CSAIL Event Calendar: Previous Series
How to Define a Sensitivity of a Gait of a Walker to Roughness of Terrain
Speaker: Anton Shiriaev , Umea University, Sweden
Abstract: Gaits of walking machines are cycles of hybrid dynamical systems, solutions of which are defined by dynamics of (controlled) mechanical systems followed instantaneous updates due to impacts. It is common that the dynamics are nonlinear, and cannot be analyzed as it is, except the situations when trial-and-error numerical investigations are satisfactory. However, some of gaits' properties can be explored based on linearization of dynamics along the cycle. As a basic example, one can refer to the classical step of linearizing the first return Poincare mapping defined for a cycle: here stability or instability of the origin of the particular linear system is conclusive for exponential stability or instability of a cycle for the nonlinear one. Even gaits are stable; they might be highly sensitive to small variations to geometrical properties of terrain, on which the robot is walking. Searching for similar (linear) comparison systems for hybrid nonlinear dynamics that can be used for analysis of such sensitivity is topic of this lecture. We present a general form of such comparison system and argue how it can be of use for analysis of the gait for impulse, step-like, periodic or arbitrary variations of terrain.