<p>Pose control under model uncertainties is essential for robotic manipulators in assembly tasks. Beyond the uncertainties inherent to the manipulator itself, few approaches have addressed the specific mismatch caused by the inevitable discrepancy between the actual and intended gripping poses when grasping modules. To overcome this challenge, we present an adaptive pose control scheme for the approach phase, during which the manipulator moves from a relatively distant location to the vicinity of the assembly pose. The proposed scheme operates directly on Lie groups, thereby allowing position and orientation control to be handled in a geometrically consistent, non-singular and unified framework. It is constructed by combining a modified zeroing neural network (ZNN) joint controller with a Lie group-based kinematic estimator to counteract the impacts due to the model uncertainty of concern. To achieve faster convergence, a smooth saturation function is introduced to the modified ZNN controller instead of the conventional linear activation function. Theoretical analysis is conducted to analytically reveal the stability and convergence of the proposed scheme. Finally, comparative simulations and physical experiments on the 7-degree-of-freedom (7-DoF) manipulator validate its superiority. The obtained results provide practical guidelines for reliable pose control and uncertainty compensation in robotic module assembly tasks.</p>