Real-time, safe, and stable motion planning in co-robot systems involving dynamic human robot interaction (HRI) remains challenging due to the time varying nature of the problem. One of the biggest challenges is to guarantee closed-loop stability of the planning algorithm in dynamic environments. Typically, this can be addressed if there exists a perfect predictor that precisely predicts the future motions of the obstacles. Unfortunately, a perfect predictor is not possible to achieve. In HRI environments in this paper, human workers and other robots are the obstacles to the ego robot. We discuss necessary conditions for the closed-loop stability of a planning problem using the framework of model predictive control (MPC). It is concluded that the predictor needs to be able to detect the obstacles’ movement mode change within a time delay allowance and the MPC needs to have a sufficient prediction horizon and a proper cost function. These allow MPC to have an uncertainty tolerance for closed-loop stability, and still avoid collision when the obstacles’ movement is not within the tolerance. Also, the closed-loop performance is investigated using a notion of M-convergence, which guarantees finite local convergence (at least M steps ahead) of the open-loop trajectories toward the closed-loop trajectory. With this notion, we verify the performance of the proposed MPC with stability enhanced prediction through simulations and experiments. With the proposed method, the robot can better deal with dynamic environments and the closed-loop cost is reduced.