Golden Gait: An Optimization Theory Perspective on Human and Humanoid Walking

Abstract

Human walking is a complex task which includes hundreds of muscles, bones and joints working together to deliver harmonic movements with the need of finding equilibrium between moving forward and maintaining stability. Many different computational approaches have been used to explain human walking mechanisms, from pendular model to fractal approaches. A new perspective can be gained from using the principles developed in the field of Optimization theory and in particularly the branch of Game Theory. In particular we provide a new insight into human walking showing as the trade-off between advancement and equilibrium managed during walking has the same solution of the Ultimatum game, one of the most famous paradigms of game theory, and this solution is the golden ratio. The golden ratio is an irrational number that was found in many biological and natural systems self-organized in a harmonic, asymmetric, and fractal structure. Recently, the golden ratio has also been found as the equilibrium point between two players involved into the Ultimatum Game. It has been suggested that this result can be due to the fact that the golden ratio is perceived as the fairest asymmetric solution by the two players. The golden ratio is also the most common proportion between stance and swing phase of human walking. This approach may explain the importance of harmony in human walking, and provide new perspectives for developing quantitative assessment of human walking, efficient humanoid robotic walkers, and effective neurorobots for rehabilitation.

Artificial Neural Network Analyzing Wearable Device Gait Data for Identifying Patients With Stroke Unable to Return to Work

“…The gait phases, and in particular the ratio between stance and swing phases, have been highlighted as fundamental for a harmonic walking because they formed, together with the double support phases, a fractal autosimilar structure of walking ( 19 ). The autosimilarity of the ratios between consecutive gait phases is altered in pathological conditions ( 20 , 21 ), but in physiological conditions, walking allows for an optimization of energy expenditure ( 21 ) and an optimal equilibrium between balance and speed ( 22 ). In our study, the FSLR showed that a longer stance phase was associated to the identification of patients (OR = 1.547).…”

Measuring Spatiotemporal Parameters on Treadmill Walking Using Wearable Inertial System

“…In this case all the spatiotemporal parameters were described as a percentage of the gait cycle, modelled as an inverted pendulum [ 20 , 21 , 39 , 40 ]. This inverted pendulum model [ 20 , 21 , 39 , 40 ] can be written in the form of an equation which describes the swinging movement of the legs according to: where SL 1 is the step length (m), L is the length of the leg (m) expressed as “the summit between the iliac crest and the floor” [ 41 ] and h is the amplitude of the center of mass (COM) oscillation during a walking pattern [ 20 , 21 , 39 , 40 ].…”

Evaluation of Golden Gait Approximation Using Smart Clothing

“…They can also be used for analyzing what we call the golden gait approximation, relating the inverted pendulum model to a fractal approach of walking, where an approximation of 1.61 ratio is seen between spatio-temporal parameters such as stance and swing of gait cycle [7][8][9][10].…”

“…The golden ratio, "phi" indeed is present in nature, math, physics, and sometimes deliberately used in design [13][14][15][16]. Iosa et al [8][9][10] restated this as a well-known expression of consecutive Fibonacci terms:…”

“…And using the previous relation (2) Iosa et al [8] defined additional relations describing the slow, fast and comfortable walking.…”