This paper presents an H₂-norm optimal control scheme for the three main axes of an overhead travelling crane, which guarantees both tracking of desired trajectories for the crane load and an active damping of crane load oscillations. For the model-based feedback control design series expansions are utilised to obtain an approximate solution of the corresponding Hamilton-Jacobi-Bellmann-equation. The tracking capabilities concerning desired trajectories for the crane load can be significantly improved by introducing feedforward control based on an inverse system model. The position of the crane load is measured by a CMOS camera using the spatial filtering principle. Desired trajectories for the crane load position in the three-dimensional workspace can be tracked independently with high accuracy. Experimental results from an implementation on a test rig show a high control performance.