical Engineering, Warsaw University of Technology, Warsaw, Poland



humanoid robot ; redundant kinematics ; joint torque minimalization

Divisions of PAS

Nauki Techniczne




Polish Academy of Sciences, Committee on Machine Building


[1] P. Gupta, V. Tirth, and R.K. Srivastava. Futuristic humanoid robots: An overview. In First International Conference on Industrial and Information Systems, pages 247–254, 2006. doi: 10.1109/ICIIS.2006.365732.
[2] S. Behnke. Humanoid robots – from fiction to reality? KI– Künstliche Intelligenz, 22(4):5–9, 2008.
[3] C.-H. Ting,W.-H Yeo, Y.-J. King, Y.-D. Chuah, J.-V Lee, and W.-B Khaw. Humanoid robot: A review of the architecture, applications and future trend. Research Journal of Applied Sciences, Engineering and Technology, 7:1178–1183, 2014. doi: 10.19026/rjaset.7.402.
[4] R. Mahum, F. Butt, K. Ayyub, S. Islam, M. Nawaz, and D. Abdullah. A review on humanoid robots. International Journal of Advanced and Applied Sciences, 4(2):83–90, 2017. doi: 10.21833/ijaas.2017.02.015.
[5] S. Saeedvand, M. Jafari, H.S. Aghdasi, and J. Baltes. A comprehensive survey on humanoid robot development. The Knowledge Engineering Review, 34:e20, 2019. doi: 10.1017/S0269888919000158.
[6] E. Krotkov, D. Hackett, L. Jackel, M. Perschbacher, J. Pippine, J. Strauss, G. Pratt, and C. Orlowski. The DARPA robotics challenge finals: Results and perspectives. Journal of Field Robotics, 34(2):229–240, 2016. doi: 10.1002/rob.21683.
[7] M. Vukobratovic and B. Borovac. Zero-Moment Point — Thirty Five Years of Its Life. International Journal of Humanoid Robotics, 01(01):157–173, 2004. doi: 10.1142/s0219843604000083.
[8] Ł. Woliński and M. Wojtyra. A novel QP-based kinematic redundancy resolution method with joint constraints satisfaction. IEEE Access, 10:41023–41037, 2022. doi: 10.1109/ACCESS.2022.3167403.
[9] B.W. Satzinger, J.I. Reid, M. Bajracharya, P. Hebert, and K. Byl. More solutions means more problems: Resolving kinematic redundancy in robot locomotion on complex terrain. In 2014 IEEE/RSJ International Conference on Intelligent Robots and Systems, pages 4861–4867. IEEE, 2014. doi: 10.1109/iros.2014.6943253.
[10] J.J. Kuffner and S.M. LaValle. RRT-connect: An efficient approach to single-query path planning. In Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065). IEEE, 2000. doi: 10.1109/robot.2000.844730.
[11] B. Siciliano and J.J.E. Slotine. A general framework for managing multiple tasks in highly redundant robotic systems. In Fifth International Conference on Advanced Robotics 'Robots in Unstructured Environments, pages 1211–1216, vol. 2, 1991. doi: 10.1109/ICAR.1991.240390.
[12] B. Siciliano, L. Sciavicco, L.Villani, and G. Oriolo. Robotics. Modelling, Planning and Control. Springer-Verlag, Wien, 1 edition, 2009. doi: 10.1007/978-1-84628-642-1.
[13] B. Siciliano and O. Khatib, editors. Springer Handbook of Robotics. Springer Handbooks. Springer, Berlin, 2 edition, 2016. doi: 10.1007/978-3-540-30301-5.
[14] S. Chiaverini. Singularity-robust task-priority redundancy resolution for real-time kinematic control of robot manipulators. IEEE Transactions on Robotics and Automation, 13(3):398–410, 1997. doi: 10.1109/70.585902.
[15] N. Mansard, O. Khatib, and A. Kheddar. A unified approach to integrate unilateral constraints in the stack of tasks. IEEE Transactions on Robotics, 25(3):670–685, 2009. doi: 10.1109/TRO.2009.2020345.
[16] F. Flacco and A. De Luca. A reverse priority approach to multi-task control of redundant robots. In 2014 IEEE/RSJ International Conference on Intelligent Robots and Systems, pages 2421–2427, 2014. doi: 10.1109/IROS.2014.6942891.
[17] A.A. Maciejewski and C.A. Klein. Obstacle avoidance for kinematically redundant manipulators in dynamically varying environments. The International Journal of Robotics Research, 4(3):109–117, 1985. doi: 10.1177/027836498500400308.
[18] A.S. Deo and I.D.Walker. Minimum effort inverse kinematics for redundant manipulators. IEEE Transactions on Robotics and Automation, 13(5):767–775, 1997. doi: 10.1109/70.631238.
[19] G.S. Chyan and S.G. Ponnambalam. Obstacle avoidance control of redundant robots using variants of particle swarm optimization. Robotics and Computer-Integrated Manufacturing, 28(2):147–153, 2011. doi: 10.1016/j.rcim.2011.08.001.
[20] M. Duguleana, F. Grigore Barbuceanu, A. Teirelbar, and G. Mogan. Obstacle avoidance of redundant manipulators using neural networks based reinforcement learning. Robotics and Computer-Integrated Manufacturing, 28(2):132–146, 2011. doi: 0.1016/j.rcim.2011.07.004.
[21] C. Yang, S. Amarjyoti, X. Wang, Z. Li, H. Ma, and C. Y. Su. Visual servoing control of baxter robot arms with obstacle avoidance using kinematic redundancy. In H. Liu, N. Kubota, X. Zhu, R. Dillmann, and D. Zhou, editors, Intelligent Robotics and Applications, pages 568–580. Springer International Publishing, Cham, 2015. doi: 10.1007/978-3-319-22879-2_52.
[22] T. Petric, A. Gams, N. Likar, and L. Žlajpah. Obstacle avoidance with industrial robots. In G. Carbone and F. Gomez-Bravo, editors, Motion and Operation Planning of Robotic Systems: Background and Practical Approaches, pages 113–145. Springer International Publishing, Cham, 2015. doi: 10.1007/978-3-319-14705-5_5.
[23] T. Winiarski, K. Banachowicz, and D. Seredyński. Multi-sensory feedback control in door approaching and opening. In D. Filev, J. Jabłkowski, J. Kacprzyk, M. Krawczak, I. Popchev, L. Rutkowski, V. Sgurev, E. Sotirova, P. Szynkarczyk, and S. Zadrożny, editors, Intelligent Systems’2014, pages 57–70, Cham, 2015. Springer International Publishing. doi: 10.1007/978-3-319-11310-4_6.
[24] M. Tanaka and F. Matsuno. Modeling and control of head raising snake robots by using kinematic redundancy. Journal of Intelligent & Robotic Systems, 75(1):53–69, 2013. doi: 10.1007/s10846-013-9866-y.
[25] C. Ye, S. Ma, B. Li, and Y. Wang. Head-raising motion of snake-like robots. In 2004 IEEE International Conference on Robotics and Biomimetics, pages 595–600, 2004. doi: 10.1109/ROBIO.2004.1521847.
[26] J.-A. Claret, G. Venture, and L. Basañez. Exploiting the robot kinematic redundancy for emotion conveyance to humans as a lower priority task. International Journal of Social Robotics, 9(2):277–292, 2017. doi: 10.1007/s12369-016-0387-2.
[27] K. Mikołajczyk, M. Szumowski, P. Płoński, and P. Żakieta. Solving inverse kinematics of humanoid robot using a redundant tree-shaped manipulator model. In Proceedings of the 2020 4th International Conference on Vision, Image and Signal Processing, ICVISP 2020, NewYork, NY, USA, 2020. Association for Computing Machinery. doi: 10.1145/3448823.3448885.
[28] M. Szumowski, M.S. Żurawska, and T. Zielińska. Preview control applied for humanoid robot motion generation. Archives of Control Sciences, 29(1):111–132, 2019. doi: 10.24425/acs.2019.127526.
[29] M. Szumowski, M.S. Zurawska, and T. Zielinska. Simplified method for humanoid robot gait generation. In T. Uhl, editor, Advances in Mechanism and Machine Science, pages 2269–2278. Springer International Publishing, 2019. doi: 10.1007/978-3-030-20131-9_224.
[30] T. Zielińska, L. Zimin, M. Szumowski, and W. Ge. Motion planning for a humanoid robot with task dependent constraints. In T. Uhl, editor, Advances in Mechanism and Machine Science, pages 1681–1690. Springer International Publishing, Cham, 2019. doi: 10.1007/978-3-030-20131-9_166.
[31] S. Kajita, F. Kanehiro, K. Kaneko, K. Fujiwara, K. Harada, K. Yokoi, and H. Hirukawa. Biped walking pattern generation by using preview control of zero-moment point. In 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422), volume 2, pages 1620–1626. IEEE, 2003. doi: 10.1109/ROBOT.2003.1241826.
[32] S.R. Buss and J.-S. Kim. Selectively damped least squares for inverse kinematics. J ournal of Graphics Tools, 10(3):37–49, 2005. doi: 10.1080/2151237X.2005.10129202.
[33] A. Ben-Israel and T.N.E. Greville. Generalized Inverses, Theory and Applications. Springer- Verlag New York, 2 edition, 2003. doi: 10.1007/b97366.
[34] P. Falco and C. Natale. On the stability of closed-loop inverse kinematics algorithms for redundant robots. IEEE Transactions on Robotics, 27(4):780–784, 2011. doi: 10.1109/TRO.2011.2135210.
[35] A. Colomé and C. Torras. Closed-loop inverse kinematics for redundant robots: Comparative assessment and two enhancements. IEEE/ASME Transactions on Mechatronics, 20(2):944–955, 2015. doi: 10.1109/TMECH.2014.2326304.
[36] D.N. Nenchev. Redundancy resolution through local optimization: A review. Journal of Robotic Systems, 6(6):769–798, 1989. doi: 10.1002/rob.4620060607.
[37] H. Zghal, R.V. Dubey, and J.A. Euler. Efficient gradient projection optimization for manipulators with multiple degrees of redundancy. In Proceedings., IEEE International Conference on Robotics and Automation, pages 1006–1011, vol. 2, 1990. doi: 10.1109/ROBOT.1990.126123.
[38] A. Liégeois. Automatic supervisory control of the configuration and behavior of multibody mechanisms. IEEE Transactions on Systems, Man, and Cybernetics, 7(12):868–871, 1977. doi: 10.1109/TSMC.1977.4309644.
[39] D.-S. Bae and E. Haug. A recursive formulation for constrained mechanical system dynamics: Part I. Open loop systems. Mechanics of Structures and Machines, 15(3):359–382, 1987. doi: 10.1080/08905458708905124.
[40] G. Rodriguez, A. Jain, and K. Kreutz-Delgado. A spatial operator algebra for manipulator modeling and control. The International Journal of Robotics Research, 10(4):371–381, 1991. doi: 10.1177/027836499101000406.
[41] K. Yamane and L. Nakamura. O(N) forward dynamics computation of open kinematic chains based on the principle of virtual work. In Proceedings 2001 ICRA. IEEE International Conference on Robotics and Automation (Cat. No.01CH37164), volume 3, pages 2824–2831, 2001. doi: 10.1109/ROBOT.2001.933050.
[42] Ł. Woliński and P. Malczyk. Dynamic modeling and analysis of a lightweight robotic manipulator in joint space. Archive of Mechanical Engineering, 62(2):279–302, 2015. doi: 10.1515/meceng-2015-0016.
[43] M.W. Spong, S. Hutchinson, and M. Vidyasagar. Robot Modeling and Control. Wiley, 2005.
[44] B. Espiau and R. Boulic. On the Computation and Control of the Mass Center of Articulated Chains. Technical Report RR-3479, INRIA, August 1998.
[45] D.A.Winter. Biomechanics and Motor Control of Human Movement. JohnWiley & Sons, Inc., 2009. doi: 10.1002/9780470549148.






DOI: 10.24425/ame.2022.140423 ; ISSN 0004-0738, e-ISSN 2300-1895