This researching work presents the design of an adaptive controller implementing the solution of the trajectory tracking for a robotic micromanipulator based on a three degrees of freedom arm that carries a piezoelectric- based gripper. The robotic arm is aimed to place the gripper at the correct position. From this spot, the gripper can handle objects of millimetric and micrometric scales. The proposed adaptive controller implements state dependent gains that drives all the articulations of the arm smoothly towards their corresponding references. The design of these gains is obtained using a class of control Lyapunov function. The type of the developed controller is also working to control the motion of the microgripper using the main mode of the piezoelectric actuators, represented by ordinary differential equations that takes into account the relation with the robotic arm. The proposed controller is tested over an actual robotic arm and evaluated considering the performance comparison with respect to a traditional state feedback control form. The experimental results confirm the effective tracking of the reference trajectories showing neither transient oscillations nor overshoots. These evaluations justify the application of the proposed method with the state dependent gains. The manipulation of millimetric objects is also used to evaluate the functionality of the developed robotic arm with its piezoelectric based gripper.