This paper investigates the safety-critical control problem for a class of mobile agents modeled as a cascade connection of an integrator and an uncertain actuation system. Previously developed quadratic programming (QP) algorithms for safety control are not applicable in the presence of dynamic uncertainty. To address this challenge, this paper proposes a refined feasible-set reshaping technique that enables a QP algorithm with the reshaped feasible set to ensure feasibility, robustness, and local Lipschitz continuity. In addition, upon transforming the closed-loop system into an interconnected system, nonlinear small-gain techniques are employed to yield safety-oriented results with respect to all position constraints. The effectiveness of the proposed method is verified by a numerical simulation based on an identified model of a quadrotor.