Direct Lyapunov design - a synthesis procedure for motor schema using a second-order Lyapunov stability theorem

In this paper we propose a new procedure for construction of motor schema typically used in behaviour-based robotics. The procedure reverses the standard stability analysis approach by searching for a control function to fit a pre-defined Lyapunov function. In order to improve the applicability of this procedure, a new Second-Order extension to Lyapunov's Second Method is proposed, allowing a stable schema to be defined directly in terms of actuator force demands. We propose a synthesis procedure called Direct Lyapunov Design, which searches for motor schema maps whose set points satisfy the second-order theorem. The procedure has been applied to a simple Subsumption Architecture controller for an inverted pendulum simulation, yielding stable behaviour.