PhD Student @ Carnegie Mellon

Research

Control and modeling of bipedal locomotion has advanced significantly over the past century and has captured a substantial amount of the physics of walking. This has provided an opportunity to not only create humanoid robots, but also to understand human walking. This understanding helps in the development of robotic prosthesis.

The earliest models of walking were based on a simple inverted pendulum[1][2], and this model has become a standard basis for which most other walking models are built upon. Adding other segments to the pendulum gave more advanced understanding of walking in bipedal systems due to the additional degrees of freedom at the joints in the legs[3]. An introduction of a spring in the single inverted pendulum, showed that humans do indeed use their limbs like springs as shown by the spring mass model[4], especially in running. This lent itself to adding springs at the joints in multi-segmented inverted pendulum models[5], which could easily be identified with human muscles[6]. Muscle models were developed and the most significantly used model is the Hill-type model[7], which shows a nonlinear relationship between muscle length, muscle velocity and the force output, which is not directly a spring, but does have spring like characteristic. An interesting part of this muscle model is that it had the potential to include neural activation, which is the body’s own control system. Therefore, controls mimicking human motion could now actually represent the physiology behind them.

One of these control methods is Central Pattern Generation (CPG)[8][9]. A set of neurons that activate different muscles are connected to each other. This basic connection, coined a neural oscillator, produces an activation signal from one neuron to a muscle, while inhibiting a neuron of an opposing muscle and then, being oscillatory in nature, does the reverse. This creates a self generating walking pattern when used between opposing leg. In order for the model to have a stable walking pattern, a complex pattern of neural connections between muscles is needed and most of these pathways have yet to be discovered.

However, looking at basic neural connections, reflex paths, in humans and animals, and implementing them in neuromuscular models has produced several robust controls, especially for the stance leg during walking[10]. The physics of the model accurately predict ground reaction forces, which is a standard validation on walking models. Additionally, similar activation patterns in the stance leg between the neuromuscular model with reflex controls are produced in the human subject muscles, as studied by EMG.

Unfortunately, a critical part of the model, the swing leg reflex controls, remain uncertain ,which leads to instability in an otherwise relatively robust model. Neural controls have been explored and are stable in certain situations due to optimizing parameters, but the underlying reflex controls that would give true predictive power have not yet been fully explored.

REFERENCES

[1] G.A. Borelli, J. Bernoulli, N. Elinger, and C.J. a Jesu, De motu animalium, Petrum Gosse, 1743.
[2] R.M. Alexander, “Mechanics of bipedal locomotion,” Perspectives in experimental biology, vol. 1, 1976, pp. 493–504.
[3] S. Mochon and T.A. McMahon, “Ballistic walking,” Journal of Biomechanics, vol. 13, 1980, pp. 49–57.
[4] R. Blickhan, “The spring-mass model for running and hopping,” Journal of Biomechanics, vol. 22, 1989, pp. 1217–1227.
[5] A. Seyfarth, M. G\ünther, and R. Blickhan, “Stable operation of an elastic three-segment leg,” Biological Cybernetics, vol. 84, 2001, pp. 365–382.
[6] M.G. Pandy, “Simple and complex models for studying muscle function in walking,” Philosophical Transactions B, vol. 358, 2003, p. 1501.
[7] A.V. Hill, “The heat of shortening and the dynamic constants of muscle,” Proceedings of the Royal Society of London. Series B, Biological Sciences, vol. 126, 1938, pp. 136–195.
[8] K. Matsuoka, “Sustained oscillations generated by mutually inhibiting neurons with adaptation,” Biological Cybernetics, vol. 52, 1985, pp. 367–376.
[9] G. Taga, Y. Yamaguchi, and H. Shimizu, “Self-organized control of bipedal locomotion by neural oscillators in unpredictable environment,” Biological Cybernetics, vol. 65, 1991, pp. 147–159.
[10] H. Geyer and H. Herr, “A Muscle-Reflex Model That Encodes Principles of Legged Mechanics Produces Human Walking Dynamics and Muscle Activities,” IEEE Transactions on Neural Systems and Rehabilitation Engineering, vol. 18, 2010, pp. 263-273.
[11] J.L. Smith and R.F. Zernicke, “Predictions for neural control based on limb dynamics,” Trends in Neurosciences, vol. 10, 1987, pp. 123–128.
[12] S.N. Whittlesey, R.E. van Emmerik, and J. Hamill, “The swing phase of human walking is not a passive movement,” MOTOR CONTROL-CHAMPAIGN-, vol. 4, 2000, pp. 273–292.
[13] D. Mena, J.M. Mansour, and S.R. Simon, “Analysis and synthesis of human swing leg motion during gait and its clinical applications,” Journal of Biomechanics, vol. 14, 1981, pp. 823–832. [14] J. Dean and A. Kuo, “Elastic coupling of limb joints enables faster bipedal walking,” Journal of The Royal Society Interface, vol. -1, 2009, pp. -1--1.