DOI QR코드

DOI QR Code

Swing Trajectory Optimization of Legged Robot by Real-Time Nonlinear Programming

실시간 비선형 최적화 알고리즘을 이용한 족형 로봇의 Swing 궤적 최적화 방법

  • Park, Kyeongduk (Department of Mechanical Engineering, Sogang University) ;
  • Choi, Jungsu (Department of Mechanical Engineering, Sogang University) ;
  • Kong, Kyoungchul (Department of Mechanical Engineering, Sogang University)
  • Received : 2015.10.06
  • Accepted : 2015.11.03
  • Published : 2015.12.01

Abstract

An effective swing trajectory of legged robots is different from the swing trajectories of humans or animals because of different dynamic characteristics. Therefore, it is important to find optimal parameters through experiments. This paper proposes a real-time nonlinear programming (RTNLP) method for optimization of the swing trajectory of the legged robot. For parameterization of the trajectory, the swing trajectory is approximated to parabolic and cubic spline curves. The robotic leg is position-controlled by a high-gain controller, and a cost function is selected such that the sum of the motor inputs and tracking errors at each joint is minimized. A simplified dynamic model is used to simulate the dynamics of a robotic leg. The purpose of the simulation is to find the feasibility of the optimization problem before an actual experiment occurs. Finally, an experiment is carried out on a real robotic leg with two degrees of freedom. For both the simulation and the experiment, the design variables converge to a feasible point, reducing the cost value.

Keywords

References

  1. Y. Sakagami, R. Watanabe, C. Aoyama, S. Matsunaga, N. Higaki, and K. Fujimura, "The intelligent ASIMO: System overview and integration," IEEE/RJS International Conference on Intelligent Robots and Systems, pp. 2478-2483, 2002.
  2. M. Raibert, K. Blankespoor, G. Nelson, R. Playter, and B.-D. Team, "Bigdog, the rough-terrain quadruped robot," Proc. of the 17th World Congress The International Federation of Automatic Control (IFAC), vol. 17, no. 1 pp. 10822-10825, Jul. 2008.
  3. I.-W. Park, J.-Y. Kim, J. Lee, and J.-H. Oh, "Mechanical design of humanoid robot platform KHR-3," IEEE-RAS International Conference on Humanoid Robot, pp. 321-326, 2005.
  4. B. Na, H. Choi, and K. Kong, "Design of a direct-driven linear actuator for a high-speed quadruped robot, Cheetaroid-I," IEEE/ASME Transactions on Mechatronics, vol. 20, no. 2 pp. 924-933, Apr. 2015. https://doi.org/10.1109/TMECH.2014.2326696
  5. H. Kang, H. Shim, B. Jun, and P. Lee, "Development of a specialized underwater leg convertible manipulator for the seabed walking robot CR200," Journal of Institute of Control, Robotics and Systems (in Korean), vol. 19, no. 8, pp. 709-717, Aug. 2013. https://doi.org/10.5302/J.ICROS.2013.13.9018
  6. J. Kim, G. Lee, and S. Lee, "Development of an effective walking system for a hexapod robot on uneven terrain," Journal of Institute of Control, Robotics and Systems (in Korean), vol. 19, no. 12, pp. 1152-1159, Dec. 2013. https://doi.org/10.5302/J.ICROS.2013.13.1936
  7. T. Kawabe, T. Honda, and T. Koseki, "Swing leg control for efficient and repeatable biped walking to emulate biological mechanisms," IEEE International Conference on Mechatronics, pp. 629-634, 2013.
  8. K. G. Che and J. H. Park, "Trajectory optimization with GA and control for quadruped robots," Journal of Mechanical Science and Technology, pp. 114-123, 2009.
  9. N. Sugimoto and J. Morimoto, "Phase-dependent trajectory optimization for CPG-based biped walking using path integral reinforcement learning," IEEE-RAS International Conference on Humanoid Robots (Humanoids), pp. 255-260, 2011.
  10. S. H. Shin and B. Kim, "Energy-efficient gait planning and control for biped robots utilizing vertical body motion and allowable ZMP region," IEEE Transactions on Industrial Electronics, vol. 62, no. 4, pp. 2277-2286, 2015. https://doi.org/10.1109/TIE.2014.2360152
  11. K. Kong, K. Inaba, and M. Tomizuka, "Real-time nonlinear programming by amplitude modulation," International Journal of Control, Automation and Systems, vol. 11, no. 4, pp. 742-751, Aug. 2013. https://doi.org/10.1007/s12555-012-0369-6
  12. M. Chan, K. Kong, and M. Tomizuka, "Automatic controller gain tuning of a multiple joint robot based on modified extremum seeking control," Proc. of the 18th World Congress The International Federation of Automatic Control (IFAC), pp. 4131-4136, 2011.
  13. C.-H. Han, K. Kong, and M. Tomizuka, "Sensor-based controller tuning of robot manipulators by real-time optimization," Robot Control, vol. 9, no. 1, pp. 567-572, 2009.
  14. J. S. Arora, Introduction to Optimum Design, 3rd Ed., McGraq-Hill, pp. 278-327, 1989.
  15. H. Choi, S. Oh, and K. Kong, "Design of a biarticular robotic manipulator and its control in the rotating coordinate system," IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM), pp. 888-891, 2014.