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

Authors: Andrea Tagliabue, Yi-Hsuan Hsiao, Urban Fasel, J. Nathan Kutz, Steven L. Brunton, YuFeng Chen, Jonathan P. How · ICRA 2023

Licences

Open Access
Paper: CC BY 4.0

Everything below draws on the full paper under its CC BY 4.0 licence; its figure is credited to the authors.

TL;DR

A two-layer neural network trained to imitate robust tube MPC, cascaded with an adaptive attitude controller, flies a 0.7 g soft-actuated MAV at 2 kHz with under 1.8 cm position RMSE.

Why it matters

It brings constraint- and uncertainty-aware, MPC-like trajectory tracking to an insect-scale robot at 2 kHz on a small offboard computer, which the authors see as a path toward onboard deployment. A new policy trains in about a minute, which speeds up tuning of the controller.

Problem

Sub-gram flapping-wing MAVs have large model uncertainty, very fast dynamics and little capacity for onboard computation, so they need robust, high-rate feedback that also respects actuator limits such as the dielectric breakdown voltage of soft actuators. MPC and robust tube MPC handle constraints and uncertainty but are too expensive to run at high rate on constrained platforms, and existing sub-gram controllers do not explicitly account for uncertainty or actuation constraints.

Proposed solution

A cascaded controller: the inner loop is a geometric attitude controller augmented with a steady-state Kalman-filter torque observer that estimates and cancels slowly varying torque disturbances. The outer loop is a fully connected network (2 hidden layers of 32 neurons) trained to imitate a trajectory-tracking robust tube MPC with a 1 s horizon (N = 50); training data comes from a high-fidelity simulator, augmented with 200 extra state–action pairs per timestep sampled inside the tube and labelled by the tube's ancillary controller.

Key insights

Sampling extra states inside the robust tube and labelling them with the ancillary controller lets a policy trained on disturbance-free simulation keep RTMPC's robustness.
Using roll and pitch rates as MPC inputs avoids discontinuous attitude commands and allows angular-velocity feed-forward to the attitude controller.
The torque observer picked up a position-dependent disturbance, possibly from the power cables or safety tether; on the circle it compensated torques of about 30% of the maximum torque authority around the body x-axis.
Thanks to its small inertia, the robot reduced its acceleration by 50% in under 200 ms after each impact.

Main results

Ramp along all three axes (Task 1, 3 runs): average position RMSE 0.6 / 0.8 / 0.1 cm on x / y / z, with maximum absolute error up to 1.6 cm on x–y and 0.2 cm on z.
This is a 60% reduction in maximum absolute error over the 4.0 cm on x–y (and 0.5 cm on z) reported in earlier SoftFly work for a hover task.
Ramp with stick pokes to the safety tether (Task 2, 1 run, accelerations above 0.25 g): RMSE 0.7 / 1.0 / 0.2 cm and maximum absolute error 2.5 / 2.1 / 0.3 cm on x / y / z.
Circle of 5.0 cm radius at 5.2 cm/s (Task 3, 3 runs): average RMSE 1.0 / 1.5 / 0.3 cm, worst-run RMSE 1.8 cm on y, maximum absolute error up to 3.1 cm.
The policy runs at 2 kHz on a Speedgoat Baseline Target Machine; training each policy takes about 1 minute (T = 350 steps) on an Intel i9-10920 with two RTX 3090 GPUs.

Limitations

The paper has no limitations section; it presents onboard deployment as a next step, as the controller ran on an offboard Speedgoat computer with Vicon motion capture providing position and attitude.
The actuator layout cannot produce torque about the body z-axis, so yaw is not actively controlled.
A separate policy was trained for each trajectory type (ramp, circle), and controller parameters were slightly tuned during the experiments.
The model assumes no wind, the robot flies on power tethers, and disturbance tests were limited to stick pokes on the safety tether in a single run.

Field impact

Finalist for the ICRA 2023 Outstanding Dynamics and Control Paper award, with 7 citations. The licensed copy does not link code, trained policies or data.

Abstract

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 [1], 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 [2], 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 (RMSEs) lower than 1.8 cm even in the more challenging maneuvers, obtaining a 60% reduction in maximum position error compared to [3], and demonstrating robustness to large external disturbances.

Open Source Robotics