This paper investigates the effect of postural disturbances and sensorimotor deficits on the robustness of the upright posture (UP) for a human body model balancing on a balance board (BB). The robustness is investigated by computing the gradient field along the basin of attraction (BoA) of an asymptotically stable equilibrium point. The human model is modeled as a double-inverted pendulum (hip and ankle joints). The human-BB system is assumed actuated by torques at the hip, BB hinge, and ankle joints. Postural disturbances induce an initial joint angle velocity either at the ankle or at the hip joint. Moreover, either proprioceptive or visual and vestibular deficits are considered in the human-BB model. The nonlinear dynamic equation of motion of the human-BB system is numerically solved to obtain the BB, ankle, and hip joint angle position and velocity profiles. The BoA of the human-BB UP equilibrium is built as the set of initial conditions whose resulting time-series profiles converge to the equilibrium. It was shown that UP is more robust to disturbances that induce hip joint initial angle velocity. That is probably due to the fact that disturbances that induce ankle joint initial velocity affect the whole body, while disturbances that induce hip joint angle initial velocity only affect the trunk. Whenever visual and vestibular deficits are considered, the UP is more robust if proprioceptive gain and BB stiffness are small. Contrarily, whenever proprioceptive deficits are considered, the UP is more robust if visual and vestibular gain and BB stiffness are large. The method proposed here (the BoA and the gradients) can be used to systemically provide understanding about the robustness of the human-BB UP to external disturbances, which may help to identify people with a higher risk of fall.
- Basin of attraction
- Human upright posture robustness
- Nonlinear analysis
- Postural disturbances