# Robust, High-Rate Trajectory Tracking on Insect-Scale Soft-Actuated Aerial Robots with Deep-Learned Tube MPC

arXiv: https://arxiv.org/abs/2209.10007 · HTML: https://mlsanity.com/paper/2209.10007/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 37 references that are in the map.
- First posted on arXiv 20 Sep 2022.

## Builds on (most cited first, 7 of 7)

- [Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and control](https://mlsanity.com/paper/2111.10992/) (2021)
- [Whole-Body MPC for a Dynamically Stable Mobile Manipulator](https://mlsanity.com/paper/1902.10415/) (2019)
- [Demonstration-Efficient Guided Policy Search via Imitation of Robust Tube MPC](https://mlsanity.com/paper/2109.09910/) (2021)
- [Linear vs Nonlinear MPC for Trajectory Tracking Applied to Rotary Wing Micro Aerial Vehicles](https://mlsanity.com/paper/1611.09240/) (2016)
- [Dynamic Tube MPC for Nonlinear Systems](https://mlsanity.com/paper/1907.06553/) (2019)
- [RoboFly: An insect-sized robot with simplified fabrication that is capable of flight, ground, and water surface locomotion](https://mlsanity.com/paper/2001.02320/) (2020)
- [Bee^+: A 95-mg Four-Winged Insect-Scale Flying Robot Driven by Twinned Unimorph Actuators](https://mlsanity.com/paper/1905.02253/) (2019)

## Built on by (most cited first, 3 of 3)

- [Efficient Deep Learning of Robust, Adaptive Policies using Tube MPC-Guided Data Augmentation](https://mlsanity.com/paper/2303.15688/) (2023)
- [Hovering Flight of Soft-Actuated Insect-Scale Micro Aerial Vehicles using Deep Reinforcement Learning](https://mlsanity.com/paper/2502.12355/) (2025)
- [Aerobatic maneuvers in insect-scale flapping-wing aerial robots via deep-learned robust tube model predictive control](https://mlsanity.com/paper/2508.03043/) (2025)

## Abstract (arXiv)

Accurate and agile trajectory tracking in sub-gram Micro Aerial Vehicles (MAVs) is challenging, as the small scale of the robot induces large model uncertainties, demanding robust feedback controllers, while the fast dynamics and computational constraints prevent the deployment of computationally expensive strategies. In this work, we present an approach for agile and computationally efficient trajectory tracking on the MIT SoftFly, a sub-gram MAV (0.7 grams). Our strategy employs a cascaded control scheme, where an adaptive attitude controller is combined with a neural network policy trained to imitate a trajectory tracking robust tube model predictive controller (RTMPC). The neural network policy is obtained using our recent work, which enables the policy to preserve the robustness of RTMPC, but at a fraction of its computational cost. We experimentally evaluate our approach, achieving position Root Mean Square Errors lower than 1.8 cm even in the more challenging maneuvers, obtaining a 60% reduction in maximum position error compared to our previous work, and demonstrating robustness to large external disturbances