Redundancy Trajectory Generation for Biped Robot Manipulators

2족 보행로봇을 위한 여유자유도 궤적 생성

  • 연제성 (한양대학교 기계공학과) ;
  • 박종현 (한양대학교 기계공학과)
  • Published : 2009.10.01


A biped robot in locomotion can be regarded to be kinetically redundant in that the link-chain from its foot on the ground to its swing foot has more degrees of freedom that needed to realize stable bipedal locomotion. This paper proposes a new method to generate a trajectory for bipedal locomotion based on this redundancy, which directly generates a locomotion trajectory at the joint level unlike some other methods such as LIPM (linear inverted-pendulum mode) and GCIPM (gravity-compensated inverted-pendulum mode), each of which generates a trajectory of the center of gravity or the hip link under the assumption of the dominance of the hip-link inertia before generating the trajectory of the whole links at the joint level. For the stability of the trajectory generated in the proposed method, a stability condition based on the ZMP (zero-moment point) is used as a constraint as well as other kinetic constraints for bipedal motions. A 6-DOF biped robot is used to show how a stable locomotion trajectory can be generated in the sagittal plane by the proposed method and to demonstrate the feasibility of the proposed method.


  1. Shuuji K. and Kazuo T., 1991 'Study of Dynamic Biped Locomotion on Rugged Terrain : Derivation and Application of the Linear Inverted Pendulum Mode,' Proceedings of the IEEE International Conference on Robotics and Automation, pp. 1405-1411
  2. Park, J. H. and Kim, K. D., 1998, 'Biped Robot Walking Using Gravity-Compensated Inverted Pendulum Mode and Computed Torque Control,' IEEE Int. Conf. on Robotics & Automation, pp. 3528-3533
  3. Shuuji K., Fumio K., Kenji K., Kiyoshi F., Kensuke H., Kazuhito Y. and Hirohisa H., 2003, 'Biped Walking Pattern Generation by using Preview control of Zero-Moment Point,' Proceedings of the IEEE International Conference on Robotics and Automation, pp. 1620-1626
  4. Lim, I., Yeon, J. S., Kwon, O. and Park, J. H., 2005, 'Stable Trajectory Generation of Biped Robots with Multiple Mass Model for Impact Force Minimization,' Proceedings of International Conference on Ubiquitous Robots and Ambient Intelligence
  5. Naoki S., Toshiyuki M. and Kouhei O., 1997, 'An Approach to Biped Robot Control Utilized Redundancy in Double Support Phase,' Proceedings in Industrial Electronics Conference, Vol. 3, pp. 1332-1336
  6. Ryoichi S., Masahiko H. and Masaaki S., 2006, 'Gait Control for Redundant Legged Biped Robot at Constant Velocity and Constant Height of the Waist,' Electrical Engineering in Japan, Vol. 156, No. 4, pp. 51-59
  7. Yoo, D., So, B. R., Yi, B. J. and Kim, W., 2004, 'Motion Planning Algorithms for kinematically Redundant Manipulator Not Fixed to the Ground,' Journal of Control, Automation and Systems Engineering, Vol. 10, No. 10, pp. 869-877
  8. Park, J. H. and Cho, H. C., 2000, 'An On-Line Trajectory Modifier for the Base Link of Biped Robots to Enhance Locomotion Stability,' IEEE Int. Conf. on Robotics & Automation, pp. 3353-3358
  9. Park, J. H. and Chung, H., 1999, 'Hybrid Control for Biped Robots Using Impedance Control and Computed-Torque Control,' IEEE Int. Conf. on Robotics & Automation, pp. 1365-1370
  10. Park, J. H. and Kwon, O., 2001, 'Reflex Control of Biped Robot Locomotion on a Slippery Surface,' IEEE Int. Conf. on Robotics & Automation, pp. 4134-4139
  11. Yeon, J. S., Kwon, O. and Park, J. H., 2006, 'Trajectory Generation and Dynamic Control of Planar Biped Robots with Curved Soles,' Journal of Mechanical Science and Technology, Vol. 20, No. 5, pp. 602-611
  12. Park, J. H., 2001, 'Impedance Control of Biped Locomotion,' IEEE Transactions on Robotics and Automation, Vol. 17, No. 6, pp. 870-882