Virtual Constraint for a Quadrotor UAV Enforcing a Body-Axis Pointing Direction

We propose a geometric control framework on $SE(3)$ for quadrotors that enforces pointing-driven missions without completing a full attitude reference. The mission is encoded through virtual constraints defining a task manifold and an associated set of admissible velocities, and invariance is achieved by a feedback law obtained from a linear system in selected inputs. Under a transversality condition with the effective actuation distribution, the invariance-enforcing input is uniquely defined, yielding a constructive control law and, for relevant tasks, closed-form expressions. We further derive a local off-manifold stabilization extension. As a case study, we lock a body axis to a prescribed line-of-sight direction while maintaining fixed altitude.