# Deep Learning for Optimization of Trajectories for Quadrotors

arXiv: https://arxiv.org/abs/2309.15191 · HTML: https://mlsanity.com/paper/2309.15191/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Sep 2023.

## Built on by (most cited first, 9 of 9)

- [FSNet: Feasibility-Seeking Neural Network for Constrained Optimization with Guarantees](https://mlsanity.com/paper/2506.00362/) (2025)
- [Dynamic Rank Adjustment in Diffusion Policies for Efficient and Flexible Training](https://mlsanity.com/paper/2502.03822/) (2025)
- [PRISM-DP: Spatial Pose-based Observations for Diffusion-Policies via Segmentation, Mesh Generation, and Pose Tracking](https://mlsanity.com/paper/2504.20359/) (2025)
- [Optimizing Active Perception for Learning Simultaneous Viewpoint Selection and Manipulation with Diffusion Policy](https://mlsanity.com/paper/2409.14615/) (2024)
- [Hybrid Diffusion Policies with Projective Geometric Algebra for Efficient Robot Manipulation Learning](https://mlsanity.com/paper/2507.05695/) (2025)
- [Fine-tuning of Large Language Models for Domain-Specific Cybersecurity Knowledge](https://mlsanity.com/paper/2509.25241/) (2025)
- [Mesh RAG: Retrieval Augmentation for Autoregressive Mesh Generation](https://mlsanity.com/paper/2511.16807/) (2025)
- [Neural-Primitive: An Efficient End-to-end Local Planner with Primitive-based Imitation Learning for Autonomous Flight](https://mlsanity.com/paper/2608.20948/) (2026)
- [ClearNav: Perception-Aligned Quadrotor Flight Using Differential-Physics](https://mlsanity.com/paper/2610.17419/) (2026)

## Abstract (arXiv)

This paper presents a novel learning-based trajectory planning framework for quadrotors that combines model-based optimization techniques with deep learning. Specifically, we formulate the trajectory optimization problem as a quadratic programming (QP) problem with dynamic and collision-free constraints using piecewise trajectory segments through safe flight corridors [1]. We train neural networks to directly learn the time allocation for each segment to generate optimal smooth and fast trajectories. Furthermore, the constrained optimization problem is applied as a separate implicit layer for backpropagation in the network, for which the differential loss function can be obtained. We introduce an additional penalty function to penalize time allocations which result in solutions that violate the constraints to accelerate the training process and increase the success rate of the original optimization problem. To this end, we enable a flexible number of sequences of piece-wise trajectories by adding an extra end-of-sentence token during training. We illustrate the performance of the proposed method via extensive simulation and experimentation and show that it works in real time in diverse, cluttered environments.