With their progressive deployment in increasingly complex environments, autonomous vehicles will more often interact with humans in shared spaces. However proactive planners, the most effective for human-aware navigation, are rarely applicable with real-world constraints because of their inherent complexity. Meanwhile classical approaches fail to navigate in cooperation with humans in complex or crowded scenarios. Therefore we propose to extend a global kinodynamic predictive collision avoidance approach with an interaction-aware behavioral prediction model for human-vehicle interactions. Thanks to a grid based Bayesian perception, our approach is versatile in modeling uncertainty and complex scenes. We deploy this solution on a robotic car and show that it can be used in real-world applications. With a qualitative and quantitative validation, we show that this interaction-aware collision avoidance solution is safe and performs well in crowded scenarios. Less computationally demanding and more versatile than proactive planners but still able to benefit from cooperation with humans, this interaction-aware approach offers a compromise between predictive and proactive planners.