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A new kinetostatic model for humanoid robots using screw theory

Published online by Cambridge University Press:  22 January 2018

Gustavo S. Toscano ,
Henrique Simas ,
Eugênio B. Castelan  and
Daniel Martins
Gustavo S. Toscano
Affiliation:
Department of Automation and Systems Engineering (DAS), Federal University of Santa Catarina (UFSC), Florianópolis, Brazil. E-mails: [email protected], [email protected]
Henrique Simas
Affiliation:
Department of Mechanical Engineering (EMC), Federal University of Santa Catarina (UFSC), Florianópolis, Brazil. E-mails: [email protected], [email protected]
Eugênio B. Castelan
Affiliation:
Department of Automation and Systems Engineering (DAS), Federal University of Santa Catarina (UFSC), Florianópolis, Brazil. E-mails: [email protected], [email protected]
Daniel Martins
Affiliation:
Department of Mechanical Engineering (EMC), Federal University of Santa Catarina (UFSC), Florianópolis, Brazil. E-mails: [email protected], [email protected]
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Summary

This study presents a new kinetostatic model for humanoid robots (HRs). Screw theory, together with Assur virtual chains and Davies' method, provides the required tools for the proposal of both the kinematic and static parts of the kinetostatic model. Our kinetostatic model is able to estimate the forces and couples generated at the axes of each joint of the robot, as well as one unknown contact condition between the robot and the environment around it. The proposed model is also very versatile and free of fixed coordinates and, therefore, it allows for an estimate of a great amount of information on the HR. Some results, obtained from computer simulation, are presented to validate the versatility of the proposed technique.

Keywords

Humanoid robotsKinetostatic modelScrew theoryDavies' methodVirtual chains
Type
Articles
Information
Robotica , Volume 36 , Issue 4 , April 2018 , pp. 570 - 587
Copyright
Copyright © Cambridge University Press 2018 

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References

1. Ionescu, T. G., “Terminology for mechanisms and machine science,” Mecha. Mach. Theory 38 (7–10), 819–825 (2003).Google Scholar
2. Khadiv, M., Moosavian, S., Ali, A. and Sadedel, M., “Dynamics modeling of fully-actuated humanoids with general robot-environment interaction,” Proceedings of the International Conference on Robotics and Mechatronics. IEEE 233–238 (2014).Google Scholar
3. Nugroho, S. A., Prihatmanto, A. S. and Rohman, A. S., “Design and implementation of kinematics model and trajectory planning for nao humanoid robot in a tic-tac-toe board game,” Proceedings of the 4th International Conference on System Engineering and Technology, IEEE 4, 1–7 (2014).Google Scholar
4. Menad, M., Derouiche, Z., Foitih, Z. A. and Nouibat, W., “Kinematic modeling of a humanoid robot with 18 dof in a virtual environment,” Proceedings of the International Conference on Innovative Computing Technology (InTECH). IEEE 424–429 (2013).CrossRefGoogle Scholar
5. Moosavian, S., Alghooneh, M. and Takhmar, A., “Modified transpose jacobian control of a biped robot,” Proceedings of the International Conference on Humanoid Robots. IEEE 282–287 (2007).Google Scholar
6. Lim, H.-O., Ishii, A. and Takanishi, A., “Emotion-based biped walking,” Robotica 22 (5), 577–586 (2004).Google Scholar
7. Mu, X. and Wu, Q., “A complete dynamic model of five-link bipedal walking,” Proceedings of the American Control Conference, IEEE6, 4926–4931 (2003).Google Scholar
8. 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
9. Liu, Y., Wensing, P. M., Orin, D. E. and Zheng, Y. F., “Trajectory generation for dynamic walking in a humanoid over uneven terrain using a 3d-actuated dual-slip model,” Proceedings of the International Conference on Intelligent Robots and Systems, IEEE, 374–380 (2015).CrossRefGoogle Scholar
10. Muscolo, G. G., Recchiuto, C. T. and Molfino, R., “Dynamic balance optimization in biped robots: Physical modeling, implementation and tests using an innovative formula,” Robotica 33 (6), 1–17 (2015).CrossRefGoogle Scholar
11. Nagarajan, U. and Yamane, K., “Automatic task-specific model reduction for humanoid robots,” Proceedings of the International Conference on Intelligent Robots and Systems, IEEE, 2578–2585 (2013).Google Scholar
12. Akash, A., Chandra, S., Abha, A. and Nandi, G., “Modeling a bipedal humanoid robot using inverted pendulum towards push recovery,” Proceedings of the International Conference on Communication, Information Computing Technology, IEEE, 1–6 (2012).CrossRefGoogle Scholar
13. Ruan, X.-g. and Li, Z.-q., “A bipedal locomotion planning with double support phase based on linear inverted pendulum mode,” WRI Global Congr. Intell. Syst., IEEE, 3, 73–77 (2009).Google Scholar
14. Erbatur, K. and Seven, U., “An inverted pendulum based approach to biped trajectory generation with swing leg dynamics,” Proceedings of the 7th International Conference on Humanoid Robots, IEEE, (2007) pp. 216–221.Google Scholar
15. Kajita, S., Matsumoto, O. and Saigo, M., “Real-time 3d walking pattern generation for a biped robot with telescopic legs,” Proceedings of the International Conference on Robotics and Automation, IEEE, (2001) vol. 3, pp. 2299–2306.Google Scholar
16. 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 International Conference on Intelligent Robots and Systems, IEEE (2001) vol. 1, pp. 239–246.Google Scholar
17. Kajita, S., Tomio, Y. and Kobayashi, A., “Dynamic walking control of a biped robot along a potential energy conserving orbit,” IEEE Trans. Robot. Autom. 8 (4), 431–438 (1992).Google Scholar
18. Umetani, Y. and Yoshida, K., “Resolved motion rate control of space manipulators with generalized jacobian matrix,” IEEE Trans. Robot. Autom. 5 (3), 303–314 (1989).Google Scholar
19. Dubowsky, S. and Papadopoulos, E., “The kinematics, dynamics, and control of free-flying and free-floating space robotic systems,” IEEE Trans. Robot. Autom. 9 (5), 531–543 (1993).Google Scholar
20. Papadopoulos, E. and Dubowsky, S., “On the nature of control algorithms for free-floating space manipulators,” IEEE Trans. Robot. Autom. 7 (6), 750–758 (1991).Google Scholar
21. Sentis, L., “Synthesis and Control of Whole-Body Behaviors in Humanoid Systems,” Ph.D. dissertation, (Stanford University, CA, USA, 2007).Google Scholar
22. Khatib, O., Sentis, L. and Park, J.-H., “A unified framework for whole-body humanoid robot control with multiple constraints and contacts,” In European Robotics Symposium (Bruyninckx, H., Preucil, L., Kulich, M., eds.) (Springer, Berlin, Heidelberg, 2008) pp. 303–312.Google Scholar
23. Mistry, M., Nakanishi, J., Cheng, G. and Schaal, S., “Inverse kinematics with floating base and constraints for full body humanoid robot control,” Proceedings of the International Conference on Humanoid Robots, IEEE (2008) pp. 22–27.Google Scholar
24. Mifsud, A., Benallegue, M. and Lamiraux, F., “Estimation of contact forces and floating base kinematics of a humanoid robot using only inertial measurement units,” Proceedings of the International Conference on Intelligent Robots and Systems, IEEE (2015) pp. 3374–3379.Google Scholar
25. Del Prete, A., Mansard, N., Nori, F., Metta, G. and Natale, L., “Partial force control of constrained floating-base robots,” Proceedings of the International Conference on Intelligent Robots and Systems, IEEE (2014) pp. 3227–3232.Google Scholar
26. Guan, Y., Neo, E. S., Yokoi, K. and Tanie, K., “Stepping over obstacles with humanoid robots,” IEEE Trans. Robot. 22 (5), 958–973 (2006).CrossRefGoogle Scholar
27. Bouyarmane, K. and Kheddar, A., “Multi-contact stances planning for multiple agents,” Proceedings of the International Conference on Robotics and Automation (2011) pp. 5246–5253.Google Scholar
28. Yokokohji, Y., Nomoto, S., and Yoshikawa, T., “Static evaluation of humanoid robot postures constrained to the surrounding environment through their limbs,” Proceedings of the International Conference on Robotics and Automation, IEEE, (2002), vol. 2, pp. 1856–1863.Google Scholar
29. Yoshida, E., Blazevic, P. and Hugel, V., “Pivoting manipulation of a large object: a study of application using humanoid platform,” Proceedings of the International Conference on Robotics and Automation IEEE (Apr. 2005), pp. 1040–1045.Google Scholar
30. Ball, R. S., A Treatise on the Theory of Screws. (Cambridge University Press, Cambridge, UK, 1900), – reprinted in 1998.Google Scholar
31. Hunt, K. H., “Don't cross-thread the screw!” In Symposium Commemorating The Legacy, Works and Life of Sir Robert Stawell Ball Upon the 100th Anniversary of A Treatise on The Theory of Screws (Duffy, Joseph, Hunt, Hugh E. M. and Lipkin, Harvey, eds.) (University of Cambridge, Trinity College. Cambridge: Cambridge University Press, 2000) pp. 1–37.Google Scholar
32. Tsai, L.-W., Robot Analysis: The Mechanics of Serial and Parallel Manipulators. (Wiley-Interscience, New York, 1999).Google Scholar
33. Campos, A., Guenther, R. and Martins, D., “Differential kinematics of serial manipulators using virtual chains,” J. Braz. Soc. Mech. Sci. Eng. 27 (4), 345–356 (2005).Google Scholar
34. Santos, C., Guenther, R., Martins, D. and De Pieri, E., “Virtual kinematic chains to solve the underwater vehicle-manipulator systems redundancy,” J. Braz. Soc. Mech. Sci. Eng. 28, 354–361 (2006).Google Scholar
35. Guenther, R., Simas, H., da Cruz, D. and Martins, D., “A new integration method for differential inverse kinematics of closed-chain robots,” Proceedings of the ABCM Symposium Series in Mechatronics, ABCM 3, 225–235 (2008).Google Scholar
36. Toscano, G. S., Simas, H. and Castelan, E. B., “Trajectory generation for a spatial humanoid robots using assur virtual chains through screw theory,” Proceedings of the ABCM Symposium Series in Mechatronics, ABCM 6, (2014).Google Scholar
37. Mozzi, G., Discorso Matematico Sopra il Rotamento Momentaneo Dei Corpi. (Stamperia di Donato Campo, 1763).Google Scholar
38. Poinsot, L., “Sur la composition des moments et la composition des aires,” J. de École Polytech. 6, 182–205 (1806).Google Scholar
39. Bottema, O. O. and Roth, B., Theoretical Kinematics. (North-Holand Pub. Co., New York, 1979).Google Scholar
40. Davies, T. H., “Kirchhoff's circulation law applied to multi-loop kinematic chains,” Mech. Mach. Theory – Elsevier 16 (3), 171–183 (1981).Google Scholar
41. Simas, H., Guenther, R., da Cruz, D. F. M. and Martins, D., “A new method to solve robot inverse kinematics using assur's virtual chains,” Robotica – Cambridge University Press 27 (07), 1017–1026 (2009).Google Scholar
42. Davidson, J. K. and Hunt, K. H., Robots and Screw Theory: Applications of Kinematics and Statics to Robotics. (Oxford University Press, Oxford, UK, 2004).Google Scholar
43. Erthal, J., “Modelo cinemático pra análise de rolagem de veículos,” Tese de doutorado, Universidade Federal de Santa Catarina (UFSC) - Departamento de Engenharia Mecânica (EMC) – Programa de Pós-graduação em Engenharia Mecânica (POSMEC), (Florianópolis – Brasil, 2010).Google Scholar
44. Davies, T. H., “Couplings, coupling network and their graphs,” Mech. Mach. Theory 30 (7), 991–1000 (1995).Google Scholar
45. Christofides, N., Graph Theory – An Algorithmic Approach. (Academic Press Inc., New York, 1975).Google Scholar
46. Vukobratovic, M., Borovac, B. and Surdilovic, D., “Zero-moment point–proper interpretation and new applications,” Proceedings of the International Conference on Humanoid Robots, IEEE, 244 (2001).Google Scholar