Safety Embedded Control of Nonlinear Systems via Barrier States

TL;DR

This paper introduces a novel safety control methodology for nonlinear systems by embedding barrier states into the control model, ensuring safety and stability simultaneously, demonstrated through linear and nonlinear control examples including robots and pendulums.

Contribution

The paper proposes a new approach that embeds barrier functions as states within control systems to guarantee safety without conflicting with control objectives.

Findings

Barrier states effectively enforce safety in control systems.

The method successfully integrates safety with stability in linear and nonlinear controls.

Applications include safe robot navigation and pendulum control.

Abstract

In many safety-critical control systems, possibly opposing safety restrictions and control performance objectives arise. To confront such a conflict, this letter proposes a novel methodology that embeds safety into stability of control systems. The development enforces safety by means of barrier functions used in optimization through the construction of barrier states (BaS) which are embedded in the control system's model. As a result, as long as the equilibrium point of interest of the closed loop system is asymptotically stable, the generated trajectories are guaranteed to be safe. Consequently, a conflict between control objectives and safety constraints is substantially avoided. To show the efficacy of the proposed technique, we employ barrier states with the simple pole placement method to design safe linear controls. Nonlinear optimal control is subsequently employed to fulfill safety, stability and performance objectives by solving the associated Hamilton-Jacobi-Bellman (HJB) which minimizes a cost functional that can involve the BaS. Following this further, we exploit optimal control with barrier states on an unstable, constrained second dimensional pendulum on a cart model that is desired to avoid low velocities regions where the system may exhibit some controllability loss and on two mobile robots to safely arrive to opposite targets with an obstacle on the way.