# Safe and Efficient Lane-Changing for Autonomous Vehicles: An Improved Double Quintic Polynomial Approach with Time-to-Collision Evaluation

## TL;DR

This paper introduces an improved double quintic polynomial method for autonomous vehicle lane-changing that incorporates real-time time-to-collision evaluation, enhancing safety and efficiency in mixed traffic environments.

## Contribution

It is the first to embed an analytic TTC penalty directly into the double-quintic polynomial trajectory solver for real-time safety-aware planning.

## Key findings

- Ensures collision avoidance in diverse traffic scenarios.
- Provides smooth and adaptive lane-changing trajectories.
- Outperforms conventional methods in safety and comfort.

## Abstract

Autonomous driving technology has made significant advancements in recent years, yet challenges remain in ensuring safe and comfortable interactions with human-driven vehicles (HDVs), particularly during lane-changing maneuvers. This paper proposes an improved double quintic polynomial approach for safe and efficient lane-changing in mixed traffic environments. The proposed method integrates a time-to-collision (TTC) based evaluation mechanism directly into the trajectory optimization process, ensuring that the ego vehicle proactively maintains a safe gap from surrounding HDVs throughout the maneuver. The framework comprises state estimation for both the autonomous vehicle (AV) and HDVs, trajectory generation using double quintic polynomials, real-time TTC computation, and adaptive trajectory evaluation. To the best of our knowledge, this is the first work to embed an analytic TTC penalty directly into the closed-form double-quintic polynomial solver, enabling real-time safety-aware trajectory generation without post-hoc validation. Extensive simulations conducted under diverse traffic scenarios demonstrate the safety, efficiency, and comfort of the proposed approach compared to conventional methods such as quintic polynomials, Bezier curves, and B-splines. The results highlight that the improved method not only avoids collisions but also ensures smooth transitions and adaptive decision-making in dynamic environments. This work bridges the gap between model-based and adaptive trajectory planning approaches, offering a stable solution for real-world autonomous driving applications.

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Source: https://tomesphere.com/paper/2509.00582