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This paper introduces a robust safety-filtering framework tailored for input-constrained underactuated linear systems facing unknown disturbances. By deriving a baseline H-$\infty$ input through a zero-sum differential game and employing a disturbance observer for error estimation, the authors establish high-order control barrier function constraints that ensure forward invariance. Simulations demonstrate the framework's effectiveness in balancing position and body-pitch constraints in a two-wheeled robot, revealing the interplay between control inputs and system safety.
A robust safety-filtering framework reveals how to maintain system stability in the presence of unknown disturbances while managing conflicting control constraints.
We present a robust safety-filtering framework for input-constrained underactuated linear systems subject to unknown disturbances. A baseline H-$\infty$ input is derived from a zero-sum differential game, while a disturbance observer supplies an estimate and a transient error bound. The baseline input is adjusted using the disturbance estimate, while the estimate and its error bound are used to define robust high-order control barrier function constraints; forward invariance holds as long as the admissible-input set remains nonempty. For scalar-input systems, pointwise feasibility is determined from an exact input interval, and the interval width defines the feasibility margin. A finite-horizon H-$\infty$ performance balance accounts for the accumulated deviation of the applied input from the baseline H-$\infty$ policy. Simulations on a linearized two-wheeled balancing robot show how position and body-pitch constraints compete for the same bounded wheel-torque input.
