Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-27T11:54:21.307Z Has data issue: false hasContentIssue false

Generating real-time trajectories for a planar biped robot crossing a wide ditch with landing uncertainties

Published online by Cambridge University Press:  13 September 2018

Janardhan V.
Affiliation:
Department of Mechanical and Aerospace Engineering, Indian Institute of Technology Hyderabad, Kandi, Telangana - 502285, India. Email: vishnavj@gmail.com
Prasanth Kumar R.*
Affiliation:
Department of Mechanical and Aerospace Engineering, Indian Institute of Technology Hyderabad, Kandi, Telangana - 502285, India. Email: vishnavj@gmail.com
*
*Corresponding author. E-mail: rpkumar@iith.ac.in

Summary

Ditch crossing is one of the essential capabilities required for a biped robot in disaster management and search and rescue operations. Present work focuses on crossing a wide ditch with landing uncertainties by an under-actuated planar biped robot with five degrees of freedom. We consider a ditch as wide for a robot when the ankle to ankle stretch required to cross it is at least equal to the leg length of the robot. Since locomotion in uncertain environments requires real-time planning, in this paper, we present a new approach for generating real-time joint trajectories using control constraints not explicitly dependent on time, considering impact, dynamic balance, and friction. As part of the approach, we introduce a novel concept called the point of feasibility for bringing the biped robot to complete rest at the end of ditch crossing. We present a study on the influence of initial posture on landing impact and net energy consumption. Through simulations, we found the best initial postures to efficiently cross a wide ditch of width 1.05 m, with less impact and without singularities. Finally, we demonstrate the advantage of the proposed approach to cross a wide ditch when the surface friction is not same on both sides of the ditch.

Type
Articles
Copyright
Copyright © Cambridge University Press 2018 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Hashimoto, K., Sugahara, Y., Ohta, A., Sunazuka, H., Tanaka, C., Kawase, M., Lim, H.-ok and Takanishi, A., “Realization of Stable Biped Walking on Public Road with New Biped Foot System Adaptable to Uneven Terrain,” Proceedings of the 1st IEEE/RAS-EMBS International Conference on Biomedical Robotics and Biomechatronics, BioRob2006, (2006) pp. 226–231.Google Scholar
2. Wei, H., Shuai, M. and Wang, Z., “Dynamically adapt to uneven terrain walking control for humanoid robot,” Chin. J. Mech. Eng. 25 (2), 214222 (2012).Google Scholar
3. Nishiwaki, K., Chestnutt, J. and Kagami, S., “Autonomous navigation of a humanoid robot over unknown rough terrain using a laser range sensor,” Int. J. Robot. Res. 31 (11), 12511262 (2012).Google Scholar
4. Luo, R. C. and Lin, S. J., “Impedance and Force Compliant Control for Bipedal Robot Walking on Uneven Terrain,” Proceedings of the IEEE International Conference on Systems, Man, and Cybernetics (SMC), (2015) pp. 228–233.Google Scholar
5. Yi, J., Zhu, Q., Xiong, R. and Wu, J., “Walking algorithm of humanoid robot on uneven terrain with terrain estimation,” Int. J. Adv. Robot. Syst. 13 (1), 35 (2016).Google Scholar
6. Guan, Y., Yokoi, K., Kheddar, A. and Tanie, K., “Object Stepping-On/Down Feasibility of Humanoid Robots,” Proceedings of the IEEE International Conference on Robotics and Biomimetics (2004).Google Scholar
7. Jafri, A. R., Huang, Q., Yang, J., Wang, Z. and Xiao, T., “Motion Planning for Stepping On/Off Obstacles by Humanoid Robot,” Proceedings of the Mechatronics and Automation ICMA, IEEE (2007) pp. 1154–1159.Google Scholar
8. Jarfi, A. R., Huang, Q., Zhang, L., Yang, J., Wang, Z. and Lv, S., “Realization and Trajectory Planning for Obstacle Stepping Over by Humanoid Robot bhr-2,” Proceedings of the IEEE International Conference on Robotics and Biomimetics ROBIO'06, IEEE (2006) pp. 1384–1389.Google Scholar
9. Seara, J. F., Lorch, O. and Schmidt, G., “Gaze Control for Goal-Oriented Humanoid Walking,” Proceedings of the IEEE/RAS International Conference on Humanoid Robots (Humanoids), Tokio, Japan, Citeseer (2001) pp. 187–195.Google Scholar
10. Verrelst, B., Yokoi, K., Stasse, O., Arisumi, H. and Vanderborght, B., “Mobility of Humanoid Robots: Stepping Over Large Obstacles Dynamically,” Proceedings of the IEEE International Conference on Mechatronics and Automation, (2006) pp. 1072–1079.Google Scholar
11. Guan, Y., Yokoi, K., Sian, N. E. and Tanie, K., “Feasibility of Humanoid Robots Stepping Over Obstacles,” Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems IROS2004, vol. 1, (2004) pp. 130–135.Google Scholar
12. Stasse, O., Verrelst, B., Vanderborght, B. and Yokoi, K., “Strategies for humanoid robots to dynamically walk over large obstacles,” IEEE Trans. Robot. 25 (4), 960967 (2009).Google Scholar
13. Guo, F., Mei, T., Luo, M., Ceccarelli, M., Zhao, Z., Li, T. and Zhao, J., “Motion planning for humanoid robot dynamically stepping over consecutive large obstacles,” Ind. Robot: Int. J. 43 (2), 204220 (2016).Google Scholar
14. Choi, B. S. and Song, S.-M., “Fully automated obstacle-crossing gaits for walking machines,” IEEE Trans. Syst., Man Cybern. 18 (6), 952964 (1988).Google Scholar
15. Cheng, J. and Pan, J., “Ditch Crossing Control for Quadruped Walking Robot,” Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems' 93, IROS'93, vol. 1, (1993) pp. 537–541.Google Scholar
16. Fattah, A. and Fakhari, A., “Trajectory Planning of Walking With Different Step Lengths of A Seven-Link Biped Robot,” Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, American Society of Mechanical Engineers (2010) pp. 1361–1369.Google Scholar
17. Vundavilli, P. R. and Pratihar, D. K., “Dynamically balanced optimal gaits of a ditch-crossing biped robot,” Robot. Auton. Syst. 58 (4), 349361 (2010).Google Scholar
18. Van der Noot, N., Ijspeert, A. J. and Ronsse, R., “Biped Gait Controller for Large Speed Variations, Combining Reflexes and a Central Pattern Generator in a Neuromuscular Model,” Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), (2015) pp. 6267–6274.Google Scholar
19. Janardhan, V. and Prasanth Kumar, R., “Generating feasible solutions for dynamically crossing a wide ditch by a biped robot,” J. Intell. Robot. Syst. 88 (1), 3756 (2017).Google Scholar
20. Janardhan, V. and Prasanth Kumar, R., “Online trajectory generation for wide ditch crossing of biped robots using control constraints,” Robot. Auton. Syst. 97 (Supplement C), 6182 (2017).Google Scholar
21. Wensing, P. M. and Orin, D. E., “Development of High-Span Running Long Jumps for Humanoids,” Proceedings of the Robotics and Automation (ICRA), IEEE (2014) pp. 222–227.Google Scholar
22. Janardhan, V. and Kumar, R. P., “Kinematic Analysis of Biped Robot Forward Jump for Safe Locomotion,” Proceedings of the 1st International and 16th National Conference on Machines and Mechanisms iNaCoMM2013, (2013) pp. 1078–1082.Google Scholar
23. Yuan, Q. and Chen, I.-M., “Planar jumping with stable landing through foot orientation design and ankle joint control,” Frontiers Mech. Eng. 7 (2), 100108 (2012).Google Scholar
24. Kaneko, T., Sekiya, M., Ogata, K., Sakaino, S. and Tsuji, T., “Force Control of a Jumping Musculoskeletal Robot with Pneumatic Artificial Muscles,” Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), (2016) pp. 5813–5818.Google Scholar
25. Blajer, W., “Dynamics and control of mechanical systems in partly specified motion,” J. Franklin Inst. 334 (3), 407426 (1997).Google Scholar
26. Rosen, A. and Edelstein, E., “Investigation of a new formulation of the lagrange method for constrained dynamic systems,” J. Appl. Mech. 64 (1), 116122 (1997).Google Scholar
27. Lam, S. H., “On lagrangian dynamics and its control formulations,” Appl. Math. Comput. 91 (2), 259284 (1998).Google Scholar
28. Rosen, A, “Applying the lagrange method to solve problems of control constraints,” J. Appl. Mech. 66 (4), 10131015 (1999).Google Scholar
29. Seifried, R. and Blajer, W., “Analysis of servo-constraint problems for underactuated multibody systems,” Mech. Sci. 4 (1), 113129 (2013).Google Scholar
30. Blajer, W. and Kołodziejczyk, K., “A geometric approach to solving problems of control constraints: Theory and a DAE framework,” Multibody Syst. Dyn. 11 (4), 343364 (2004).Google Scholar
31. Morisawa, M., Kanehiro, F., Kaneko, K., Kajita, S. and Yokoi, K., “Reactive Biped Walking Control For A Collision of A Swinging Foot on Uneven Terrain,” Proceedings of the 11th IEEE-RAS International Conference on Humanoid Robots (Humanoids), (2011) pp. 768–773.Google Scholar
32. Pratt, J., Carff, J., Drakunov, S. and Goswami, A., “Capture Point: A Step Toward Humanoid Push Recovery,” Proceedings of the 6th IEEE-RAS International Conference on Humanoid Robots, (2006) pp. 200–207.Google Scholar
33. Chevallereau, C., Grizzle, J. W. and Shih, C.-L., “Asymptotically stable walking of a five-link underactuated 3-d bipedal robot,” IEEE Trans. Robot. 25 (1), 3750 (2009).Google Scholar
34. Mu, X. and Wu, Q., “Dynamic Modeling and Sliding Mode Control of a Five-Link Biped During the Double Support Phase,” Proceedings of the American Control Conference, vol. 3, (2004) pp. 2609–2614.Google Scholar
35. Garcia, M., Chatterjee, A., Ruina, A. and Coleman, M., “The simplest walking model: Stability, complexity, and scaling,” J. Biomech. Eng. 120 (2), 281288 (1998).Google Scholar
36. Westervelt, E. R., Grizzle, J., Chevallereau, C., Choi, J. H. and Morris, B.,” Feedback Control of Dynamic Bipedal Robot Locomotion, vol. 28 (CRC PRESS – Taylor & Francis group - Boca Raton, London, New York, 2007).Google Scholar
37. Nikravesh, P. E., Planar Multibody Dynamics: Formulation, Programming and Applications (CRC PRESS – Taylor & Francis group - Boca Raton, London, New York, Washington, 2007).Google Scholar
38. Murray, R. M., Li, Z. and Sastry, S. S., A Mathematical Introduction to Robotic Manipulation (CRC PRESS – Taylor & Francis group - Boca Raton, London, New York, 1994).Google Scholar
39. Vukobratović, M. and Borovac, B., “Zero-moment point thirty five years of its life,” I. J. Humanoid Robot. 1 (01), 157173 (2004).Google Scholar
40. Shih, C.-L., “Ascending and descending stairs for a biped robot,” IEEE Trans. Syst., Man Cybern., Part A: Syst. Humans 29 (3), 255268 (1999).Google Scholar
41. Caballero, R. and Armada, M., “Zero Moment Point Modeling Using Harmonic Balance,” In: Climbing and Walking Robots (Armada, M. A. and de-Santos, P G., eds.) (Springer, 2005) pp. 689699.Google Scholar
42. Sardain, P. and Bessonnet, G., “Forces acting on a biped robot. Center of pressure-zero moment point,” IEEE Trans. Syst., Man, Cybern.-Part A: Syst. Humans 34 (5), 630637 (2004).Google Scholar
43. 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).Google Scholar
44. Anitescu, M., Potra, F. and Stewart, D. E., “Time-stepping for three-dimensional rigid body dynamics,” Comput. Methods Appl. Mech. Engrg 177 (3), 183197 (1999).Google Scholar
45. Hurmuzlu, Y., GéNot, F. and Brogliato, B., “Modeling, stability and control of biped robotsa general framework,” Automatica 40 (10), 16471664 (2004).Google Scholar
46. Al-shuka, H. F. N., Corves, B. J., Zhu, W.-H. and Vanderborght, B., “A simple algorithm for generating stable biped walking patterns,” Int. J. Comput. Appl 101 (4), 2933 (2014).Google Scholar
47. Goswami, A. and Kallem, V., “Rate of Change of Angular Momentum and Balance Maintenance of Biped Robots,” Proceedings of the Robotics and Automation ICRA'04, vol. 4, IEEE (2004) pp. 3785–3790.Google Scholar
48. Tzafestas, S., Raibert, M. and Tzafestas, C., “Robust sliding-mode control applied to a 5-link biped robot,” J. Intell. Robot Syst. 15 (1), 67133 (1996).Google Scholar
49. Azevedo, C., Poignet, P. and Espiau, B., “On Line Optimal Control for Biped Robots,” Proceedings of the IFAC 15th World Congress (2002).Google Scholar
50. Tözeren, A.,” Human Body Dynamics: Classical Mechanics and Human Movement (Springer-Verlag, New York, Berlin, Heidelberg, 2000).Google Scholar
51. El-Sherbiny, Y. M., Hasouna, A. T. and Ali, W. Y., “Friction coefficient of rubber sliding against flooring materials,” J. Eng. Appl. Sci. 7 (1), 121126 (2012).Google Scholar
52. Verrelst, B., Stasse, O., Yokoi, K. and Vanderborght, B., “Dynamically Stepping Over Obstacles by the Humanoid Robot hrp-2,” Proceedings of the Humanoid Robots, 6th IEEE-RAS, IEEE (2006) pp. 117–123.Google Scholar