C-3TO: Continuous 3D Trajectory Optimization on Neural Euclidean Signed Distance Fields

Abstract-- 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. 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. The source code is open source and can be found at: https://anonymous.4open.science/r/icra2026_ I. Introduction Aerial robots have become increasingly popular for a wide range of real-world applications due to their ability to perform hazardous tasks more efficiently and, most importantly, more safely than humans [1][2]. Fast trajectory replanning remains a critical area of research, particularly in dynamic and unstructured environments. Equally important is maintaining a continuously updated representation of the drone's surroundings, which is essential for generating continuous, safe, and smooth 3D local trajectories in real time. This paper presents a framework for planning a continuous local trajectory on an online, neurally-generated, distance field.