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In this paper, we propose a unified whole-body control framework for velocity-controlled mobile collaborative robots which can distribute task motion into the arm and mobile base according to specific task requirements by adjusting weighting factors. Our framework focuses on addressing two challenging issues in whole-body coordination: 1) different dynamic characteristics of the mobile base and the arm; 2) avoidance of violating both safety and configuration constraints. In addition, our controller involves Coupling Dynamic Movement Primitives to enable the essential capabilities for collaboration and interaction applications, such as obstacle avoidance, human teaching, and compliance control. Based on these, we design an adaptive motion mode for intuitive physical human-robot interaction through adjusting the weighting factors. The proposed controller is in closed-form and thus quite computationally efficient. Several typical experiments carried out on a real mobile collaborative robot validate the effectiveness of the proposed controller.