A space robot working in a controlled-floating mode can be used for performing in-orbit telescope assembly through simultaneously controlling the motion of the spacecraft base and its robotic arm. Handling and assembling optical mirrors requires the space robot to achieve slow and precise manoeuvres regardless of the disturbances and errors in the trajectory. The robustness offered by the nonlinear H∞controller, in the presence of environmental disturbances and parametric uncertainties, makes it a viable solution. However, using fixed tuning parameters for this controller does not always result in the desired performance as the arm's trajectory is not known a priori for orbital assembly missions. In this paper, a complete study on the impact of the different tuning parameters is performed and a new adaptive H∞controller is developed based on bounded functions. The simulation results presented show that the proposed adaptive H∞controller guarantees robustness and precise tracking using a minimal amount of forces and torques for assembly operations using a small space robot.