Autonomous cooperative planning (ACP) is a promising technique to improve the efficiency and safety of multi-vehicle interactions for future intelligent transportation systems. However, realizing robust ACP is a challenge due to the aggregation of perception, motion, and communication uncertainties. This paper proposes a novel multi-uncertainty aware ACP (MUACP) framework that simultaneously accounts for multiple types of uncertainties via regularized cooperative model predictive control (RC-MPC). The regularizers and constraints for perception, motion, and communication are constructed according to the confidence levels, weather conditions, and outage probabilities, respectively. The effectiveness of the proposed method is evaluated in the Car Learning to Act (CARLA) simulation platform. Results demonstrate that the proposed MUACP efficiently performs cooperative formation in real time and outperforms other benchmark approaches in various scenarios under imperfect knowledge of the environment.