arXiv:2611.14414v1 Announce Type: new Abstract: Despite the widespread adoption of autonomous vehicle technologies, reliable navigation within cluttered environments remains arduous due to the necessity of interaction-aware strategies; example scenarios include: narrow passages with multiple agents, lane changing in dense traffic, and crossing unsignalized intersections. These scenarios often require highly proactive strategies, simultaneously demanding interpretability and quick adaptability, which challenge end-to-end and data-driven methods. An effective strategy requires: scalability to multiple agents, adaptability to changes in other agents' behavior, and harmony with surrounding traffic without freezing or becoming overly conservative. To meet these requirements, we present SIGMO, a sigmoid-gated interaction-aware motion planner, with two main contributions. First, we formulate polynomial sigmoid functions that analytically estimate yield scores of surrounding agents using physics-grounded interaction features that capture driving intuitions. Second, we integrate the polynomial sigmoid functions into a receding-horizon planner, which facilitates interaction-aware planning with arbitrary trajectory predictions. We validate SIGMO in interaction-intensive simulations and hardware experiments. The results show that SIGMO balances proactive and defensive behavior while remaining computationally lightweight, serving as a strong baseline in a mobility stack. The simulation and hardware experiment videos are available here: https://sites.google.com/view/sigmoid-polygate.