Trajectory Planning and Gait Analysis for the Dynamic Stability of a Quadruped Robot

  • Mayuresh S. MaradkarEmail author
  • P. V. Manivannan
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 670)


Trajectory planning of robot’s center of gravity (CoG) is the main concern when a legged robot is walking. The trajectory of the robot should be framed such that the center of pressure (CoP) of the robot should lie within supporting polygon at all time. This paper deals with the study of support polygon and graphical analysis to find the location of CoG, where the robot has high chances to go to instability. The quadrilateral supporting phases are utilized to avoid these instability locations. Further, the analysis is done to find the timely sequence of lift and touchdown of legs (lift and touch are called as events of legs). Based on the sequence of events and the support polygon analysis, trajectory of the robot is defined, which can produce smooth, steady, and stable robot motion. Though the robot gains static stability by trajectory planning, its dynamic stability should also be verified. This is done using zero moment point (ZMP) method. The analysis done in this paper is for the unswaying robot, walking on flat terrain.


Quadruped Support polygon Margin of stability Gait Zero moment point (ZMP) 


  1. 1.
    Anon.: Logistical Vehicle Off-Road Mobility. Project TCCO 62–5; U. S. Army Transportation Combat Developments Agency; Fort Eustis, Va (1967).Google Scholar
  2. 2.
    D. Vishal, P. V. Mannvannan.: Design and analysis of active vibration and stability control of a bio-inspired quadruped robot. Int. Jou. Computational Vision and Robotics (2016).Google Scholar
  3. 3.
    Boston Dynamics Corp, Big Dog Overview [online]. Big Dog: An Overview.
  4. 4.
    D. Vishal, P. V. Manivannan.: Multibody dynamics simulation and gait pattern analysis of a bio-inspired quadruped robot for unstructured terrain using adaptive stroke length, Artificial Life and Robotics-Springer (2016).Google Scholar
  5. 5.
    Min‐Hsiung Hung, Fan‐Tien Cheng, Hao‐Lun Lee & David E. Orin.: Increasing the stability margin of multilegged vehicles through body sway. Journal of the Chinese Institute of Engineers, Vol. 28, No. 1, pp. 39–54 (2005).Google Scholar
  6. 6.
    A. A. Frank.: Automatic Control System for Legged Locomotion Machines,” USC Rept., p. 273 (1969).Google Scholar
  7. 7.
    McGhee, R. B., and Frank, A. A.: On the Stability of Quadruped Creeping Gaits. Mathematical Biosciences, Vol. 3, No. 3/4, pp. 331–353.Google Scholar
  8. 8.
    Hironori Adachi, Noriho Koyachi, and Eiji Nakano.: Mechanism and Control of a Quadruped Walking Robot, IEEE Control Systems Magazine.Google Scholar
  9. 9.
    Reza Yazdani, Vahid. Johari Majd, and Reza Oftadeh.: Dynamically Stable Trajectory Planning for a Quadruped Robot. 20th Iranian Conference on Electrical Engineering, (ICEE2012), Tehran, Iran (2012).Google Scholar
  10. 10.
    W. Scott Persons, Victoria Arbour, Jessica Edwards, Matthew Vavrek, Philip Currie, and Eva Koppelhus.: DINO101- Moving Around, University of Alberta.Google Scholar
  11. 11.
    Mayuresh Maradkar, Aaditya Chandramouli, P. V. Manivannan.: Bio-inspired Reconfigurable Robot: Conceptual Design of an All-terrain Robot Capable of Transforming from an Erect to Sprawling Posture. 3rd Int. Conf. Mechatronics and Robotic Engineering (ICMRE), Paris, France (2017).Google Scholar
  12. 12.
    Mayuresh Maradkar, P. V. Manivannan.: Kinematics and Multi-body Dynamics of a Bio-inspired Quadruped Robot with Nine Linked Closed Chain Legs. International Conference on Robotics: Current Trends and Future Challenges (RCTFC), Thanjavur, India, (2016).Google Scholar
  13. 13.
    Shuaishuai Zhang, Xuewen Rong, Yibin Li and Bin Li.: A Composite COG Trajectory Planning Method for the Quadruped Robot Walking on Rough Terrain. International Journal of Control and Automation Vol. 8, No. 9, pp. 101–118, (2015).Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Indian Institute of Technology MadrasChennaiIndia
  2. 2.Department of Mechanical EngineeringIndian Institute of Technology MadrasChennaiIndia

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