GP-Based Motion Control Design for the Double-Integrator System Subject to Velocity Constraint

The motion control problem for the double-integrator system subject to velocity constraint is addressed. A novel methodology, which consists of a two-stage process and regards a trade-off between natural and learned behaviors to develop a family of analytic controllers, is proposed. To this end, firstly, a natural behavior is designed to achieve asymptotic tracking of a desired continuous trajectory by using a Control-Theory approach. Secondly, learned behaviors are discovered by using a Genetic Programming approach to synthesize an analytic controller to ensure a bounded velocity of the system. The integration of these approaches allows the system to exhibit a good tracking performance while keeping the velocity bounded to a desired value, freely set by the user. Simulation results are provided to illustrate the effectiveness of the proposal, and a comparison with a traditional Control-Theory-Based solution is also given and discussed.