Considerable research efforts have been devoted to the development of motion planning algorithms, which form a cornerstone of the autonomous driving system (ADS). However, obtaining an interactive and secure trajectory for the ADS remains a formidable task, especially in scenarios with significant interaction complexities. Many contemporary prediction-based planning methods frequently overlook interaction modeling, leading to less effective planning performance. This paper introduces a novel prediction-based interactive planning framework that explicitly and mathematically models interactions among traffic entities during the planning process. Our method incorporates interaction reasoning into spatio-temporal (s-t) planning by defining interaction conditions and constraints. Furthermore, it records and continually updates interaction relations for each planned state throughout the forward search. We assess the performance of our approach alongside state-of-the-art methods using a series of experiments conducted in both single and multi-modal scenarios. These experiments encompass variations in the accuracy of prediction outcomes and different degrees of planner aggressiveness. The experimental findings demonstrate the effectiveness and robustness of our method, yielding insights applicable to the wider field of autonomous driving. For the community's reference, our code is accessible at https://github.com/ChenYingbing/IR-STP-Planner.
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