# Search-based Motion Planning for Quadrotors using Linear Quadratic Minimum Time Control

arXiv: https://arxiv.org/abs/1709.05401 · HTML: https://mlsanity.com/paper/1709.05401/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Sep 2017.

## Built on by (most cited first, 11 of 11)

- [DPMPC-Planner: A real-time UAV trajectory planning framework for complex static environments with dynamic obstacles](https://mlsanity.com/paper/2109.07024/) (2021)
- [RAPID: Robust and Agile Planner Using Inverse Reinforcement Learning for Vision-Based Drone Navigation](https://mlsanity.com/paper/2502.02054/) (2025)
- [Reinforcement Learning for Agile Active Target Sensing with a UAV](https://mlsanity.com/paper/2212.08214/) (2022)
- [Time-optimal Flight in Cluttered Environments via Safe Reinforcement Learning](https://mlsanity.com/paper/2406.19646/) (2024)
- [From Distances to Trajectories: Real-Time Signed Distance Function Mapping and Distance-Accelerated Motion Planning for UAVs](https://mlsanity.com/paper/2607.19306/) (2026)
- [LEA*: An A* Variant Algorithm with Improved Edge Efficiency for Robot Motion Planning](https://mlsanity.com/paper/2309.10722/) (2023)
- [Language-guided Robust Navigation for Mobile Robots in Dynamically-changing Environments](https://mlsanity.com/paper/2409.19459/) (2024)
- [Real-Time Sampling-based Online Planning for Drone Interception](https://mlsanity.com/paper/2502.14231/) (2025)
- [Unified Linear Parametric Map Modeling and Perception-aware Trajectory Planning for Mobile Robotics](https://mlsanity.com/paper/2507.09340/) (2025)
- [Conflict-Based Lazy Search for Fast Multi-Manipulator Planning](https://mlsanity.com/paper/2607.04124/) (2026)
- [ClearNav: Perception-Aligned Quadrotor Flight Using Differential-Physics](https://mlsanity.com/paper/2610.17419/) (2026)

## Abstract (arXiv)

In this work, we propose a search-based planning method to compute dynamically feasible trajectories for a quadrotor flying in an obstacle-cluttered environment. Our approach searches for smooth, minimum-time trajectories by exploring the map using a set of short-duration motion primitives. The primitives are generated by solving an optimal control problem and induce a finite lattice discretization on the state space which can be explored using a graph-search algorithm. The proposed approach is able to generate resolution-complete (i.e., optimal in the discretized space), safe, dynamically feasibility trajectories efficiently by exploiting the explicit solution of a Linear Quadratic Minimum Time problem. It does not assume a hovering initial condition and, hence, is suitable for fast online re-planning while the robot is moving. Quadrotor navigation with online re-planning is demonstrated using the proposed approach in simulation and physical experiments and comparisons with trajectory generation based on state-of-art quadratic programming are presented.