This paper presents a novel solution for UAV control in cooperative multi-robot systems, which can be used in various scenarios such as leader-following, landing on a moving base, or specific relative motion with a target. Unlike classical methods that tackle UAV control in the world frame, we directly control the UAV in the target coordinate frame, without making motion assumptions about the target. In detail, we formulate a non-linear model predictive controller of a UAV, referred to as the agent, within a non-inertial frame (i.e., the target frame). The system requires the relative states (pose and velocity), the angular velocity and the accelerations of the target, which can be obtained by relative localization methods and ubiquitous MEMS IMU sensors, respectively. This framework eliminates dependencies that are vital in classical solutions, such as accurate state estimation for both the agent and target, prior knowledge of the target motion model, and continuous trajectory re-planning for some complex tasks. We have performed extensive simulations to investigate the control performance with varying motion characteristics of the target. Furthermore, we conducted real robot experiments, employing either simulated relative pose estimation from motion capture systems indoors or directly from our previous relative pose estimation devices outdoors, to validate the applicability and feasibility of the proposed approach.