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.
Harper, C., & Winfield, A. (2002). Direct Lyapunov design - A synthesis procedure for motor schema using a second-order Lyapunov stability theorem. In IEEE/RSJ International Conference on Intelligent Robots and Systems (2085-2090). https://doi.org/10.1109/IRDS.2002.1041573