### Meeting Abstract

**S2-6** 10:30 - 11:00 **Gait stability of the spring-mass model of planar locomotion on inclines** *Foster, KL*; Selvitella, AM; Ball State University; Purdue University Fort Wayne* klfoster@bsu.edu http://www.comparativebiomechanics.com

The planar spring-mass model is a model of locomotion aimed at defining the essential mathematical laws of the trajectory of the center of mass in humans and other animals during compliant or bouncing gaits, such as hopping, running, trotting, and galloping. This reductionist mechanical system has been extensively studied in the context of locomotion over horizontal surfaces, but has been largely neglected on other ecologically relevant surfaces, like inclines. As a result, it is unclear how the degree of inclination impacts the dynamics of the center of mass. In this work, we derive a mathematical model which extends the spring-mass model to slightly inclined surfaces. Among our results, we derive an approximate solution of the system assuming a small angular sweep of the limb and a small spring compression of the leg during stance. Furthermore, we derive theoretical bounds on the difference between the Lagrangian and Lagrange equations of the true and approximate system, as well as the locomotor stability of the approximate solutions. We test our models through a sensitivity analysis using parameters relevant to the locomotion of bipedal animals (e.g. humans and ostriches) on different inclines, with different leg stiffness, and at different locomotor velocities. The simplicity of extreme reductionist models, like the spring-mass model, can be valuable tools that provide insight into the fundamental governing principles of locomotion. Expanding our understanding of the center of mass dynamics of legged locomotion beyond uniform, horizontal surfaces is important not only for clarifying the mechanisms underpinning locomotion in the heterogeneous conditions of the natural world, but for elucidating the important properties and control mechanisms for proper functioning of artificial devices like robots.