With quadrotors becoming immensely popular in applications such as relief operations, infrastructure maintenance etc., a key control design challenge arises when the quadrotor has to manoeuvre through constrained spaces during various operational scenarios: for example, inspecting a pipeline within predefined velocity and space, dropping relief material at a precise location under tight spaces etc., under the face of parametric uncertainties and external disturbances. To tackle such scenarios, a controller needs to ensure a predefined tracking accuracy so as not to violate the constraints while simultaneously tackling uncertainties and disturbances. However, state-of-the-art controllers dealing with constrained system motion are either not applicable for an underactuated system like quadrotor, or cannot tackle system uncertainties under full state constraints. This work attempts to fill such a gap in literature by designing Barrier Lyapunov Function (BLF) based robust controllers to satisfy multiple state-constraints while simultaneously negotiating parametric uncertainties and external disturbances. The superiority of the BLF control method over a typical unconstrained controller is demonstrated, followed by a robust control design to satisfy position and orientation constraints on quadrotor dynamics. Finally, full state-constraints on a quadrotor(i.e., constraints on the position, orientation, linear velocity and angular velocity) are satisfied with robust control. For each control design, the closed-loop system stability is studied analytically and the efficacy of the design is validated extensively either via realistic simulation scenarios or via experiments performed on a real quadrotor.