In our previous work [1] we introduced the Anticipative Kinodynamic Planning (AKP): a robot navigation algorithm in dynamic urban environments that seeks to minimize its disruption to nearby pedestrians. In the present paper, we maintain all the advantages of the AKP, and we overcome the previous limitations by presenting novel contributions to our approach. Firstly, we present a multi-objective cost function to consider different and independent criteria and a well-posed procedure to build a joint cost function in order to select the best path. Then, we improve the construction of the planner tree by introducing a cost-to-go function that will be shown to outperform a classical Euclidean distance approach. In order to achieve real time calculations, we have used a steering heuristic that dramatically speeds up the process. Plenty of simulations and real experiments have been carried out to demonstrate the success of the AKP.