In this paper, we investigate controlled movement of optically trapped nano-particles in an interference optical lattice. The suggested interferometric optical tweezers setup utilizes the superposition of three orthogonal Gaussian standing waves to create 3D optical lattices. Dynamic control over the constructed lattices can be achieved simply by changing the incident beam parameters using a polarizer or a phase shifter. The trapping properties of the generated optical lattices for a dielectric Rayleigh particle are numerically evaluated using a MATLAB program. The simulation results showed that the generated lattices can be translated by altering the relative phase between the interfering beams. More complex transformations and geometries can be achieved by changing other properties of the interfering beams such as polarization state. This simple setup enables to construct a rich variety of dynamic optical lattices and offers promising applications in colloidal and biological science such as control the diffusion of colloidal particles and stretching or compressing tethered polymeric molecules. This interferometric method can also be used in light-driven nanomotor with high controllability.