A team of researchers at IISc have studied the physical constraints involved in walking and identified the optimal walking positions with minimal energy consumption. This work can be utilized in designing and developing bipedal robots – robots with two legs like humans, and human exoskeletons (think Ironman!). Prof. Loganathan Umanand and his graduate student Lalit Patnaik from the Department of Electronic Systems Engineering at Indian Institute of Science, Bangalore, carried out this study.
Walking, a seemingly simple physical activity, is quite complex in reality. Numerous muscles and nerves work in tandem using energy to help us keep a foot forward. The act of walking is modeled as an “inverted pendulum” to understand the physics behind it. “The inverted pendulum model is the classical way of describing how humans walk. It is the natural way humans walk without an assisted walker”, explains Mr. Patnaik, one of the members of the team.
If you've tried balancing a stick on your hand, you know what an inverted pendulum is. In fact, we ourselves are inverted pendulums as we stand and walk. “Imagine a vertical stick resting on the ground with a heavy bob stuck at its top end. The stick represents the weight-bearing or 'stance' leg. The other leg that is not bearing the weight at that instant and is lifted off the ground is called the 'swing' leg. The ‘swing’ leg has minimal effect on the overall dynamics of walking and hence not considered a part of the model. The bob lumps together the entire mass of the body at its center of mass (CoM) near the person's hip” - Mr. Patnaik explains in simple terms.
The act of walking is studied based on this model – “If you give a very slight push to this stick and bob model, starting from the vertical position, it falls under the influence of gravity and the bob gains speed as it loses height. In technical terms, potential energy is converted to kinetic energy”, adds Lalit. If you wondered how you could walk several kilometers with just a meal, here is the answer in his words – “Walking is such an efficient mode of locomotion. With only a slight push at the start, we have achieved forward motion of the bob at a finite velocity. Walking makes use of the inherent dynamics of the system”.
But there is a problem. In this model, this single falling inverted pendulum means that we would fall on our face. How would that be prevented? “We arrest the fall by placing the next leg forward. What was the swing leg in the earlier instance now becomes the stance leg and this alternation of roles keeps happening. And thus walking becomes a sequence of controlled falls”, clarifies Lalit.
During the course of this research, the team identified five physical constraints which limit how one walks. These constraints hold good for any bipedal dynamic walker - biological or engineered. They also limit how fast one can walk and how large the steps can be. This also depends on the environment in which one is walking and on the pushing capacity of the muscles (or motors in the case of a robot!). Also, the analysis of the study can be used to determine the upper limits of speed and step lengths for a person with emaciated calf muscles or a robot with a low-torque motor.
Another aspect of the study included finding the best way to walk for a robotic walker with minimal mechanical energy consumption. Energy is a limited resource in most of the scenarios where robots are used. The study proposes a method to minimize energy consumption under a controlled setting. An appropriately chosen constant step length was found to minimize mechanical energy consumption over a broad range of speeds.
This study identifies the physical constraints for bipedal walking and optimizes the walking process to conserve energy. The team is looking beyond to further enhance this work. “In future, we aim to refine our models to more accurately capture the effects of the heel striking the ground, and the energy spent to lift and place legs of finite mass”, signs off Lalit.
Prof. Loganathan Umanand
Department of Electronics System Engineering
Indian Institute of Science, Bangalore
Phone: 23600810 Ext 233
Prof. L. Umanand is an Associate Professor at the Department of Electronics System Engineering, Indian Institute of Science, Bangalore and Lalit Patnaik is a graduate student in the same department. This study was published in the Journal of Bioinspiration and Biomimetics, Vol. 10, 2015 titled “Physical constraints, fundamental limits, and optimal locus of operating points for an inverted pendulum based actuated dynamic walker”.