Hostname: page-component-76fb5796d-vfjqv Total loading time: 0 Render date: 2024-04-26T11:18:09.840Z Has data issue: false hasContentIssue false
  • English
  • Français

Energy expenditure of a biped walking robot: instantaneous and degree-of-freedom-based instrumentation with human gait implications

Published online by Cambridge University Press:  14 January 2016

Dustyn Roberts ,
Joseph Quacinella  and
Joo H. Kim
Dustyn Roberts
Affiliation:
Department of Mechanical and Aerospace Engineering, New York University, Brooklyn, New York, USA Emails: dustyn@udel.edu, j.quacinella@gmail.com
Joseph Quacinella
Affiliation:
Department of Mechanical and Aerospace Engineering, New York University, Brooklyn, New York, USA Emails: dustyn@udel.edu, j.quacinella@gmail.com
Joo H. Kim*
Affiliation:
Department of Mechanical and Aerospace Engineering, New York University, Brooklyn, New York, USA Emails: dustyn@udel.edu, j.quacinella@gmail.com
*
*Corresponding author. E-mail: joo.h.kim@nyu.edu
Get access Rights & Permissions [Opens in a new window]

Summary

Energy expenditure (EE) is an important criterion for design and control of biped walking robots. However, the cause-effect analyses enabled by total EE, which is lumped over a time duration and all system degrees-of-freedom (DOFs), are limited. In this study, robotic gait energetics is evaluated through a DOF-based instrumentation system designed for instantaneous evaluation of bidirectional current and applied voltage at each joint actuator. The instrumentation system includes a dual-module arrangement of buffers and attenuators, and accommodates and synchronizes the voltage and current measurements from multiple actuators. For illustrative purposes, this system is implemented at each DC servomotor in a biped robot, DARwIn-OP, to analyze the electrical EE rates for walking at various speeds. In addition, a DOF-based model of instantaneous human EE rate is employed to enable quantitative characterization of robotic walking EE relative to that of humans. The robot's instantaneous lower-body EE rates are consistent with its periodic walking cycle, and their relative trends between single and double support phases are analogous to those of humans. The robotic cost of transport (COT) curve as a function of normalized speed is also consistent with the human COT in terms of its convexity. Conversely, the contrasting distributions of EE throughout the robot and human DOFs and the robotic COT curve's considerably larger magnitudes, smaller speed ranges, and higher sensitivity to speed illustrate the energetic consequences of stable but inefficient static walking in the biped robot relative to the more efficient dynamic walking of humans. These energetic characteristics enable the identification of the joints and gait cycle phases associated with inefficiency in biped robotic gait, and reflect the noticeable differences in the system parameters (rigid and flat versus segmented feet) and gait control strategies (bent versus straight knees, instants of peak ankle actuator torques, static versus dynamic balance stability). The proposed general instrumentation provides a quantitative approach to benchmarking human gait as well as general guidelines for the development of energy-efficient walking robots.

Keywords

Bidirectional current and voltageBiped walking robotCost of transport (COT)Degree of freedom (DOF)Instantaneous energy expenditureInstrumentation
Type
Articles
Information
Robotica , Volume 35 , Issue 5 , May 2017 , pp. 1054 - 1071
Copyright
Copyright © Cambridge University Press 2016 

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.)

Footnotes

† These authors contributed equally to this work.

References

1. Remy, C. D., Buffinton, K. and Siegwart, R., “Comparison of Cost Functions for Electrically Driven Running Robots,” Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), Saint Paul, MN (2012) pp. 2343–2350.Google Scholar
2. Bhounsule, P. A., Cortell, J., Grewal, A., Hendriksen, B., Karssen, J. G. D., Paul, C. and Ruina, A., “Low-bandwidth reflex-based control for lower power walking: 65 km on a single battery charge,” Int. J. Robot. Res. 33 (10), 1305–1321 (Sep. 2014).Google Scholar
3. Shin, H.-K. and Kim, B. K., “Energy-efficient gait planning and control for biped robots utilizing the allowable ZMP region,” IEEE Trans. Robot. 30 (4) 986–993 (2014).Google Scholar
4. Ur-Rehman, R., Caro, S., Chablat, D. and Wenger, P., “Multi-objective path placement optimization of parallel kinematics machines based on energy consumption, shaking forces and maximum actuator torques: Application to the Orthoglide,” Mech. Mach. Theory 45 (8), 1125–1141 (Aug. 2010).Google Scholar
5. Ma, S., “Time-optimal control of robotic manipulators with limit heat characteristics of the actuator,” Adv. Robot. 16 (4), 309–324 (2002).Google Scholar
6. Broderick, J., Tilbury, D. and Atkins, E., “Maximizing Coverage for Mobile Robots while Conserving Energy,” Proceedings of the ASME International Design Engineering Technical Conference and Computers and Information in Engineering Conference (IDETC/CIE), Chicago, IL, USA (2012).Google Scholar
7. Sadrpour, A., Jin, J. and Ulsoy, A. G., “Mission Energy Prediction for Unmanned Ground Vehicles,” Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), Saint Paul, MN (2012) pp. 2229–2234.Google Scholar
8. Potts, A. S. and da Cruz, J. J., “Optimal power loss motion planning in legged robots,” Robotica 34 (2), 423–448 (February 2016).Google Scholar
9. Lofaro, D., Chunyang, S. and Oh, P., “Humanoid Pitching at a Major League Baseball Game: Challenges, Approach, Implementation and Lessons Learned,” IEEE-RAS International Conference on Humanoid Robots (Humanoids), Osaka, Japan, (2012) pp. 423–428.Google Scholar
10. Shintaku, E., “Minimum energy trajectory for an underwater manipulator and its simple planning method by using a genetic algorithm,” Adv. Robot. 13 (2), 115–138 (1998).CrossRefGoogle Scholar
11. Mummolo, C. and Kim, J. H., “Passive and dynamic gait measures for biped mechanism: Formulation and simulation analysis,” Robotica 31 (4), 555–572 (Jul. 2013).Google Scholar
12. Sengupta, A., Chakraborti, T., Konar, A. and Nagar, A., “Energy efficient trajectory planning by a robot arm using invasive weed optimization technique,” World Congress on Nature and Biologically Inspired Computing (NaBIC), Salamanca, Spain (2011) pp. 311–316.Google Scholar
13. Zarrouk, D. and Fearing, R. S., “Cost of Locomotion of a Dynamic Hexapedal Robot,” Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), Karlsruhe, Germany (2013) pp. 2548–2553.Google Scholar
14. Duindam, V., Modeling and Control for Efficient Bipedal Walking Robots: A Port-Based Approach, 2009 ed. (Springer, Berlin, 2009).Google Scholar
15. Jin, B., Chen, C. and Li, W., “Power consumption optimization for a hexapod walking robot,” J. Intell. Robot. Syst. 71 (2) 195–209 (Aug. 2013).Google Scholar
16. de Santos, P. G., Garcia, E., Ponticelli, R. and Armada, M., “Minimizing energy consumption in hexapod robots,” Adv. Robot. 23 (6), 681–704 (Apr. 2009).Google Scholar
17. Kaneko, M., Tachi, S., Tanie, K. and Abe, M., “Basic study on similarity in walking machine from a point of energetic efficiency,” IEEE J. Robot. Autom. 3 (1), 19–30 (Feb. 1987).Google Scholar
18. Hirakawa, A. R. and Kawamura, A., “Proposal of Trajectory Generation for Redundant Manipulators using Variational Approach Applied to Minimization of Consumed Electrical Energy,” Proceedings of the International Workshop on Advanced Motion Control (1996) pp. 687–692.Google Scholar
19. Hirakawa, A. R. and Kawamura, A., “Trajectory Planning of Redundant Manipulators for Minimum Energy Consumption Without Matrix Inversion,” Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), Albequerque, NM (1997) pp. 2415–2420.Google Scholar
20. Miller, R. H., “A comparison of muscle energy models for simulating human walking in three dimensions,” J. Biomech. 47 (6), 1373–1381 (Apr. 2014).Google Scholar
21. Kulk, J. and Welsh, J., “A Low Power Walk for the NAO Robot,” Proceedings of Australasian Conference on Robotics and Automation (ACRA), Canberra, Australia (2008).Google Scholar
22. Kim, M.-S., Kim, I., Park, S. and Oh, J. H., “Realization of Stretch-Legged Walking of the Humanoid Robot,” Proceedings of the IEEE-RAS International Conference on Humanoid Robots (Humanoids) (2008) pp. 118–124.Google Scholar
23. Park, I.-W., Kim, J.-Y., Lee, J. and Oh, J.-H., “Mechanical design of the humanoid robot platform, HUBO,” Adv. Robot. 21 (11), 1305–1322 (2007).CrossRefGoogle Scholar
24. Traversaro, S., Del Prete, A., Muradore, R., Natale, L. and Nori, F., “Inertial Parameter Identification Including Friction and Motor Dynamics,” Proceedings of the IEEE-RAS International Conference on Humanoid Robots (Humanoids), Atlanta, GA (2013) pp. 68–73.Google Scholar
25. Collins, S. H. and Ruina, A., “A Bipedal Walking Robot with Efficient and Human-Like Gait,” Proceedings of the IEEE International Conference on Robotics and Automation (ICRA) (2005) pp. 1983–1988.Google Scholar
26. Collins, S., Ruina, A., Tedrake, R. and Wisse, M., “Efficient bipedal robots based on passive-dynamic walkers,” Science 307 (5712), 1082–1085 (Feb. 2005).Google Scholar
27. Moro, F. L., Tsagarakis, N. G. and Caldwell, D. G., “Efficient Human-Like Walking for the COmpliant huMANoid COMAN Based on Kinematic Motion Primitives (kMPs),” Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), Saint Paul, MN (2012) pp. 2007–2014.Google Scholar
28. Kormushev, P., Ugurlu, B., Calinon, S., Tsagarakis, N. G. and Caldwell, D. G., “Bipedal Walking Energy Minimization by Reinforcement Learning with Evolving Policy Parameterization,” Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) (2011), pp. 318–324.Google Scholar
29. Flynn, L., Jafari, R., Hellum, A. and Mukherjee, R., “An Energy Optimal Gait for the MSU Active Synthetic Wheel Biped,” Proceedings of the ASME Dynamic Systems and Control Conference (DSC), Cambridge, MA, USA (2010) pp. 1–8.Google Scholar
30. Ziegler, S., Woodward, R. C., Iu, H. H.-C. and Borle, L. J., “Current sensing techniques: A review,” IEEE Sens. J. 9 (4), 354–376 (Apr. 2009).Google Scholar
31. Mummolo, C., Mangialardi, L. and Kim, J. H., “Quantifying dynamic characteristics of human walking for comprehensive gait cycle,” J. Biomech. Eng.-Trans. ASME 135 (9), 091006-1-091006-10 (Jul. 2013).Google Scholar
32. McGeer, T., “Passive dynamic walking,” Int. J. Robot. Res. 9 (2), 62–82 (Apr. 1990).CrossRefGoogle Scholar
33. Li, J. and Chen, W., “Energy-efficient gait generation for biped robot based on the passive inverted pendulum model,” Robotica 29 (04), 595–605 (Jul. 2011).Google Scholar
34. Rostami, M. and Bessonnet, G., “Sagittal gait of a biped robot during the single support phase. Part 1: Passive motion,” Robotica 19 (02), 163–176 (Mar. 2001).Google Scholar
35. Long, L. L. and Srinivasan, M., “Walking, running, and resting under time, distance, and average speed constraints: Optimality of walk–run–rest mixtures,” J. R. Soc. Interface 10 (81), 1–10 (Apr. 2013).CrossRefGoogle ScholarPubMed
36. Torricelli, D., Gonzalez-Vargas, J., Veneman, J. F., Mombaur, K., Tsagarakis, N., del Ama, A. J., Gil-Agudo, A., Moreno, J. C. and Pons, J. L., “Benchmarking bipedal locomotion: A unified scheme for humanoids, wearable robots, and humans,” IEEE Robot. Autom. Mag. 22 (3), 103–115 (Sept. 2015).Google Scholar
37. Au, S. K., Weber, J. and Herr, H., “Powered ankle-foot prosthesis improves walking metabolic economy,” IEEE Trans. Robot. 25 (1), 51–66 (2009).CrossRefGoogle Scholar
38. Kuo, A. D., “Choosing your steps carefully,” IEEE Robot. Autom. Mag. 14 (2), 18–29 (Jun. 2007).Google Scholar
39. Nahon, M. and Angeles, J., “Minimization of power losses in cooperating manipulators,” J. Dyn. Sys. Meas. Control 114 (2), 213–219 (Jun. 1992).Google Scholar
40. Ha, I., Tamura, Y. and Asama, H., “Development of open platform humanoid robot DARwIn-OP,” Adv. Robot. 27 (3), 223–232 (Feb. 2013).Google Scholar
41. Ha, I., Tamura, Y., Asama, H., Han, J. and Hong, D. W., “Development of Open Humanoid Platform DARwIn-OP,” Proceedings of International Conference on Instrumentation, Control, Information Technology and System Integration (SICE), Tokyo, Japan (2011) pp. 2178–2181.Google Scholar
42. Ha, I., Tamura, Y. and Asama, H., “Gait Pattern Generation and Stabilization for Humanoid Robot Based on Coupled Oscillators,” Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), San Francisco, CA (2011) pp. 3207–3212.Google Scholar
43. “Walking Tuner.” [Online]. Available: http://support.robotis.com/en/product/darwin-op/development/tools/walking_tuner.htm. [Accessed: 30-Jun-2014].Google Scholar
44. Kramer, P. A. and Sarton-Miller, I., “The energetics of human walking: Is Froude number (Fr) useful for metabolic comparisons?,” Gait Posture 27 (2), 209–215 (Feb. 2008).Google Scholar
45. Roberts, D., Hillstrom, H. and Kim, J. H., “Joint-Space Dynamic Model of Metabolic Cost with Subject-Specific Energetic Parameters,” Proceedings of the ASME International Design Engineering Technical Conf. and Computers and Information in Engineering Conference (IDETC/CIE), Buffalo, NY (2014).Google Scholar
46. Bhargava, L. J., Pandy, M. G. and Anderson, F. C., “A phenomenological model for estimating metabolic energy consumption in muscle contraction,” J. Biomech. 37 (1), 81–88 (Jan. 2004).Google Scholar
47. Kim, J. H., Yang, J. and Abdel-Malek, K., “Planning load-effective dynamic motions of highly articulated human model for generic tasks,” Robotica 27 (5), 739–747 (Sep. 2009).Google Scholar
48. Milner, T., “Adaptation to destabilizing dynamics by means of muscle cocontraction,” Exp. Brain Res. 143 (4), 406–416 (2002).Google Scholar
49. Milner, T. E., Cloutier, C., Leger, A. B. and Franklin, D. W., “Inability to activate muscles maximally during cocontraction and the effect on joint stiffness,” Exp. Brain Res. 107 (2), 293–305 (Dec. 1995).Google Scholar
50. Millard, M., Uchida, T., Seth, A. and Delp, S. L., “Flexing computational muscle: Modeling and simulation of musculotendon dynamics,” J. Biomech. Eng.-Trans. ASME 135 (2), 021004-1-021004-11 (Feb. 2013).CrossRefGoogle ScholarPubMed
51. Uth, N., Sørensen, H., Overgaard, K. and Pedersen, P. K., “Estimation of $\dot{\rm V}$ O2max from the ratio between HRmax and HRrest – the heart rate ratio method,” Eur. J. Appl. Physiol. 91 (1), 111–115 (Jan. 2004).Google Scholar
52. Tanaka, H., Monahan, K. D. and Seals, D. R., “Age-predicted maximal heart rate revisited,” J. Am. Coll. Cardiol. 37 (1), 153–156 (Jan. 2001).Google Scholar
53. Anderson, D. E., Madigan, M. L. and Nussbaum, M. A., “Maximum voluntary joint torque as a function of joint angle and angular velocity: Model development and application to the lower limb,” J. Biomech. 40 (14), 3105–3113 (Jan. 2007).Google Scholar
54. Holzbaur, K. R. S., Delp, S. L., Gold, G. E. and Murray, W. M., “Moment-generating capacity of upper limb muscles in healthy adults,” J. Biomech. 40 (11), 2442–2449 (Jan. 2007).CrossRefGoogle ScholarPubMed
55. Vaughan, C. L., Davis, B. L. and O'Connor, J. C., Dynamics of Human Gait, 2nd ed. (Kiboho Publishers, Cape Town, South Africa, 1999).Google Scholar
56. Perry, J., Gait Analysis: Normal and Pathological Function (SLACK Incorporated, Thorofare, NJ, 1992).Google Scholar
57. Ogura, Y., Kataoka, T., Aikawa, H., Shimomura, K., Lim, H. and Takanishi, A., “Evaluation of Various Walking Patterns of Biped Humanoid Robot,” Proceedings of the IEEE International Conference on Robotics and Automation (ICRA) (2005) pp. 603–608.Google Scholar
58. Vaughan, C. L., “Theories of bipedal walking: An odyssey,” J. Biomech. 36 (4), 513–523 (Apr. 2003).Google Scholar
59. Kuo, A., “The six determinants of gait and the inverted pendulum analogy: A dynamic walking perspective,” Hum. Mov. Sci. 26 (4), 617–656 (Aug. 2007).Google Scholar
60. Carey, T. S. and Crompton, R. H., “The metabolic costs of ‘bent-hip, bent-knee’ walking in humans,” J. Hum. Evol. 48 (1), 25–44 (Jan. 2005).Google Scholar
61. Pratt, J. and Pratt, G., “Intuitive Control of a Planar Bipedal Walking Robot,” Proceedings of the IEEE International Conference on Robotics and Automation (ICRA) (1998), pp. 2014–2021.Google Scholar
62. Winter, D. A., Biomechanics and Motor Control of Human Movement, 4th ed. (Wiley, Hoboken, NJ, 2009).Google Scholar
63. Waters, R. L. and Mulroy, S., “The energy expenditure of normal and pathologic gait,” Gait Posture 9 (3), 207–231 (Jul. 1999).Google Scholar
64. Donelan, J. M., Kram, R. and Kuo, A. D., “Mechanical work for step-to-step transitions is a major determinant of the metabolic cost of human walking,” J. Exp. Biol. 205 (23), 3717–3727 (2002).Google Scholar
65. Kim, J. H. and Joo, C. B., “Numerical construction of balanced state manifold for single-support legged mechanism in sagittal plane,” Multibody Syst. Dyn. 31 (3), 257–281 (Mar. 2014).Google Scholar
66. Kim, J.-Y., Park, I.-W., Lee, J., Kim, M.-S., Cho, B. and Oh, J.-H., “System Design and Dynamic Walking of Humanoid Robot KHR-2,” Proceedings of the IEEE International Conference on Robotics and Automation (ICRA) (2005) pp. 1431–1436.Google Scholar
67. Pratt, J. E., Exploiting Inherent Robustness and Natural Dynamics in the Control of Biped Walking Robots Ph.D. Dissertation (Massachusettes Institute of Technology (MIT), Cambridge, MA, 2000).Google Scholar
68. Radhakrishnan, V., “Locomotion: Dealing with friction,” PNAS 95 (10), 5448–5455 (May 1998).Google Scholar
69. Margaria, R., “Positive and negative work performances and their efficiencies in human locomotion,” Int. Z. fur Angew. Physiologie 25, 339–351 (May 1968).Google Scholar
70. Goswami, A., “Postural stability of biped robots and the foot-rotation indicator (FRI) point,” Int. J. Robot. Res. 18 (6), 523–533 (1999).CrossRefGoogle Scholar
71. Azevedo, C., Andreff, N. and Arias, S., “Bipedal walking: From gait design to experimental analysis,” Mechatronics 14 (6), 639–665 (Jul. 2004).Google Scholar