Skip to main content

Trajectory generation and step planning of a 12 DoF biped robot on uneven surface

  • Gaurav Gupta (a1) and Ashish Dutta (a1)

One of the primary goals of biped locomotion is to generate and execute joint trajectories on a corresponding step plan that takes the robot from a start point to a goal while avoiding obstacles and consuming as little energy as possible. Past researchers have studied trajectory generation and step planning independently, mainly because optimal generation of robot gait using dynamic formulation cannot be done in real time. Also, most step-planning studies are for flat terrain guided by search heuristics. In the proposed method, a framework for generating trajectories as well as an overall step plan for navigation of a 12 degrees of freedom biped on an uneven terrain with obstacles is presented. In order to accomplish this, a dynamic model of the robot is developed and a trajectory generation program is integrated with it using gait variables. The variables are determined using a genetic algorithm based optimization program with the objective of minimizing energy consumption subject to balance and kinematic constraints of the biped. A database of these variables for various terrain angles and walking motions is used to train two neural networks, one for real-time trajectory generation and another for energy estimation. To develop a global navigation strategy, a weighted A* search is used to generate the footstep plan with energy considerations in sight. The efficacy of the approach is exhibited through simulation-based results on a variety of terrains.

Corresponding author
*Corresponding author. E-mail:
Hide All
1. Vukobratović, M. and Borovac, B., “Zero-moment point – Thirty five years of its life,” Int. J. Humanoid Robot. 1 (01), 157173 (2004).
2. Sardain, P. and Bessonnet, G., “Forces acting on a biped robot. Center of pressure-zero moment point,” IEEE Trans. Syst. Man Cybernet. Part A: Syst. Hum. 34 (5), 630637 (2004).
3. Huang, Q., Yokoi, K., Kajita, S., Kaneko, K., Arai, H., Koyachi, N. and Tanie, K., “Planning walking patterns for a biped robot,” IEEE Trans. Robot. Autom. 17 (3), 280289, (2001).
4. Kajita, S., Kanehiro, F., Kaneko, K., Yokoi, K. and Hirukawa, H., “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, vol. 1 (2001) pp. 239–246.
5. Park, I.-W., Kim, J.-Y., Lee, J. and Oh, J.-H., “Online Free Walking Trajectory Generation for Biped Humanoid Robot KHR-3 (HUBO),” Proceedings of the IEEE International Conference on Robotics and Automation ICRA2006 (2006) pp. 1231–1236.
6. Vermeulen, J., Verrelst, B., Vanderborght, B., Lefeber, D. and Guillaume, P., “Trajectory planning for the walking biped Lucy,” Int. J. Robot. Res. 25 (9), 867887 (2006).
7. Gao, W., Jia, Z. and Fu, C., “Increase the feasible step region of biped robots through active vertical flexion and extension motions,” Robotica 35 (7), 15411561 (2017).
8. Takanishi, A., Takeya, T., Karaki, H. and Kato, I., “A Control Method for Dynamic Biped Walking Under Unknown External Force,” Proceedings of the IEEE International Workshop on Intelligent Robots and Systems IROS'90, Towards a New Frontier of Applications (1990) pp. 795–801.
9. Vundavilli, P. R. and Pratihar, D. K., “Soft computing-based gait planners for a dynamically balanced biped robot negotiating sloping surfaces,” Appl. Soft Comput. 9 (1), 191208 (2009).
10. Manchester, I. R., Mettin, U., Iida, F. and Tedrake, R., “Stable dynamic walking over uneven terrain,” Int. J. Robot. Res. 30 (3), 265279 (2011).
11. Bi, S., Zhuang, Z.-J., Xia, T., Mo, H.-X., Min, H.-Q. and Luo, R.-H., “Multi-objective Optimization for a Humanoid Robot Walking on Slopes,” Proceedings of the International Conference on Machine Learning and Cybernetics ICMLC2011, vol. 3 (2011) pp. 1261–1267.
12. Huang, W., Chew, C.-M., Zheng, Y. and Hong, G.-S., “Pattern Generation for Bipedal Walking on Slopes and Stairs,” Proceedings of the 8th IEEE-RAS International Conference on Humanoid Robots Humanoids2008 (2008) pp. 205–210.
13. Zheng, Y., Lin, M. C., Manocha, D., Adiwahono, A. H. and Chew, C.-M., “A Walking Pattern Generator for Biped Robots on Uneven Terrains,” Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems IROS2010 (2010) pp. 4483–4488.
14. Arakawa, T. and Fukuda, T., “Natural Motion Generation of Biped Locomotion Robot Using Hierarchical Trajectory Generation Method Consisting of GA, EP Layers,” Proceedings of the IEEE International Conference on Robotics and Automation, vol. 1 (1997) pp. 211–216.
15. Sarkar, A. and Dutta, A., “8-DoF biped robot with compliant-links,” Robot. Autonom. Syst. 63, 5767 (2015).
16. Lim, I.-s., Kwon, O. and Park, J. H., “Gait optimization of biped robots based on human motion analysis,” Robot. Autonom. Syst. 62 (2), 229240 (2014).
17. Cardenas-Maciel, S. L., Castillo, O. and Aguilar, L. T., “Generation of walking periodic motions for a biped robot via genetic algorithms,” Appl. Soft Comput. 11 (8), 53065314 (2011).
18. Gong, D., Yan, J. and Zuo, G., “A review of gait optimization based on evolutionary computation,” Appl. Computat. Intell. Soft Comput., vol. 2010 (2010) p. 12.
19. Capi, G., Nasu, Y., Barolli, L., Yamano, M., Mitobe, K. and Takeda, K., “A Neural Network Implementation of Biped Robot Optimal Gait During Walking Generated by Genetic Algorithm,” Proceedings of the Mediterranean Conference on Control and Automation, Dubrovnik, Croatia (2001).
20. Nagasue, J., Konishi, Y., Araki, N., Sato, T. and Ishigaki, H., “Slope-walking of a Biped Robot with k Nearest Neighbor Method,” Proceedings of the 4th International Conference on Innovative Computing, Information and Control ICICIC2009 (2009) pp. 173–176.
21. Ferreira, J. P., Crisostomo, M. M. and Coimbra, A. P., “SVR versus neural-fuzzy network controllers for the sagittal balance of a biped robot,” IEEE Trans. Neural Netw. 20 (12), 18851897 (2009).
22. Vundavilli, P. R. and Pratihar, D. K., “Dynamically balanced optimal gaits of a ditch-crossing biped robot,” Robot. Autonom. Syst. 58 (4), 349361 (2010).
23. Liu, Z., Wang, L., Zhang, Y. and Chen, C. P., “A SVM controller for the stable walking of biped robots based on small sample sizes,” Appl. Soft Comput. 38, 738753 (2016).
24. Chestnutt, J., Kuffner, J., Nishiwaki, K. and Kagami, S., “Planning Biped Navigation Strategies in Complex Environments,” Proceedings of the IEEE International Conference on Humanoid Robots, Munich, Germany (2003).
25. Chestnutt, J. and Kuffner, J. J., “A Tiered Planning Strategy for Biped Navigation,” Proceedings of the 4th IEEE/RAS International Conference on Humanoid Robots, vol. 1 (2004) pp. 422–436.
26. Huang, W., Kim, J. and Atkeson, C. G., “Energy-based Optimal Step Planning for Humanoids,” Proceedings of the IEEE International Conference on Robotics and Automation ICRA2013 (2013) pp. 3124–3129.
27. Hornung, A., Maier, D. and Bennewitz, M., “Search-based Footstep Planning,” Proceedings of the ICRA Workshop on Progress and Open Problems in Motion Planning and Navigation for Humanoids (Karlsruhe, Germany, 2013).
28. Li, T.-Y., Chen, P.-F. and Huang, P.-Z., “Motion Planning for Humanoid Walking in a Layered Environment,” Proceedings of the IEEE International Conference on Robotics and Automation ICRA2003, vol. 3 (2003) pp. 3421–3427.
29. Cupec, R., Aleksi, I. and Schmidt, G., “Step sequence planning for a biped robot by means of a cylindrical shape model and a high-resolution 2.5 D map,” Robot. Autonom. Syst. 59 (2), 84100 (2011).
30. Gutmann, J.-S., Fukuchi, M. and Fujita, M., “Real-time Path Planning for Humanoid Robot Navigation,” Proceedings of the International Joint Conference on Artificial Intelligence, vol. 19 (Lawrence Erlbaum Associates Ltd., 2005) p. 1232.
31. Candido, S., Kim, Y.-T. and Hutchinson, S., “An Improved Hierarchical Motion Planner for Humanoid Robots,” Proceedings of the 8th IEEE-RAS International Conference on Humanoid Robots Humanoids2008 (2008) pp. 654–661.
32. Prasanth, H. and Sudheer, A., “A hybrid approach to motion planning for stepping over and obstacle avoidance in humanoids,” Proceedings of the CAD/CAM, Robotics and Factories of the Future (Springer, 2016) pp. 651–664.
33. Ryu, S.-H., Kang, Y., Kim, S.-J., Lee, K., You, B.-J. and Doh, N. L., “Humanoid path planning from hri perspective: A scalable approach via waypoints with a time index,” IEEE Trans. Cybernet. 43 (1), 217229 (2013).
34. Perrin, N., Stasse, O., Baudouin, L., Lamiraux, F. and Yoshida, E., “Fast humanoid robot collision-free footstep planning using swept volume approximations,” IEEE Trans. Cybernet. 28 (2), 427439 (2012).
35. Craig, J. J., Introduction to Robotics: Mechanics and Control, vol. 3 (Pearson/Prentice Hall, Upper Saddle River, 2005).
36. Fu, K. S., Gonzalez, R. and Lee, C. G., Robotics: Control, Sensing, Vision, and Intelligence (Tata McGraw-Hill Education, Singapore, 1988).
37. Dasgupta, A. and Nakamura, Y., “Making Feasible Walking Motion of Humanoid Robots from Human Motion Capture Data,” Proceedings of the IEEE International Conference on Robotics and Automation, vol. 2 (1999) pp. 1044–1049.
38. Dai, H., Valenzuela, A. and Tedrake, R., “Whole-body Motion Planning with Centroidal Dynamics and Full Kinematics,” Proceedings of the 14th IEEE-RAS International Conference on Humanoid Robots Humanoids2014 (2014) pp. 295–302.
39. Silva, F. M. and Machado, J. T., “Energy Analysis During Biped Walking,” Proceedings of the IEEE International Conference on Robotics and Automation, vol. 1 (1999) pp. 59–64.
40. Koch, K. H., Mombaur, K. and Soueres, P., “Optimization-based walking generation for humanoid robot,” IFAC Proc. Vol. 45 (22), 498504 (2012).
41. Srinivasan, M. and Ruina, A., “Computer optimization of a minimal biped model discovers walking and running,” Nature 439 (7072), 7275 (2006).
42. Chevallereau, C. and Aoustin, Y., “Optimal reference trajectories for walking and running of a biped robot,” Robotica 19 (5), 557569 (2001).
43. Capi, G., Nasu, Y., Barolli, L., Mitobe, K. and Takeda, K., “Application of genetic algorithms for biped robot gait synthesis optimization during walking and going up-stairs,” Adv. Robot. 15 (6), 675694 (2001).
44. Hart, P. E., Nilsson, N. J. and Raphael, B., “A formal basis for the heuristic determination of minimum cost paths,” IEEE Trans. Syst. Sci. Cybernet. 4 (2), 100107 (1968).
45. Pohl, I., “The Avoidance of (Relative) Catastrophe, Heuristic Competence, Genuine Dynamic Weighting and Computational Issues in Heuristic Problem Solving,” Proceedings of the 3rd International Joint Conference on Artificial intelligence (Morgan Kaufmann Publishers Inc., 1973) pp. 12–17.
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: 38 *
Loading metrics...

Abstract views

Total abstract views: 103 *
Loading metrics...

* Views captured on Cambridge Core between 26th February 2018 - 18th March 2018. This data will be updated every 24 hours.