Recent mathematical models of human posture have been explored to better understand the space of control parameters that result in stable upright balance. These models have demonstrated that there are two types of instabilities - a leaning instability and an instability leading to excessive oscillation. While these models provide insight into the stability of upright bipedal stance, they are not sufficient for individuals that require the aid of assistive technologies, such as a passive-cane or a walker. Without a valid model one is unable to understand the control parameters required for maintain upright posture or if similar instabilities even exist when assistive technologies are used. Therefore in this study, we developed a mathematical model of human posture while using a passive-cane to examine the nonlinear dynamics of stance. First, we developed a simple mathematical model of cane assisted human stance by adapting the inverted pendulum model of Chagdes et al., [1]. We modeled the human body, upper arm, forearm, cane, and ground as a two-degree-of-freedom, five-bar-linkage with pin joints representing the ankle, shoulder, elbow, and wrist joints. Second, we investigate upright stability in the parameter space of feedback gain and time-delay. We hypothesize that the analysis will show similar instabilities compared to that of a human standing without assistive technology. We also hypothesize that the space of control parameters which stabilize upright equilibrium posture will increase when a cane is incorporated. This study has two potential applications. First, the developed mathematical model could allow clinicians to better assess technology assisted balance and if needed help clinicians to customize a treatment plan for an individual that allows them to avoid unstable postural dynamics. Second, the mathematical model can be used to design customized assistive technology for people of difference physical properties and impairments.
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