Skip to main content

Footstep adaptation strategy for reactive omnidirectional walking in humanoid robots

  • Jiwen Zhang (a1) (a2) (a3), Zeyang Xia (a4), Li Liu (a1) (a2) (a3) and Ken Chen (a1) (a2) (a3)

Stability, high response quality and rapidity are required for reactive omnidirectional walking in humanoids. Early schemes focused on generating gaits for predefined footstep locations and suffered from the risk of falling over because they lacked the ability to suitably adapt foot placement. Later methods combining stride adaptation and center of mass (COM) trajectory modification experienced difficulties related to increasing computing loads and an unwanted bias from the desired commands. In this paper, a hierarchical planning framework is proposed in which the footstep adaption task is separated from that of COM trajectory generation. A novel omnidirectional vehicle model and the inequalities deduced therefrom are adopted to describe the inter-pace connection relationship. A constrained nonlinear optimization problem is formulated and solved based on these inequalities to generate the optimal strides. A black-box optimization problem is then constructed and solved to determine the model constants using a surrogate-model-based approach. A simulation-based verification of the method and its implementation on a physical robot with a strictly limited computing capacity are reported. The proposed method is found to offer improved response quality while maintaining rapidity and stability, to reduce the online computing load required for reactive walking and to eliminate unnecessary bias from walking intentions.

Corresponding author
*Corresponding author. Email:
Hide All
1. Chestnutt J. et al. “An Intelligent Joystick for Biped Control,” Proceedings of the IEEE International Conference on Robotics and Automation, Piscataway, NJ (May 15–19, 2006) pp. 860–865.
2. Dune C. et al., “Cancelling the Sway Motion of Dynamic Walking in Visual Servoing,” Proceedings of IEEE International Conference on Intelligent Robots and Systems, Piscataway, NJ (Oct. 18–22, 2010) pp. 3175–3180.
3. Kajita S. et al., “The 3D Linear Inverted Pendulum Mode: A Simple Modeling for a Biped Walking Pattern Generation,” Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, Piscataway, NJ, Vol. 1 (Oct. 29–Nov. 03, 2001) pp. 239–246.
4. Kajita S. et al. “Biped Walking Pattern Generation by Using Preview Control of Zero-Moment Point,” Proceedings of IEEE International Conference on Robotics and Automation, Piscataway, NJ, Vol. 2 (Sep. 14–19, 2003) pp. 1620–1626.
5. Czarnetzki S., Kerner S. and Urbann O., “Observer-based dynamic walking control for biped robots,” Robot. Auton. Syst. 57, 839845 (2009).
6. Zeyang X., Jing X. and Ken C., “Global navigation for humanoid robots using sampling-based footstep planners,” IEEE/ASME Trans. Mechatronics 16, 716723 (2011).
7. Zeyang X., Jing X. and Ken C., “Parameter self-adaptation in biped navigation employing nonuniform randomized footstep planner,” Robotica 28, 929936 (2010).
8. Morisawa M. et al., “Motion Planning of Emergency Stop for Humanoid Robot by State Space Approach,” Proceedings of IEEE International Conference on Intelligent Robots and Systems, Piscataway, NJ (Oct. 9–15, 2006) pp. 2986–2992.
9. Herdt A. et al., “Online walking motion generation with automatic footstep placement,” Adv. Robot. 24, 719737 (2010).
10. Piperakis S., Orfanoudakis E. and Lagoudakis M. G., “Predictive Control for Dynamic Locomotion of Real Humanoid Robots,” Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems, Piscataway, NJ (Sep. 14–18, 2014) pp. 4036–4043.
11. Dimitrov D., Paolillo A. and Wieber P. B., “Walking Motion Generation with Online Foot Position Adaptation Based on l-1 and l-∞ Norm Penalty Formulations,” Proceedings of IEEE International Conference on Robotics and Automation, Piscataway, NJ (May 9–13, 2011) pp. 3523–3529.
12. Zhang J., Liu L., Li C. and Chen K., “Parametric omnidirectional gait planning of humanoid robots(in Chinese),” Robotica 36, 210217 (2014).
13. Qiang H. et al., “Planning walking patterns for a biped robot,” IEEE Trans. Robot. Autom. 17, 280289 (2001).
14. Dip G., Prahlad V. and Kien P. D., “Genetic algorithm-based optimal bipedal walking gait synthesis considering tradeoff between stability margin and speed,” Robotica 27, 355365 (2009).
15. Hu L., Zhou C. and Sun Z., “Estimating biped gait using spline-based probability distribution function with Q-learning,” IEEE Trans. Ind. Electron. 55, 14441452 (2008).
16. Kensuke H. et al.An analytical method on real-time gait planning for a humanoid robot,” Int. J. Humanoid Robot. 3, 119 (2006).
17. Strom J., Slavov G. and Chown E., “Omnidirectional Walking Using ZMP and Preview Control for the NAO Humanoid Robot,” In: RoboCup 2009: Robot Soccer World Cup XIII (Springer, Berlin Heideiberg, 2010) pp. 378389.
18. Gouaillier D., Collette C. and Kilner C., “Omnidirectional Closed-Loop Walk for NAO,” Proceedings of 2010 IEEE-RAS International Conference on Humanoid Robots, Piscataway, NJ (Dec. 6–8, 2010) pp. 448–454.
19. Shafii N. et al., “Omnidirectional Walking and Active Balance for Soccer Humanoid Robot,” In: Progress in Artificial Intelligence (Springer, Berlin, Heidelberg, 2013) pp. 283294.
20. Graf C. and Thomas R., “A Closed-loop 3D-LIPM Gait for the RoboCup Standard Platform League Humanoid,” Proceedings of the 4th Workshop on Humanoid Soccer Robots in Conjunction with the 2009 IEEE-RAS International Conference on Humanoid Robots, Piscataway, NJ (2009) pp. 30–37.
21. Song S., Ryoo Y. J. and Hong D. W. “Development of An Omnidirectional Walking Engine for Full-Sized Lightweight Humanoid Robots,” Proceedings of the ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (Aug. 28–31, 2011) pp. 847–854.
22. Alcaraz-Jimenez J., Herrero-Perez D. and Martinez-Barbera H., “Motion planning for omnidirectional dynamic gait in humanoid soccer robots. J. Phys. Agents 5, 2534 (2011).
23. Wieber P. B., Trajectory Free Linear Model Predictive Control for Stable Walking in the Presence of Strong Perturbation,” Proceedings of IEEE International Conference on Humanoid Robots, Piscataway, NJ (Dec. 4–6, 2006) pp. 137–142.
24. Vukobratovic M. and Stepanenko Y., On the stability of anthropomorphic systems. Math. Biosci. 15, 137 (1972).
25. Herdt A., Perrin N. and Wieber P. B., “Walking without Thinking About It,” Proceedings of 2010 IEEE/RSJ International Conference on Intelligent Robots and Systems, Piscataway, NJ (Oct. 18–22, 2010) pp. 190–195.
26. Garcia M. et al., “Vision-guided motion primitives for humanoid reactive walking: Decoupled versus coupled approaches. Int. J. Robot. Res. 34, 402419 (2014).
27. Dimitrov D., Sherikov A. and Wieber P. B, “A Sparse Model Predictive Control Formulation for Walking Motion Generation,” Proceedings of 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems, Piscataway, NJ (Sep. 25–30, 2011) pp. 2292–2299.
28. Pratt J. et al., “Capture Point: A Step Toward Humanoid Push Recovery,” Proceedings of IEEE-RAS International Conference on Humanoid Robots (2006) pp. 200–207.
29. Svanberg K., “A class of globally convergent optimization methods based on conservative convex separable approximations,” SIAM J. Optim. 12, 555573 (2002).
30. Conn A. R., Gould M. and Toint P., “A globally convergent augmented Lagrangian algorithm for optimization with general constraints and simple bounds,” SIAM J. Numer. Anal. 28, 545572 (1991).
31. Orin D., Goswami A. and Lee H., “Centroidal dynamics of a humanoid robot,” Auton. Robots 35 (2–3), 161176 (2013).
32. Hemker T., Stelzer M. and Stryk O. V., “Efficient walking speed optimization of a humanoid robot,” Int. J. Robot. Res. 28, 303314 (2009).
33. Sacks J. et al.Design and analysis of computer experiments. Stat. Sci. 4, 409435 (1989).
34. Jones D. R., Schonlau M. and Welch W. J., “Efficient global optimization of expensive black-box functions,” J. Global Opt. 13, 455492 (1998).
35. Bates S. J., Sienz J. and Toropov V. V., “Formulation of the optimal Latin hypercube design of experiments using a permutation genetic algorithm,” AIAA J. 2011, 17 (2004).
36. Kanehiro F., Hirukawa H. and Kajita S., “OpenHRP: Open architecture humanoid robotics platform,” Int. J. Robot. Res. 23, 155165 (2004).
37. Johnson S. G., “The NLopt Nonlinear-Optimization Package,” (2014). Available from: [cited Sep. 22, 2015].
38. Viana FAC, SURROGATES Toolbox User's Guide, Version 3.0 ed. Gainesville, FL, USA (2011). Available at
39. Lophaven S. N., Nielsen H. B. and Sndergaard J., “DACE: A MATLAB Kriging Toolbox,” (2007). Available at [accessed Nov. 7, 2007].
40. Xiao X. et al. “Team TH-MOS,” (2014). Available at
41. Bi J. et al. “Team Description Paper for Team I-KID RoboCup 2014,” (2014). Available at
42. Picheny V. et al., “Quantile-based optimization of noisy computer experiments with tunable precision,” Technometrics 55, 213 (2013).
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

  • ISSN: 0263-5747
  • EISSN: 1469-8668
  • URL: /core/journals/robotica
Please enter your name
Please enter a valid email address
Who would you like to send this to? *



Full text views

Total number of HTML views: 0
Total number of PDF views: 52 *
Loading metrics...

Abstract views

Total abstract views: 274 *
Loading metrics...

* Views captured on Cambridge Core between 12th April 2017 - 21st November 2017. This data will be updated every 24 hours.