This paper develops a new function approximation technique (FAT)-based adaptive controller for the control of rigid robots called the adaptive passivity function approximation technique (APFAT) controller. This controller utilizes the passivity-based approach and simplifies the FAT controller design by eliminating the need for simultaneous estimation of the robot’s inertia matrix, Coriolis matrix, and gravity vector. The controller achieves its simplicity by treating the product of the regressor matrix and parameter vector as an unknown time-varying function to be approximated. The controller can be implemented in robots where the dynamic equations of motion are unknown. The stability of the controller is verified with Lyapunov functions by taking advantage of the passivity property of the robot dynamics. Simulation results on a three degree-of-freedom (DOF) PUMA500 robot demonstrate the ability to track reference trajectories using reasonable control signals when the inertia matrix, Coriolis matrix, and gravity vector are unavailable.