Safety Embedded Control of Nonlinear Systems via Barrier States [article]

Hassan Almubarak, Nader Sadegh, Evangelos A. Theodorou
<span title="2021-03-08">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In many safety critical control systems, possibly opposing safety restrictions and control performance objectives may arise. To confront such a conflict, this paper proposes a methodology that embeds safety into stability of control systems. The development enforces safety by means of barrier functions used in optimization which are used to construct barrier states (BaS) that are embedded in the control system's model. As a result, as long as the equilibrium point of interest of the closed loop
more &raquo; ... 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 the simple pole placement method on a linear control system to generate a safely stabilizing controller. 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 barrier states. Following this further, we exploit optimal control on a 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 simple mobile robots that are sent to opposite targets with an obstacle on the way which may potentially result in a collision.
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="">arXiv:2102.10253v2</a> <a target="_blank" rel="external noopener" href="">fatcat:kaxom2npdrd3nate3awuaawhnu</a> </span>
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