Integrated Guidance and Control of Driftless Control-affine Systems with Control Constraints and State Exclusion Zones

This paper presents an integrated guidance and control scheme for autonomous control-affine systems with a convex and compact ellipsoidal set of admissible control inputs with the origin in its interior, and convex ellipsoidal exclusion zones to be avoided in the state space. In addition, the feedback system is designed to converge in a stable manner to a target set in the state space that has no intersection with the exclusion zones. The technical approach is based on the newly developed method of integral control barrier functions. A smooth barrier function is designed such that the target set of states is a zero sublevel set of this function. To avoid the given exclusion zones in the state space, barrier functions with compact support are constructed with these exclusion zones as their zero superlevel sets. Finally, an integral control law is designed using a control barrier function that has a convex and compact set of admissible controls as its zero sublevel set. These components are combined together to provide an integral control barrier function for the feedback system. The resulting integrated guidance and control scheme ensures stable convergence of states to the desired safe set in the state space, while avoiding the unsafe exclusion zones in the state space and maintaining control input constraints. The analytical development is followed by a set of numerical simulation results, which confirm the analytical findings.