# MADER: Trajectory Planner in Multi-Agent and Dynamic Environments

arXiv: https://arxiv.org/abs/2010.11061 · HTML: https://mlsanity.com/paper/2010.11061/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Oct 2020.

## Built on by (most cited first, 21 of 21)

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- [Advanced Algorithms of Collision Free Navigation and Flocking for Autonomous UAVs](https://mlsanity.com/paper/2111.00166/) (2021)
- [Learning to Initialize Trajectory Optimization for Vision-Based Autonomous Flight in Unknown Environments](https://mlsanity.com/paper/2309.10683/) (2023)
- [PRIMER: Perception-Aware Robust Learning-based Multiagent Trajectory Planner](https://mlsanity.com/paper/2406.10060/) (2024)
- [D4orm: Multi-Robot Trajectories with Dynamics-aware Diffusion Denoised Deformations](https://mlsanity.com/paper/2503.12204/) (2025)
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- [Communication-Free Collective Navigation for a Swarm of UAVs via LiDAR-Based Deep Reinforcement Learning](https://mlsanity.com/paper/2601.13657/) (2026)
- [VORL-EXPLORE: A Hybrid Learning Planning Approach to Multi-Robot Exploration in Dynamic Environments](https://mlsanity.com/paper/2603.07973/) (2026)
- [PILOT: Privileged Imitation Learning for End-to-End Motion Planning of Autonomous UAVs under Partial Observability](https://mlsanity.com/paper/2608.14082/) (2026)

## Abstract (arXiv)

This paper presents MADER, a 3D decentralized and asynchronous trajectory planner for UAVs that generates collision-free trajectories in environments with static obstacles, dynamic obstacles, and other planning agents. Real-time collision avoidance with other dynamic obstacles or agents is done by performing outer polyhedral representations of every interval of the trajectories and then including the plane that separates each pair of polyhedra as a decision variable in the optimization problem. MADER uses our recently developed MINVO basis to obtain outer polyhedral representations with volumes 2.36 and 254.9 times, respectively, smaller than the Bernstein or B-Spline bases used extensively in the planning literature. Our decentralized and asynchronous algorithm guarantees safety with respect to other agents by including their committed trajectories as constraints in the optimization and then executing a collision check-recheck scheme. Finally, extensive simulations in challenging cluttered environments show up to a 33.9% reduction in the flight time, and a 88.8% reduction in the number of stops compared to the Bernstein and B-Spline bases, shorter flight distances than centralized approaches, and shorter total times on average than synchronous decentralized approaches.