Robust Trajectory Free Model Predictive Control of Biped Robots with Adaptive Gait Length

Document Type: Original Article


Iran University of Science and Technology


This paper employs nonlinear disturbance observer (NDO) for robust trajectory-free Nonlinear Model Predictive Control (NMPC) of biped robots. The NDO is used to reject the additive disturbances caused by parameter uncertainties, unmodeled dynamics, joints friction, and external slow-varying forces acting on the biped robots. In contrary to the slow-varying disturbances, handling sudden pushing disturbances acting on the biped robots is much more complicated and using the NDO doesn’t guarantee the biped walking stability. In order to reject these kinds of disturbances, the motion controller must be able to make suitable decisions for quick changing of the gait length or the walking speed. However, the gait length change is not possible while tracking fixed predefined joint trajectories. Hence, in this paper the NMPC is designed in such a way that it has the ability to change the gait length appropriately. In addition, some schemes will be proposed to reduce the computation time of the NMPC. Simulating results show good performance of the proposed method in trajectory-free walking of biped robots as well as disturbance rejection.


Zohdy M. A. and Zaher A. A., “Robust control of biped’ robots,” American Control Conference, Chicaao, Illinois, 2000.

Chuangfeng H. and Yuefa F., “Robust control for stable dynamic walking of biped robot,” International Conference on Intelligent Robots and Systems, Beijing, China, 2006.

Liu L. M., Tian Y. T, Sui1 Zh., and Huang X. L., “Finitetime robust trajectory tracking control for the under actuated biped robot based on poincarélike-alter-cell-to-cell mapping method,” 4th International Conference on Autonomous Robots and Agents, Wellington, pp. 686-691, New Zealand, 2009.

Nakao M., Ohnishi K., and Miyachi, “A robust decentralized joint control based on interference estimation,” IEEE International Conference on Robotics and Automation, Raleigh, NC, 1987.

Smadi I. and Fujimoto Y., “On nonlinear disturbance observer base control of euler-lagrange systems,” Journal of System Design and Dynamics, Vol. 3, No. 3, pp. 330- 343, 2009.

Gupta A., Disturbance Observer Based Closed Loop Control of Haptic Interfaces, PhD Dissertation, Department of Mechanical Engineering and Materials Science, Rice University, Houston, Texas, 2008.

Young Doo Y., Jung E., and Sul S. k., “Application of a disturbance observer for a relative position control system,” IEEE Transactions on Industry Applications, Vol. 46, Issue 2, 2010.

Azevedo Ch., Poignet Ph., Espiau B., “Moving horizon control for biped robots without reference trajectory,” International Conference on Robotics & Automation, Washington D.C., 2002.

Azevedo CH., Poignet PH., and Espiau B., “Artificial locomotion control: from human to robots,” Journal of Robotics and Autonomous Systems, Vol.43, pp. 203-223, 2004.

Zhu Zh., Wang Y., and Chen X., “Real-time control of full actuated biped robot based on nonlinear model predictive control,” Intelligent Robotics and Applications, Vol. 5314, pp. 873-882, Springer Verlag, 2008.

Mu X., Dynamics and Motion Regulation of a Five-link Biped Robot Walking in the Sagittal Plane, PhD Thesis, Department of Mechanical and Manufacturing Engineering, University of Manitoba, Canada, 2004.

Vukobratovic M. and Stepanenko Y., ”Mathematical models of general anthropomorphic systems,” International Journal of Mathematical Biosciences, Vol.17, pp.191-242. 1973.

Mitobe K., Mori N., Nasu Y. and Adachi N. “Control of a biped walking robot during the double support phase,” Journal of Autonomous Robots, Vol. 4, No. 3, pp. 287-296, 1997.

Bagheri A., Felezi M., and Mousavi P. “Adaptive control and simulation of a seven-link biped robot for the combined trajectory motion and stability investigations,” WSEAS Transactions on Systems, Vol. 5, No. 5, pp. 1214-1222, 2006.

Diedam H., Dimitrov D., Wieber P., Mombaur K., and Diehl M., “Online walking gait generation with adaptive foot positioning through linear model predictive control,” International Conference on Intelligent Robots and Systems, Nice, France, 2008.

Dimitrov D., Wieber P., Ferreau H., and Diehl M., “On the implementation of model predictive control for on-line walking pattern generation,” International Conference on Robotics and Automation, Pasadena, CA, USA, 2008.

Wieber P., “Viability and predictive control for safe locomotion,” International Conference on Intelligent Robots and Systems, Nice, France, 2008.

A. Nikoobin and R. Haghighi, “Lyapunov-based nonlinear disturbance observer for serial n-link robot manipulators,” Journal of Intelligent and Robotic Systems, Vol. 55, No. 2- 3y, pp. 135-153, 2009.

Espiau B. and Sardain P., “The anthropomorphic biped robot BIP2000,” IEEE International Conference on Robotics & Automation, San Francisco, CA, 2000.