Additive manufacturing, also known as 3D printing, is an emerging technology. The existing additive manufacturing technologies deploy 3-axis printing mechanism where the material accumulation grows only in the z-direction. This results in limited printing freedom. Apart from this, support structures are needed to print overhang structures. Removal of these support mechanism ultimately reduces print quality. This paper proposes a novel robot assisted additive manufacturing along with a control system framework, which possesses multi-directional printing without support structures. Taking the advantage of its high stiffness and high payload-to-weight ratio, a 6-degree of freedom Stewart platform manipulator is designed to substitute the printer build plate. The kinematics and dynamics of the manipulator is formulated. Then, an extended proportion-derivation sliding mode controller is designed for trajectory tracking. The modified grey wolf optimization algorithm is applied to compute the optimal controller parameters. The integral absolute error (IAE) is used as a cost function and its global minimum value is reached in the iteration interval [75,100]. The analytical model simulation in MATLAB is run for 10 seconds, and the results show that the desired length trajectories of the six legs of the manipulator are achieved after 3.5 seconds. The performance of the analytical model is verified on the automated dynamic analysis of mechanical systems (ADAMS).