Human Foot Force Informs Balance Control Strategies when Standing on a Narrow Beam

Despite the abundance of studies on the control of standing balance, insights about the roles of biomechanics and neural control have been limited. Previous work introduced an analysis combining the direction and orientation of ground reaction forces. The “intersection point” of the lines of actions of these forces exhibited a consistent pattern across healthy, young subjects when computed for different frequency components of the center of pressure signal. To investigate the control strategy of quiet stance, we applied this intersection point analysis to experimental data of 15 healthy, young subjects balancing in tandem stance on a narrow beam and on the ground. Data from the sagittal and frontal planes were analyzed separately. The task was modeled as a double-inverted pendulum controlled by an optimal controller with torque-actuated ankle and hip joints and additive white noise. To test our prediction that the controller that minimized overall joint effort would yield the best fit across the tested conditions and planes of analyses, experimental results were compared to simulation outcomes. The controller that minimized overall effort produced the best fit in both balance conditions and planes of analyses. For some conditions, the relative penalty on the hip and ankle joints varied in a way relevant to the balance condition or to the plane of analysis. These results suggest that unimpaired quiet balance in a challenging environment can be best described by a controller that maintains minimal effort through the adjustment of relative ankle and hip joint torques. NEW & NOTEWORTHY This study explored balance control in humans during a challenging task using the novel intersection point analysis, based on ground reaction force direction and point of application. Experimental data of subjects standing on a narrow beam in tandem stance were compared with modeling results of a double-inverted pendulum. The analysis showed that individuals minimized effort by adjusting ankle and hip torques, shedding light on the interplay of biomechanics and neural control in maintaining balance. ### Competing Interest Statement The authors have declared no competing interest. * z IP : Intersection point height x CoP : Center of pressure position CoM : Center of mass F : Ground reaction force vector F x : Horizontal component of the ground reaction force vector F z : Vertical component of the ground reaction force vector θ F : Ground reaction force vector direction τ : Joint torque control input σ r : Parameter that determines the ratio between noise on the ankle and hip joints; when it is set to be large, there is more noise in the ankle LQR : Linear quadratic regulator R : Design matrix that determines the cost of control effort α : Parameter that determines the relative cost of control effort with respect to the cost on state deviation; when it is set to be large, minimal control is achieved β : Parameter that determines the relative cost of control effort in the ankle compared to the hip joint; when it is set to be large, the ankle is penalized more than the hip RMSE : Root-mean-squared error