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Walking Robots
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  Steve Collins, Steven H. Collins, S.H. Collins, Dynamics, Mechanics, Locomotion, passive-dynamics, passive-dynamic, Robots, BioRobotics, Robotics, Minimally Powered Robots, Efficient Robots, efficient bipeds, efficiency, Walking Robots, humanoid robot, biomimetic robot, anthropomorphic robot, Tad McGeer, University of Michigan, Art Kuo, Cornell University, Andy Ruina, nonholonomic booboobechu
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Robots can be used to test theories of human locomotion in ways impossible in human subject experiments, because robots allow for direct evaluation of proposed neuromuscular coordination strategies. However, the robot's morphology must be a good model of the human musculoskeletal system. Walking robots based on the mainstream control paradigm of precise joint-angle control use an order of magnitude more power than humans and require actuators with much higher precision and frequency response than human muscle. In the late 1980's, Tad McGeer suggested passive-dynamics as an alternative paradigm. |
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Passive-dynamics presupposes that the motion we understand as walking may in fact largely be the natural dynamical consequence of the mass properties of the human body. That is, people may mostly let their legs swing as they would on their own, then add a little control and power, yielding a gait with inherently low energetic and control demands. In contrast to rigidly joint-controlled robots, walking robots based on passive-dynamic principles can have human-like efficiency and actuation requirements (e.g. McGeer 1990, Collins et al 2005). The simplicity, efficiency, ease of control, and low cost of passive-dynamics based robots may also make them more practical in autonomous robotic applications. |
3-D Passive Dynamic Walking Machine with Two Legs and Knees

Click images to enlarge.   Photos on right by Hank Morgan.
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This walking machine is described in detail in the paper below and can be seen walking in the movies below. In my first experience in research as an undergraduate at Cornell University, and with the help of past advisor Andy Ruina and visiting student Martijn Wisse, I constructed this fully-passive walking machine. It walks without any active power or control, restoring energy lost to heel-strike collisions by traveling down a small slope. The mass properties and geometry were carefully chosen such that a stable gait is a natural property of the mechanical system. The dynamics were especially sensitive to foot shape and arm articulation. |
Paper: Collins, S.H., Wisse, M., Ruina, A. (2001) A 3-D Passive Dynamic Walking Robot with Two Legs and Knees, International Journal of Robotics Research, 20 (7):607-615. (html version) |
Movies:
  passive_angle.mov (3.8 meg) A view at an angle of the passive machine walking down a shallow ramp.
              passive_behind.mov (3.6 meg) A view from behind of one ramp walk.
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Related links:   Cornell site   Delft site |
A Bipedal Walking Robot with Efficient and Human-Like Gait
Left to right: CAD renderings; First prototype; Brains (top) and Knees; Feet and ankles; Final version.  Click images to enlarge.
This walking robot is described in detail in the papers below and can be seen walking in the movies below. The Science paper presents our main findings and results, while the ICRA proceedings paper acts as a supplement with detailed documentation of the device's design and a more thorough comparison of energy use. This project was aimed at accomplishing three goals: to show that the desirable properties of a passive machine could be transferred to an actively powered robot; to use this fact to build the most energy efficient bipedal walking robot to date; and to better understand the fundamentals of the neuromuscular coordination of human walking. |
Actuating a passive walker, it turns out, can be relatively easy. The geometry and mass properties of this machine are very similar to those of its passive parent (above). In the demonstration videos below, you can see that the hips swing freely, with an angle bisection mechanism keeping the head/torso upright, and the knees swing freely until they reach full extension where a passive latch locks them in place. The only significant difference is that this robot has ankles that extend once per step to add power through push-off of the trailing leg. To maintain the energy efficiency of the passive machine, we used energy storage and actuation systems with high conversion efficiency and low peak power to produce, and rarely absorb, mechanical work. |
Energy Efficiency in level-ground locomotion is measured by the dimensionless specific cost of transport, which is the amount of energy required to carry a unit weight a unit distance (Tucker 1975). The lower the cost of transport, the better the efficiency. This robot walks at 0.44 m/s, weighs 125 N (12.7 kg), and consumes 11.0 W of electricity to do so. This yields an energetic cost of transport of 0.20, an order of magnitude lower than any known walking robot. By comparison, Honda's Asimo, which is a marvel of engineering but does not utilize the passive-dynamics of its own limbs, walks at 0.44 m/s, weighs 510 N, consumes about 768 W (1 hp), and thus has a specific cost of transport of about 3.2. (See bar graph at right and table in ICRA paper for more comparisons) |
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Human evolution and learning have presumably selected against excessive energy use in locomotion (Alexander 2003). Humans have a specific metabolic cost of transport of about 0.2, which is very similar to our robot and much lower than other walking robots. Humans also seem to use both ankle push-off and accelerated leg swing to walk efficiently (Donelan 2002), powering schemes that are demonstrated on passive-dynamics based machines here and in Martijn Wisse's robots, respectively. Finally, passive-dynamics based robots have a gait that looks characteristically human. All of these facts strongly suggest that people utilize the natural dynamics of their limbs as they walk. |
Paper: Collins, S.H., Ruina, A.L., Tedrake, R., Wisse, M. (2005) Efficient bipedal robots based on passive-dynamic Walkers, Science, 307: 1082-1085. |
Proceedings: Collins, S. H., Ruina, A. (2005) A bipedal walking robot with efficient and human-like gait. In Proc. IEEE International Conference on Robotics and Automation, Barcelona, Spain, April 2005, in press. |
Movies: |
Compilation.mov (8 meg) | A compilation of walks on the level walking platform, laboratory floor, and hallway. |
| 2WalksAngle.mpg (5 meg) | Two consecutive launches and walks on the level walking platform. |
| DemoFeet.mpg (1 meg) | Demonstration of ankle extension push-off, triggered by contact of contralateral foot. |
| DemoHips.mpg (1 meg) | Demonstration of the hip angle bisecting mechanism working on the torso. |
| DemoKnee.mpg (1 meg) | Demonstration of the knees swinging passively, then locking at full extension. |
| DemoSide.mpg (1 meg) | Demonstration of the arms moving in sync with the contralateral leg. |
Related links:   Cornell site   Delft site   MIT site   Press | |
This work has been funded by Cornell University and National Science Foundation (NSF) Biomechanics and Robotics grants.
Last updated: 2/19/2005
References
| | Alexander, R. M. (2003) Principles of Animal Locomotion. New Jersey: Princeton University Press. | |
| | Coleman, M, Ruina, A. (1998) An Uncontrolled Walking Toy That Cannot Stand Still. Physical Review Letters 80:16 3658 - 3661 | |
| | Coleman, M. (1997) A stability study of a three-dimensional passive-dynamic model of human gait. Ph.D. Thesis, Cornell University, Ithaca, NY USA. | |
| | Collins, S.H., Wisse, M., Ruina, A. (2001) A 3-D Passive Dynamic Walking Robot with Two Legs and Knees, International Journal of Robotics Research, 20 (7):607-615. (html version) | |
| | Collins, S.H., Ruina, A.L., Tedrake, R., Wisse, M. (2005) Efficient bipedal robots based on passive-dynamic Walkers, Science, 307: 1082-1085. | |
| | Collins, S. H., Ruina, A. (2005) A bipedal walking robot with efficient and human-like gait. In Proc. IEEE Int. Conf. Robotics and Automation, Barcelona, Spain, in press. | |
| | Donelan, J. M., Kram, R., and Kuo, A. D. (2002)
Mechanical and metabolic costs of step-to-step transitions in human walking. J. Experimental Biology, : 3717-3727. | |
| | Garcia, M. (1998) Stability, scaling, and chaos in passive-dynamic gait models. Ph.D. Thesis, Cornell University, Ithaca, NY USA. | |
| | Kuo, A. D. (1999) Stabilization of lateral motion in passive dynamic walking, International Journal of Robotics Research, 18 (9): 917-930. | |
| | Kuo, A.D. (2001) A simple model of bipedal walking predicts the preferred speed-step length relationship, Journal of Biomechanical Engineering, 123: 264-269. | |
| | Kuo, A. D. (2002) Energetics of actively powered locomotion using the simplest walking model, Journal of Biomechanical Engineering, 124: 113-120. | |
| | McGeer, T. (1989) Powered flight, child's play, silly wheels, and walking
machines. In: Proc. IEEE Robotics and Automation Conference, Piscataway, NJ : pp. 1592-1597. | |
| | McGeer, T. (1990) Passive dynamic walking. International Journal of Robotics Research. 9(2): 68-82. | |
| | McGeer, T. (1990) Passive dynamic running. Proceedings of the Royal Society of London B. 1240: 107-134. | |
| | McGeer, T. (1990) Passive walking with knees. In: Proc. IEEE Robotics and Automation Conference, Cincinnati, OH : pp. 1640-1645. | |
| | McGeer, T. (1991) Passive dynamic biped catalogue. In: Proc. 2nd Int. Symp. of Experimental Robotics, Toulouse, France: pp. 465-490. | |
| | McGeer, T. (1992) Principles of walking and running. In Advances in Comparative and Environmental Physiology, Vol. 11, Mechanics of Animal Locomotion (Alexander, R. M., ed.). Berlin: Springer-Verlag | |
| | McGeer, T. (1993) Dynamics and control of bipedal locomotion. Journal of Theoretical Biology. 163: 277-314. | |
| | Tedrake, R., Zhand, T.W., Fong, M.F., Seung, H.S. (2004) Actuating a Simple 3D Passive Dynamic Walker. In Proc. IEEE Int. Conf. Robotics & Automation, New Orleans, LA: 4656-4661. | |
| | Tucker, V. A. (1975) The energetic cost of moving about. American Scientist. 63(4): 413-419. | |
| | Wisse, M., Frankenhuyzen, J.V. (2003) Design and construction of Mike; a 2D autonomous biped based on passive dynamic walking. In Proc. 2nd Int. Symp. on Adaptive Motion of Animals and Machines, Kyoto, Japan. | |
| | Wisse, M. (2004) Essentials of dynamic walking; analysis and design of two-legged robots. Ph.D. Thesis, Technische Universiteit Delft. | |
   
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