Publishing house Radiotekhnika

"Publishing house Radiotekhnika":
scientific and technical literature.
Books and journals of publishing houses: IPRZHR, RS-PRESS, SCIENCE-PRESS

Тел.: +7 (495) 625-9241


Kinematics model of hexapod. Part 1. Matix models


V.Kh. Ankudinov – Post-graduate Student, Department «Computer systems and networks», Kaluga branch of the Bauman MSTU E-mail: A.V. Maksimov – Ph. D. (Eng.), Associate Professor, Department «Computer systems and networks», Kaluga branch of the Bauman MSTU E-mail:

Hexapod – a six-legged walking robot. Due to the fact that for the static stability of the robot only three legs are needed, hexapods have high stability and maneuverability. Hexapods thus are promising robots for research, capable of working in dangerous areas otherwise inaccessible for humans, such as repairs to the engine rooms of ships, pipes, removing debris, or space exploration. For the synthesis of the statically stable gait of the robot, it\'s necessary to solve the problem of inverse kinematics. To do so, one must first solve the forward kinematics problem, namely, to find the coordinates of the ends of the robot legs with given values for the joint angles. To solve the problem of forward kinematics, a kinematic scheme should be described. There are many kinematic schemes for hexapods. The most widely used among researchers is an insect like scheme with three degrees of freedom for each leg: one for the horizontal plane and two for the vertical. This arrangement combines simplicity and flexibility, that is to say that three – is the minimum necessary number of degrees of freedom to allow the arbitrary specifications of foot end coordinates. Kinematic schemes of hexapods are also divided according to the method of leg placement: symmetrical in the longitudinal plane, or axisymmetric, each of which has its own advantages and disadvantages. The Hexapod design «Snejinka» has an axis of symmetry and has a number of features associated with the desire to reduce the load on the servos and make the design more compact, which led to the placement of two of the three servos for each leg in the coxa. A more compact design causes the coxa-femur hinge to be displaced not only along the axis X but also along Y and Z. Thus the generic hexapod kinematic scheme, that allows for specifying hinge displacements in many axis was introduced. It was shown that generalized kinematics scheme can be easily reduced to different simplified schemes, thus, methods developed from the example of axisymmetric hexapod «Snejinka» using generalized kinematic scheme applicable to the broader class of hexapods, namely to all insect like hexapods with three degrees of freedom for each leg, wherein the first coupling hinge rotates in the horizontal plane, and the second and third in the vertical (twisting of joints along the X axis are absent, the place of contact with the ground is considered to be a point at the end of the leg and the position of this point at the leg is considered to be the same. In the first part of the article for the described kinematic scheme, the solution for the forward kinematics problem using homogeneous matrices is presented. The results can be used to further solve the inverse kinematics problem in different ways.


  1. Chàvez-Clemente D. Gait Optimization for Multi-legged Walking Robots, with Application to a Lunar Hexapod. Ph.D. Thesis. Stanford University, California. CA. USA. 2011.
  2. Carbone G., Ceccarelli M. Legged robotic systems // In Cutting Edge Robotics. Kordic V., Lazinica A., Merdan M. Eds. InTech: Vienna. Austria. 2005. P. 553−576.
  3. Cigola M., Pelliccio A., Salotto O., Carbone G., Ottaviano E., Ceccarelli M. Application of robots for inspection and restoration of historical sites. In Proceedings of the International Symposium on Automation and Robotics in Construction of the Conference, Ferrara. Italy. 11−14 September 2005. P. 37.
  4. Jun B.H., Shim H., Kim B., Park J.Y., Baek H., Yoo S., Lee P.M. Development of seabed walking robot CR200 // Proceedings of the OCEANS’13 MTS/IEEE of the Conference, San Diego, CA. USA. 23−26 September 2013. P. 1−5.
  5. Georgiades C. Simulation and Control of an Underwater Hexapod Robot. M.D. Thesis. McGill University, Montreal. QC, Canada. 2005.
  6. Bares J., Hebert M., Kanade T., Krotkov E., Mitchell T., Simmons R., Whittaker W. Ambler: An autonomous rover for planetary exploration. IEEE Comput. 1989. 26. 6−18.
  7. Preumont A., Alexandre P., Doroftei I., Goffin F. A conceptual walking vehicle for planetary exploration. Mechatronics 1997. 7. 287−296.
  8. Bartholet T., Crawson R. Robot Applications for Nuclear Power Plant Maintenance // EPRI Report-NP-3941, Research Report Center: Palo Alto, CA, USA. 1985.
  9. Oku M., Yang H., Paio G., Harada Y., Adachi K., Barai R., Nonami K. Development of hydraulically actuated hexapod robot COMET-IV-The 1st report: System design and configuration // Proceedings of the 2007 JSME Conference on Robotics and Mechatronics, Akita, Japan. 26−28 May 2007.
  10. Franco Tedeschi, Giuseppe Carbone Design Issues for Hexapod Walking Robots // Robotics 2014. 3. 181−206.
  11. Ankudinov V.KH., Maksimov A.V. Konstrukcija geksapoda «Snezhinka V0.1.4» // Materialy Vseros. nauchno-tekhnich. konf. «Naukoemkie tekhnologii v priboro- i mashinostroenii i razvitie innovacionnojj dejatelnosti v vuze». M.: Izd-vo MGTU im. N.EH. Baumana. 2014. T. 4. S. 55−58.
  12. Fu K., Gonsales P., Li K. Robototekhnika. M.: Mir. 1989. 621 s.


© Издательство «РАДИОТЕХНИКА», 2004-2017            Тел.: (495) 625-9241                   Designed by [SWAP]Studio