Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-13T04:13:38.918Z Has data issue: false hasContentIssue false
  • English
  • Français

Compliance and frequency optimization for energy efficiency in cyclic tasks

Published online by Cambridge University Press:  10 February 2017

Mohammad Shushtari ,
Rezvan Nasiri ,
Mohammad Javad Yazdanpanah  and
Majid Nili Ahmadabadi
Mohammad Shushtari
Affiliation:
Cognitive Systems Laboratory, Control and Intelligent Processing Center of Excellence (CIPCE), School of Electrical and Computer Engineering, College of Engineering, University of Tehran, Tehran, Iran. E-mails: nasiri.rezvan@gmail.com, sm.shushtari@gmail.com, mnili@ut.ac.ir
Rezvan Nasiri*
Affiliation:
Cognitive Systems Laboratory, Control and Intelligent Processing Center of Excellence (CIPCE), School of Electrical and Computer Engineering, College of Engineering, University of Tehran, Tehran, Iran. E-mails: nasiri.rezvan@gmail.com, sm.shushtari@gmail.com, mnili@ut.ac.ir
Mohammad Javad Yazdanpanah
Affiliation:
Advanced Control Systems Laboratory, Control and Intelligent Processing Center of Excellence (CIPCE), School of Electrical and Computer Engineering, College of Engineering, University of Tehran, Tehran, Iran. E-mail: yazdan@ut.ac.ir
Majid Nili Ahmadabadi
Affiliation:
Cognitive Systems Laboratory, Control and Intelligent Processing Center of Excellence (CIPCE), School of Electrical and Computer Engineering, College of Engineering, University of Tehran, Tehran, Iran. E-mails: nasiri.rezvan@gmail.com, sm.shushtari@gmail.com, mnili@ut.ac.ir
*
*Corresponding author. E-mail: nasiri.rezvan@gmail.com
Get access Rights & Permissions [Opens in a new window]

Summary

We present an analytical method for the concurrent calculation of optimal parallel compliant elements and frequency of reference trajectories for serial manipulators performing cyclic tasks. In this approach, we simultaneously shape and exploit the robot's natural dynamics by finding a set of compliant elements and task frequency that result in minimization of an energy-based cost function. The cost function is the integral of a weighted squared norm of the generalized forces. We prove that the generalized force needed for tracking the reference trajectory is a linear function of compliance coefficients and a quadratic function of task frequency. Therefore, the cost function is quadratic with respect to stiffness coefficients and quartic with respect to the task frequency. These properties lead to a well-posed optimization problem with a closed-form solution. Using three case studies, we elucidate the properties of our method.

Keywords

Energy efficiencyOptimum complianceOptimum FrequencyCyclic tasksNatural dynamics
Type
Articles
Information
Robotica , Volume 35 , Issue 12 , December 2017 , pp. 2363 - 2380
Copyright
Copyright © Cambridge University Press 2017 

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. Bauer, F., Römer, U., Fidlin, A. and Seemann, W., “Optimization of energy efficiency of walking bipedal robots by use of elastic couplings in the form of mechanical springs,” Nonlinear Dyn. 83, 1275–1301 (2016).Google Scholar
2. Bidgoly, H. J., Ahmadabadi, M. N. and Zakerzadeh, M. R., “Design and Modeling of a Compact Rotational Nonlinear Spring,” Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), IEEE, Daejeon, Korea (2016) pp. 4356–4361.Google Scholar
3. Buchli, J., Iida, F. and Ijspeert, A. J., “Finding Resonance: Adaptive Frequency Oscillators for Dynamic Legged Locomotion,” Proceedings of the IEEE/RSJ International Conference of Intelligent Robots and Systems, IEEE, Beijing, China (2006) pp. 3903–3909.Google Scholar
4. Collins, S., Ruina, A., Tedrake, R. and Wisse, M., “Efficient bipedal robots based on passive-dynamic walkers,” Science 307, 1082–1085 (2005).Google Scholar
5. Cotton, S., Olaru, I. M. C., Bellman, M., Van der Ven, T., Godowski, J. and Pratt, J., “Fastrunner: A Fast, Efficient and Robust Bipedal Robot. Concept and Planar Simulation,” Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), IEEE, St. Paul, MN, USA (2012) pp. 2358–2364.Google Scholar
6. Grimmer, M., Eslamy, M., Gliech, S. and Seyfarth, A., “A Comparison of Parallel-and Series Elastic Elements in an Actuator for Mimicking Human Ankle Joint in Walking and Running,” Proceedings of the 2012 IEEE International Conference on Robotics and Automation (ICRA), IEEE, St. Paul, MN, USA (2012) pp. 2463–2470.Google Scholar
7. Ijspeert, A. J., “Central pattern generators for locomotion control in animals and robots: A review,” Neural Netw. 21, 642–653 (2008).Google Scholar
8. Jafari, A., Tsagarakis, N. G. and Caldwell, D. G., “A novel intrinsically energy efficient actuator with adjustable stiffness (awas),” IEEE/ASME Trans. Mechatron. 18, 355–365 (2013).Google Scholar
9. Khoramshahi, M., Nasiri, R., Ijspeert, A. and Ahmadabadi, M. N., “Energy Efficient Locomotion with Adaptive Natural Oscillator,” Dynamic Walking 2014, EPFL-CONF-199765 (2014).Google Scholar
10. Khoramshahi, M., Parsa, A., Ijspeert, A. and Ahmadabadi, M. N., “Natural Dynamics Modification for Energy Efficiency: A Data Driven Parallel Compliance Design Method,” Proceedings of the International Conference on Robotics and Automation (ICRA), IEEE, Hong Kong, China (2014) pp. 2412–2417.Google Scholar
11. Martínez, S., Monje, C. A., Jardón, A., Pierro, P., Balaguer, C. and Munoz, D., “Teo: Full-size humanoid robot design powered by a fuel cell system,” Cybern. Syst. 43, 163–180 (2012).Google Scholar
12. MATLAB (2015-b). Mathworks Inc. http://www.mathworks.com.Google Scholar
13. McGeer, T., “Passive dynamic walking,” Int. J. Robot. Res. 9, 62–82 (1990).Google Scholar
14. Mozaffari, S., Rekabi, E., Nasiri, R. and Ahmadabadi, M. N., “Design and Modeling of a Novel Multi-Functional Elastic Actuator (MFEA),” Proceedings of the 4th International Conference on Robotics and Mechatronics (ICROM), IEEE, University of Tehran, Tehran, Iran (2016).Google Scholar
15. Nasiri, R., Khoramshahi, M. and Ahmadabadi, M. N., “Design of a Nonlinear Adaptive Natural Oscillator: Towards Natural Dynamics Exploitation in Cyclic Tasks,” Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), IEEE, I Daejeon, Korea (2016) pp. 3653–3658.Google Scholar
16. Nasiri, R., Khoramshahi, M., Shushtari, M. and Ahmadabadi, M. N., “Adaptation in variable parallel compliance: Towards energy efficiency in cyclic tasks,” IEEE/ASME Trans. Mechatron., IEEE (2016). Available at: http://ieeexplore.ieee.org/document/7778166/.Google Scholar
17. Pérez, D. and Quintana, Y., “A survey on the weierstrass approximation theorem,” Divulgaciones Matemáticas 16, 231–247 (2008).Google Scholar
18. Peters, J., Mistry, M., Udwadia, F., Nakanishi, J. and Schaal, S., “A unifying framework for robot control with redundant dofs,” Auton. Robots 24, 1–12 (2008).CrossRefGoogle Scholar
19. Righetti, L., Buchli, J. and Ijspeert, A. J., “Dynamic hebbian learning in adaptive frequency oscillators,” Phys. D: Nonlinear Phenom. 216, 269–281 (2006).CrossRefGoogle Scholar
20. Schaal, S., Peters, J., Nakanishi, J. and Ijspeert, A., “Learning Movement Primitives,” Proceedings of the 11th International Symposium Robotics Research, Springer (2005) pp. 561–572.Google Scholar
21. Schepelmann, A., Geberth, K. A. and Geyer, H., “Compact Nonlinear Springs with User Defined Torque-Deflection Profiles for Series Elastic Actuators,” Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), IEEE, Hong Kong, China (2014) pp. 3411–3416.Google Scholar
22. Schmit, N. and Okada, M., “Simultaneous Optimization of Robot Trajectory and Nonlinear Springs to Minimize Actuator Torque,” Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), IEEE, St. Paul, MN, USA (2012) pp. 2806–2811.Google Scholar
23. Schmit, N. and Okada, M., “Optimal design of nonlinear springs in robot mechanism: simultaneous design of trajectory and spring force profiles,” Adv. Robot. 27, 33–46 (2013).Google Scholar
24. Seok, S., Wang, A., Chuah, M. Y., Otten, D., Lang, J. and Kim, S., “Design Principles for Highly Efficient Quadrupeds and Implementation on the Mit Cheetah Robot,” Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), IEEE, Karlsruhe, Germany (2013) pp. 3307–3312.Google Scholar
25. Shafii, N., Lau, N. and Reis, L. P., “Generalized Learning to Create an Energy Efficient zmp-Based Walking,” Robocup 2014: Robot World Cup xviii, Springer (2015) pp. 583–595.Google Scholar
26. Shakiba, M., Shadmehr, M. H., Mohseni, O., Nasiri, R. and Ahmadabadi, M. N., “An Adaptable Cat-Inspired Leg Design with Frequency-Amplitude Coupling,” Proceedings of the 4th RSI International Conference on Robotics and Mechatronics (ICROM), IEEE, University of Tehran, Tehran, Iran (2016).Google Scholar
27. 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, 986–993 (2014).CrossRefGoogle Scholar
28. Spong, M. W., Hutchinson, S. and Vidyasagar, M., Robot Modeling and Control, vol. 3 (Wiley, New York, 2006).Google Scholar
29. Sreenath, K., Park, H.-W., Poulakakis, I. and Grizzle, J. W., “A compliant hybrid zero dynamics controller for stable, efficient and fast bipedal walking on mabel,” Int. J. Robot. Res. 30, 1170–1193 (2011).Google Scholar
30. Tsagarakis, N. G., Li, Z., Saglia, J. and Caldwell, D. G., “The Design of the Lower Body of the Compliant Humanoid robot Ccub,” Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), IEEE, International Conference Center, Shanghai, China (2011) pp. 2035–2040.Google Scholar
31. Uemura, M., Goya, H. and Kawamura, S., “Motion control with stiffness adaptation for torque minimization in multijoint robots,” IEEE Trans. Robot. 30, 352–364 (2014).Google Scholar
32. Van Ham, R., Vanderborght, B., Van Damme, M., Verrelst, B. and Lefeber, D., “Maccepa, the mechanically adjustable compliance and controllable equilibrium position actuator: Design and implementation in a biped robot,” Robot. Auton. Syst. 55, 761–768 (2007).Google Scholar
33. Vanderborght, B., Albu-Schaeffer, A., Bicchi, A., Burdet, E., Caldwell, D. G., Carloni, R., Catalano, M., Eiberger, O., Friedl, W. and Ganesh, G., “Variable impedance actuators: A review,” Robot. Auton. Syst. 61, 1601–1614 (2013).Google Scholar
34. Visser, L. C., Carloni, R., Unal, R. and Stramigioli, S., “Modeling and Design of Energy Efficient Variable Stiffness Actuators,” Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), IEEE, Egan Convention Center, Anchorage, AK, USA (2010) pp. 3273–3278.Google Scholar