Abstract by Isaac Becker
Robotic Stability through Sums of Squares Construction of Lyapunov Functions
The classical method for controlling robots is efficient and effective -the robot will do what you ask it to do regardless of the obstacles in its way. Unfortunately, this makes robots high-risk tools to use around humans. Recent control algorithms can be used to guide a robot to its destination in a smooth and safe fashion but proving these methods are stable, i.e. the robot will come to a complete stop, is difficult. Using sums of squares on the states (location) of the robot a Lyapunov function can be constructed which is sufficient to show that over time the robot's position will converge to the desired location. This approach is being applied to both hard (traditional) robots and newly developed soft robots.