This paper introduces a novel framework for continuous 3D trajectory optimization in cluttered environments, leveraging online neural Euclidean Signed Distance Fields (ESDFs). Unlike prior approaches that rely on discretized ESDF grids with interpolation, our method directly optimizes smooth trajectories represented by fifth-order polynomials over a continuous neural ESDF, ensuring precise gradient information throughout the entire trajectory. The framework integrates a two-stage nonlinear optimization pipeline that balances efficiency, safety and smoothness. Experimental results demonstrate that C-3TO produces collision-aware and dynamically feasible trajectories. Moreover, its flexibility in defining local window sizes and optimization parameters enables straightforward adaptation to diverse user's needs without compromising performance. By combining continuous trajectory parameterization with a continuously updated neural ESDF, C-3TO establishes a robust and generalizable foundation for safe and efficient local replanning in aerial robotics.

翻译：本文提出了一种新型框架，用于在杂乱环境中实现连续三维轨迹优化，该框架利用在线神经欧几里得有符号距离场（ESDF）。与先前依赖离散化ESDF网格加插值的方法不同，本方法直接在连续神经ESDF上对由五阶多项式表示的光滑轨迹进行优化，确保整条轨迹的精确梯度信息。该框架集成了一个两阶段非线性优化管线，在效率、安全性和平滑性之间取得平衡。实验结果表明，C-3TO能够生成碰撞感知且动力学可行的轨迹。此外，其在定义局部窗口大小和优化参数方面的灵活性，使得无需牺牲性能即可轻松适应不同用户需求。通过将连续轨迹参数化与持续更新的神经ESDF相结合，C-3TO为空中机器人的安全高效局部重规划建立了鲁棒且可泛化的基础。