We study the dynamics of circular disk-shaped active particles on a two-dimensional periodic undulated surface. Each particle has an internal energy mechanism which is modeled by an active friction force and it is controlled by an activity parameter [Formula: see text]. It acts as negative friction if the speed of the particle is smaller than [Formula: see text] and normal friction otherwise. Surface undulation is modeled by the periodic undulation of fixed amplitude and wavelength. The dynamics of the particle is studied for different activities and surface undulations (SU). Three types of particle dynamic is observed on varying activity and SU: confined, early time subdiffusion to diffusion and super diffusion to late time diffusion. An effective equilibrium is established by showing the Green-Kubo relation between the effective diffusivity and the velocity auto-correlation function for all activities and small SU.