Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-23T02:13:35.443Z Has data issue: false hasContentIssue false
  • English
  • Français

Application of phase-plane method in generating minimum time solution for stable walking of biped robot with specified pattern of motion

Published online by Cambridge University Press:  21 February 2013

Mohammad Jafar Sadigh  and
Saeed Mansouri
Mohammad Jafar Sadigh*
Affiliation:
Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, Iran
Saeed Mansouri
Affiliation:
Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, Iran
*
*Corresponding author. E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Summary

Walking with a maximum speed is an interesting subject in the field of biped motion. Giving an answer to the question of “what is the maximum achievable speed of a certain biped walking with a physically acceptable pattern?” is the main objective of this work. In this paper, minimum time motion of biped was studied during one step that consists of single support phase (SSP) and double support phase (DSP). The minimum time problem is formulated with stability and non-slip conditions along with actuator limits expressed as some inequality constraints. In addition, certain kinematic constraints in terms of hip joint position are considered that ensure an acceptable walking pattern. A phase-plane technique is used to find the minimum time solution. A numerical simulation is given to shed some light on how the proposed method works. Validity and effectiveness of the method are verified by comparing the results with those of other researches.

Keywords

Minimum time motionBipedsStability and non-slip conditionPhase-plane analysis
Type
Articles
Information
Robotica , Volume 31 , Issue 6 , September 2013 , pp. 837 - 851
Copyright
Copyright © Cambridge University Press 2013 

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.Vukobratovic, M. and Stepanenko, J., “On the stability of anthropomorphic systems,” Math. Biosci. 15, 1–37 (1972).CrossRefGoogle Scholar
2.Vukobratovic, M. and Borovac, B., “Zero-moment point: Thirty-five years of its life,” Int. J. Humanoid Robot. 1 (1), 157–173 (2004).CrossRefGoogle Scholar
3.Kajita, S. and Tani, K., “Study of Dynamic Biped Locomotion on Rugged Terrain: Derivation and Application of the Linear Inverted Pendulum Mode,” Proceedings of the IEEE ICRA, Sacramento, CA (Apr. 9–11, 1991) pp. 1405–1411.Google Scholar
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, Maui, HI (Oct. 29–Nov. 3, 2001) pp. 239–246.Google Scholar
5.Park, J. H. and Kim, K. D, “Biped Robot Walking Using Gravity-Compensated Inverted Pendulum Mode and Computed Torque Control,” Proceedings of IEEE ICRA, Leuven, Belgium (May 16–20, 1998) pp. 3528–3533.Google Scholar
6.Erbatur, K. and Kurt, O., “Natural ZMP trajectories for biped robot reference generation,” IEEE Trans. Ind. Electron. 56 (3), 835–845 (2009).CrossRefGoogle Scholar
7.Takanishi, A., Tochizawa, M., Karkai, H. and Kato, I., “Dynamic Biped Walking Stabilized with Optimal Trunk and Waist Motion,” Proceedings of IEEE/RSJ International Workshop on Intelligent Robots and Systems, Tsukuba, Japan (Sep. 4–6, 1989) pp. 187–192.Google Scholar
8.Yamaguchi, J. I., Takanishi, A. and Kato, I., “Development of Biped Walking Robot Compensating for Three-Axis Moment by Trunk Motion,” Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems, Yokohama, Japan (Jul. 26–30, 1993) pp. 561–566.Google Scholar
9.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), 280–289 (2001).CrossRefGoogle Scholar
10.Channon, P. H., Hopkins, S. H. and Pham, D. T., “Derivation of optimal walking motions for a bipedal walking robot,” Robotica 10, 165–172 (1992).CrossRefGoogle Scholar
11.Park, J. H. and Choi, M. S., “Generation of an optimal gait trajectory for biped robots using a genetic algorithm,” JSME Int. J. Series C 47 (2), 715–721 (2004).CrossRefGoogle Scholar
12.Dau, V. H., Chew, C. M. and Poo, A. N., “Achieving energy-efficient bipedal walking trajectory through GA-based optimization of key parameters,” Int. J. Humanoid Robot. 6 (4), 609–629 (2009).CrossRefGoogle Scholar
13.Rostami, M. and Bessonet, G., “Sagittal gait of a biped robot during the single support phase. Part 2: Optimal motion,” Robotica 19, 241–253 (2001).CrossRefGoogle Scholar
14.Capi, G., Nasu, Y., Barolli, L., Mitobe, K. and Takeda, K., “Application of genetic algorithms for biped gait synthesis optimization during walking and going up-stairs,” Adv. Robot. 15 (6), 675–694 (2001).CrossRefGoogle Scholar
15.Saidouni, T. and Bessonnet, G., “Generating globally optimised sagittal gait cycles of a biped robot,” Robotica 21, 199–210 (2003).CrossRefGoogle Scholar
16.Bessonnet, G., Chesse, S. and Sardain, P., “Optimal gait synthesis of a seven-link planar biped,” Int. J. Robot. Res. 23 (10–11), 1059–1073 (2004).CrossRefGoogle Scholar
17.Chevallereau, C. and Aoustin, Y., “Optimal reference trajectories for walking and running of a biped robot,” Robotica 19, 557–569 (2001).CrossRefGoogle Scholar
18.Miossec, S. and Aoustin, Y., “A simplified stability study for a biped walk with underactuated and overactuated phases,” J. Robot. Res. 24 (7), 537–551 (2005).CrossRefGoogle Scholar
19.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, 355–365 (2009).CrossRefGoogle Scholar
20.Tlalolini, D., Chevallereau, C. and Aoustin, Y., “Comparison of different gaits with rotation of the feet for a planar biped,” J. Robot. Auton. Syst. 57 (4), 371–383 (2009).CrossRefGoogle Scholar
21.Sadigh, M. J. and Mansouri, S., “Effect of Step Size and Step Period on Feasible Motion of a Biped Robot,” Proceedings of IEEE International Conference on Robotics and Biomimetics (ROBIO), Tianjin, P. R. China (Dec. 14–18, 2010) pp. 1–6.Google Scholar
22.Bobrow, J. E., Dubowsky, S. and Gibson, J. S., “Time-optimal control of robotic manipulators along specified paths,” Int. J. Robot. Res. 4 (3), 3–17 (1985).CrossRefGoogle Scholar
23.Pfeiffer, F. and Johanni, R., “A concept for manipulator trajectory planning,” IEEE Trans. Robot. Autom. 3 (2), 115–123 (1987).CrossRefGoogle Scholar
24.Zlajpah, L., “On Time Optimal Path Control of Manipulators with Bounded Joint Velocities and Torques,” Proceedings of IEEE ICRA, Minneapolis, MN (1996) pp. 1572–1577.Google Scholar
25.Ghasemi, M. H. and Sadigh, M. J., “A direct algorithm to compute the switching curve for time-optimal motion of cooperative multi-manipulators moving on a specified path,” Adv. Robot. 22, 493–506 (2008).CrossRefGoogle Scholar
26.Verscheure, D., Demeulenaere, B., Swevers, J., De Schutter, J. and Diehl, M., “Time-optimal path tracking for robots: A convex optimization approach,” IEEE Trans. Autom. Control 54 (10), 2318–2327 (2009).CrossRefGoogle Scholar
27.Moon, S. B. and Ahmad, S., “Time optimal trajectories for cooperative multi-robot systems,” Proc. IEEE Int. Conf. Decision Control 2, 1126–1127 (1990).Google Scholar
28.Moon, S. B. and Ahmad, S., “Time scaling of cooperative multi robot trajectory,” IEEE Trans. Syst. Man Cybern. 21 (4), 900–908 (1991).CrossRefGoogle Scholar
29.Bobrow, J. E., McCarthy, J. M. and Chu, V. K., “Minimum-time trajectories for two robots holding the same workpiece,” Proc. IEEE Int. Conf. Decision Control 6, 3102–3107 (1990).Google Scholar
30.Sadigh, M. J. and Ghasemi, M. H., “A Fast Algorithm Time Optimal Control of a Cooperative Multi Manipulator System on Specified Path,” Proceedings of 5th Vienna Conference on Mathematical Modeling (MATHMOD), Vienna, Austria (Feb. 8–10, 2006) pp. 1–7.Google Scholar
31.Ghasemi, M. H., Coordinated Minimum Time Motion of a Cooperative Multi Manipulator System Along a Specified Path, PhD Dissertation (Isfahan: Department of Mechanical Engineering, Isfahan University of Technology, 2008, in Persian).Google Scholar
32.Sadigh, M. J., Ghasemi, M. H. and Keshmiri, M., “A Direct Algorithm to Compute Switching Curve for Time Optimal Motion of Cooperative Multi-Manipulators Moving on Specified Path,” Proceedings of 13th IEEE IFAC International Conference on Methods and Models in Automation and Robotics (MMAR), Szczecin, Poland (Aug. 27–30, 2007) pp. 875–882.Google Scholar
33.McCarthy, J. M. and Bobrow, J. E., “The number of saturated actuators and constraint forces during time-optimal movement of a general robotic system,” IEEE Trans. Robot. Autom. 8 (3), 407–409 (1992).CrossRefGoogle Scholar