In this work, one improved symmetric time-variant logarithmic barrier, Lyapunov function (BLF), is developed for the first time to handle the state constraint problem of nonlinear systems. It is universal in the sense that the improved barrier function is a general one that can be used not only in systems with constrained requirements but also in systems without constrained requirements, without altering the designed controller. First of all, the n-link robotic system is transformed into a kind of multi-input and multi-output (MIMO) system. Then, a trajectory tracking control scheme is designed by combining the improved time-variant logarithmic BLF with the disturbance observer to solve the problems of model uncertainty and position constraint for the robotic system. We give that under the proposed controller, all the robotic system’s error vectors can trend to the equilibrium point asymptotically while the constraint conditions on the position are always met. Finally, the effectiveness of the presented scheme is indicated by completing two simulation experiment cases.