This paper presents a unified control framework for Unmanned Aerial Manipulators (UAMs) that achieves robust Cartesian trajectory tracking within prescribed safety limits, achieves finite-time convergence, and actively regulates redundant self-motion. An application-focused study is presented showing that, for the safety-envelope task, the integration of a Barrier Lyapunov Function (BLF)-based Cartesian controller with a non-singular terminal sliding-mode function and a dynamic null-space regulator yields constraint satisfaction and self-motion suppression without altering the primary task. First, a BLF-based Cartesian controller is proposed, so it enforces the position and orientation bounds on the end-effector by embedding logarithmic functions into the control surface. Second, a non-singular terminal sliding-mode control, to ensure finite-time convergence, is designed. Last, a dynamic null-space regulator is incorporated, based on redundancy resolution theory, to regulate internal joint motions without affecting the primary task. The resulting closed-loop system admits a compact analytic form, constraint compliance, and self-motion regulation. A MATLAB simulation is presented: the end-effector converges in finite time within its safety envelope, and redundant joint motions are regulated; no safety-envelope violations were observed in the reported scenario. The feasibility of the proposed scheme is validated through rigorous numerical simulations and a computational timing analysis consistent with embedded system requirements.
