Considering manipulation tasks of redundant manipulators in complex environments, this article presents a general scheme that integrates model-based obstacle avoidance, Cartesian space trajectory tracking, and joint physical limit avoidance. Based on the minimum velocity norm scheme, the proposed scheme combines the escape velocity-based obstacle avoidance with Gilbert-Johnson-Keerthi (GJK) algorithm-based critical point detection, empowering the manipulator with model-based obstacle avoidance capabilities. Additionally, a multi-critical point restriction set is proposed, improving the success rate of obstacle avoidance in extreme situations. Moreover, the scheme introduces sampling time to joint physical constraints, ensuring that the physical limits of joints are not violated at the next sampling time. Finally, comparative experiments and simulations are conducted to verify the feasibility and the potential of practical application of the proposed scheme.