Sains Malaysiana 48(12)(2019): 2759–2766
            
          
              http://dx.doi.org/10.17576/jsm-2019-4812-17 
                 
          
             
          
          Application of Variable
            Zero-Moment Point in Walking Control of the Biped Robot
            
          
              (Penggunaan 
                Pemboleh Ubah 
                Titik Momen Sifar 
                pada Kawalan 
                Berjalan Robot Dua Kaki)  
          
             
          
          CHENGLIN JING*
            
          
          
             
          
          School
            of Mathematics and Statistics, Guizhou University of
            Finance and Economics, Guiyang, 550025
            
          
          China
            
          
          
             
          
          Diserahkan: 21 Februari 2019/Diterima: 23 Disember 2019
            
          
          
             
          
          ABSTRACT
            
          
          Using the predictive control based on zero-moment point (ZMP),
            the biped robot can walk comparatively stably. However, the problems such as
            lack of self-adaptivity are also highlighted mainly
            on account of modeling errors and environmental perturbations; specifically,
            the tracking errors of ZMP are generated, leading to a
            reduced walking stability. To address this problem, in the present work, the
            expected ZMP was decomposed into the reference ZMP which
            is pre-planned offline, and the variable ZMP which can be varied in real
            time. With the addition of the variable ZMP, the outside interferences
            can be eliminated. By combining the predictive control system and the inverse
            system of variable ZMP, the walking pattern of the robot
            with favorable self-adaptivity can be achieved.
            Finally, the simulation results indicate that the self-adaptivity of the robot can be effectively improved using the proposed control system.
            
          
          Keywords: Biped robot; inverse system; predictive control; self-adaptivity; variable zero-moment point (ZMP)
            
          
          
             
          
          ABSTRAK
            
          
              Penggunaan kawalan 
                ramalan berdasarkan 
                titik momen sifar 
                (ZMP), 
                robot dua kaki boleh berjalan 
                dengan agak stabil. 
                Walau bagaimanapun, 
                masalah seperti kekurangan penyesuaian diri juga diketengahkan 
                terutamanya pada 
                kesilapan pemodelan dan alam sekitar; 
                secara khusus, 
                kesilapan pengesanan ZMP 
                dijana, membawa kepada pengurangan kestabilan berjalan. Untuk menangani masalah ini dalam 
                kajian semasa, 
                ZMP 
                yang dijangka telah 
                reput ke dalam 
                rujukan ZMP yang dipra-rancang 
                secara luar 
                talian, dan pemboleh 
                ubah ZMP yang boleh 
                diubah dalam 
                masa nyata. Dengan penambahan 
                pemboleh ubah 
                ZMP, 
                gangguan luar 
                boleh dihapuskan. Dengan menggabungkan sistem kawalan ramalan dan sistem 
                songsang pemboleh 
                ubah ZMP, pola 
                berjalan robot dengan penyesuaian diri yang menggalakkan boleh dicapai. Kesimpulannya, keputusan simulasi menunjukkan bahawa penyesuaian diri robot boleh diperbaiki dengan berkesan menggunakan sistem kawalan cadangan.  
                
              Kata kunci: Kawalan 
                ramalan; pemboleh 
                ubah titik momen 
                sifar (ZMP); penyesuaian 
                diri; robot dua kaki; sistem 
                songsang  
          
             
          
          RUJUKAN
            
          
          Chang,
            J. & Liu, G. 2012. Designing a control system for humanoid soccer robots. Computer
              Applications and Software 29(11): 302-304, 333.
            
          
          Czarnetzki, S., Kerner, S. & Urbann, O. 2009.
            Observer-based dynamic walking control for biped robots. Robotics and Autonomous
              Systems 57(2009): 839-845.
            
          
          Fu,
            G., Yang, Y., Chen, J. & Li, J. 2013. Walking control for humanoid robot
            based on ZMP error correction. Robot 35(1): 39-44.
            
          
          Gao,
            W. & Wang, W.F. 2017. The fifth geometric-arithmetic index of bridge graph
            and carbon nanocones. Journal of Difference
              Equations and Applications 23(1-2SI): 100-109.
            
          
          Hans,
            S., Tripathi, D., Mogbademu,
            A.A. & Tyagi, B. 2018. Inequalities for rational
            functions with prescribed poles. Journal of Interdisciplinary Mathematics 21(1):
            157-169.
            
          
          Huy, T.D., Phuong,
            N.T., Loc, H.D. & Cuong,
            N.C. 2013. A simple walking control method for biped robot with stable gait. Journal
              of Computer Science and Cybernetics 29(2): 105-118.
            
          
          Jimmy,
            O.R. 2010. A hybrid CPG-ZMP control system for stable walking of a simulated
            flexible spine humanoid robot. Neural Networks 23(1): 452-460.
            
          
          Jing,
            C., Xue, F., Zhang, H. & Li, Z. 2010.
            Implementation method of predictive control for biped robot stabilization
            walking pattern. Chinese Journal of Scientific Instrument 31(12):
            2700-2705.
            
          
          Kajita, S. & Guan,
            Y. 2007. Humanoid Robots. Beijing: Tsinghua University Press.
            
          
          Kajita, S., Morisawa, M., Harada, K., Kaneko, K., Kanehiro,
            F. & Fujiwara, K. 2006. Biped walking pattern generator allowing auxiliary
            ZMP Control. Internationonal Conference on
              Intelligent Robots and Systems. Beijing, China. pp. 2993- 2999.
            
          
          Kajita, S., Kanehiro, F., Kaneko, K., Fujiwara, K., Harada, K., Yokoi,
            K. & Hirukawa, H. 2003. Biped walking pattern
            generation by using preview control of zero-moment point. Conference on
              Robotics & Automation. Taiwan, China. pp. 1620-1626.
            
          
          Katayama,
            T., Ohki, T. & Inoue, T. 1985. Design of an optimal controller for a
            discrete time system subject to previewable demand. International
              Journal of Control 41(3): 677-699.
            
          
          Khusainov, R., Afanasyev, I., Sabirova, L. & Magid, E. 2016. Bipedal robot locomotion modelling
            with virtual height inverted pendulum and preview control approaches in
            Simulink environment. Journal of Robotics, Networking and Artificial Life 3(3):
            182-187.
            
          
          Kljuno, E. &
            Williams, R.L. 2010. Humanoid walking robot: Modeling, inverse dynamics, and
            gain scheduling control. Journal of Robotics 2010: Article ID: 278597.
            
          
          Kunimatsu, S., Fukuda, T., Nakasaki, K. & Ishitobi, M.
            2008. l͚ Preview
              control for biped walking pattern generation. SICE Annual Conference. Japan:
              The University Electro- Communications. pp. 1916-1919.
              
            
          Liu, Z., Peng, W., Zare, Y., Hui, D. & Rhee, K.Y. 2018. Predicting the
            electrical conductivity in polymer carbon nanotube nanocomposites based on the
            volume fractions and resistances of the nanoparticle, interphase, and tunneling
            regions in conductive networks. RSC
              Advances 8(34): 19001-19010.
            
          
          Mansour, T. & Shattuck, M. 2017. Set partitions and
            parity successions. Journal of Discrete Mathematical Sciences and
              Cryptography 20(8): 1651-1674.
            
          
          New
            ASIMO. 2011. Honda Motor Co. Ltd., New ASIMO [EB/ OL].
            http://world.honda.com/HDTV/ASIM-O/New-ASIMO-run- 6kmh-slomo/index.htm.
            
          
          Park,
            J. & Youm, Y. 2007. General ZMP preview control
            for bipedal walking. IEEE International Conference on Robotics and
              Automation. Roma, Italy. pp. 2682-2687.
            
          
          Peng,
            W.X., Wang, L.S., Mirzaee, M., Ahmadi, H., Esfahani, M. & JFremaux, S.
            2017. Hydrogen and syngas production by catalytic biomass gasification. Energy
              Conversion and Management 135: 270-273.
            
          
          Promsakon, C. 2018. Edge colorability of unitary endo-cayley graphs of cyclic groups. Journal of Discrete Mathematical Sciences and
            Cryptography 2(1): 191-198.
            
          
          Shimmyo, S., Sato, T.
            & Ohnishi, K. 2013. Biped walking pattern generation by using preview
            control based on three-mass model. IEEE Transactions on Industrial
              Electronics 60(11): 5137-5147.
            
          
          Sugihara,
            T. & Yamamoto, T. 2017. Foot-guided agile control of a biped robot through
            ZMP manipulation. IEEE International Conference on Intelligent Robots and
              Systems. Vancouver, Canada. pp. 4546-4551.
            
          
          Xue, F. & Chen,
            X. 2012. Novel gait pattern planning method for increasing flexibility of biped
            robot. Journal of Chinese Computer Systems 33(9): 1928-1933.
            
          
          Yu,
            X., Wei, S. & Liao, Q. 2009. Development and technology research of
            humanoid robot. Journal of Mechanical Engineering 45(3): 71-75.
            
          
          Zeng,
            H. & Yang, Y. 2014. On-line gait planning by using preview control of zero
            moment point. Journal of Computer Applications 34(2): 514-518.
            
          
          
             
          
          *Pengarang untuk surat-menyurat; email: 1265805946@qq.com