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Data-Driven MPC for Quadrotors

This repo contains the code associated to our paper Data-Driven MPC for Quadrotors.

Data-Driven MPC for Quadrotors


If you use this code in an academic context, please cite the following publication:

Paper: Data-Driven MPC for Quadrotors

Video: YouTube

  title={Data-Driven MPC for Quadrotors},
  author={Torrente, Guillem and Kaufmann, Elia and Foehn, Philipp and Scaramuzza, Davide},
  journal={IEEE Robotics and Automation Letters},


Copyright (C) 2020-2021 Guillem Torrente, Elia Kaufmann, Philipp Foehn, Davide Scaramuzza, Robotics and Perception Group, University of Zurich

This is research code, expect that it changes often and any fitness for a particular purpose is disclaimed. For a commercial license, please contact Davide Scaramuzza.

This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.

This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
GNU General Public License for more details.

You should have received a copy of the GNU General Public License
along with this program.  If not, see <>.

This work depends on the ACADOS Toolkit, developed by the Optimization in Engineering Center (OPTEC) under supervision of Moritz Diehl. Licensing detail can be found on the ACADOS github. It is released under the BSD license.


Minimal Requirements

The code was tested with Ubuntu 18.04, Python 3.6 and ROS Melodic. We additionally provide python3.8 support tested with ROS Noetic in Ubuntu 20.04 in the branch python3.8_support. Different OS and ROS versions are possible but not supported.

Recommended: Create a Python virtual environment for this package:

sudo pip3 install virtualenv
virtualenv gp_mpc_venv --python=/usr/bin/python3.6
source gp_mpc_venv/bin/activate

Installation of acados and its Python interface :

Additional Requirements

The code that runs on the Gazebo Simulation environment builds on rpg_quadrotor_control. You may skip this step if intending to use only the Simplified Simulation.
Otherwise, create a catkin workspace following these installation instructions.
After these steps you should have all the ROS packages required to run the RPG Quadrotor simulation also in the Gazebo Simulation.

Initial setup

  1. Source Python virtual environment if created.

    source <path_to_gp_mpc_venv>/bin/activate
  2. Clone this repository into your catkin workspace.

    cd <CATKIN_WS_DIR>
    git clone
  3. Install the rest of required Python libraries:

    cd data_driven_mpc
    python install
  4. Build the catkin workspace:

    cd <CATKIN_WS_DIR>
    catkin build
    source devel/setup.bash

Running the package in Simulation

We provide instructions of how to use this package in two different simulators. In the paper we call them Simplified Simulation and Gazebo Simulation. While the Simplified Simulation is a lightweight Python simulator, the Gazebo Simulation builds on the well-known RotorS extension.

First make sure to add to your Python path the main directory of this package. Also activate the virtual environment if created.

export PYTHONPATH=$PYTHONPATH:<CATKIN_WS_DIR>/src/data_driven_mpc/ros_gp_mpc

First steps

To verify the correct installation of the package, execute first a test flight on the Simplified Simulation.

roscd ros_gp_mpc
python src/experiments/

After the simulation finishes, a correct installation should produce a result very similar to the following (Mean optinization time may vary).

:::::::::::::: SIMULATION SETUP ::::::::::::::

Simulation: Applied disturbances: 
{"noisy": true, "drag": true, "payload": false, "motor_noise": true}

Model: No regression model loaded

Reference: Executed trajectory `loop` with a peak axial velocity of 8 m/s, and a maximum speed of 8.273 m/s

::::::::::::: SIMULATION RESULTS :::::::::::::

Mean optimization time: 1.488 ms
Tracking RMSE: 0.2410 m

Further details

You may edit the configuration variables for the Simplified Simulator in the file config/ for better visualization. Within the class SimpleSimConfig:

# Set to True to show a real-time Matplotlib animation of the experiments for the Simplified Simulator. Execution 
# will be slower if the GUI is turned on. Note: setting to True may require some further library installation work.
custom_sim_gui = True

# Set to True to display a plot describing the trajectory tracking results after the execution.
result_plots = True

Also, note that in this configuration file the disturbance settings of the Simplified Simulation are defined. Setting all of them to False reproduces the Ideal (as we call in our paper) scenario where the MPC has perfect knowledge of the quadrotor dynamics, and therefore will yield a much lower tracking error:

# Choice of disturbances modeled in our Simplified Simulator. For more details about the parameters used refer to 
# the script: src/quad_mpc/
simulation_disturbances = {
    "noisy": True,                       # Thrust and torque gaussian noises
    "drag": True,                        # 2nd order polynomial aerodynamic drag effect
    "payload": False,                    # Payload force in the Z axis
    "motor_noise": True                  # Asymmetric voltage noise in the motors

You may also vary the peak velocity and acceleration of the reference trajectory, or use the lemniscate trajectory instead of the circle (loop) one. All of these options can be specified in the script arguments. Further information can be displayed by typing:

python src/experiments/ --help

Model Fitting Tutorial

Next, we collect a dataset for fitting GP and RDRv models in the Simplified Simulator. This procedure will be very similar for the Gazebo Simulator (explained later).

Data collection

First, run the following script to collect a few minutes of flight samples.

python src/experiments/ --recording --dataset_name simplified_sim_dataset --simulation_time 300

After the simulation ends, you can verify that the collected data now appears at the directory ros_gp_mpc/data/simplified_sim_dataset. We can use this data to fit our regression models.

Fitting a GP model

First, edit the following variables of configuration file in config/ (class ModelFitConfig) so that the training script is referenced to the desired dataset. For redundancy, in order to identify the correct data file, we require to specify both the name of the dataset as well as the parameters used while acquiring the data. In other words, you must input the simulator options used while running the previous python script. If you did not modify these variables earlier, you don't need to change anything this time as the default setting will work:

    # ## Dataset loading ## #
    ds_name = "simplified_sim_dataset"
    ds_metadata = {
        "noisy": True,
        "drag": True,
        "payload": False,
        "motor_noise": True

In our approach, we train 3 independent GP's for every velocity dimension v_x, v_y, v_z, so we run three times the GP training script. To indicate that the model must map v_x to acceleration correction a_x (and similarly with y and z), run the following commands. Indices 7,8,9 correspond to v_x, v_y, v_z respectively in our data structures. The arguments --x and --y are used to specify the X and Y variables of the regression problem. We assign a name to the model for future referencing, e.g.: simple_sim_gp:

python src/model_fitting/ --n_points 20 --model_name simple_sim_gp --x 7 --y 7
python src/model_fitting/ --n_points 20 --model_name simple_sim_gp --x 8 --y 8
python src/model_fitting/ --n_points 20 --model_name simple_sim_gp --x 9 --y 9

The models will be saved under the directory ros_gp_mpc/results/model_fitting/<git_hash>/.

You can visualize the performance of the combined three models using the visualization script. Make sure to input the correct model version (git hash) and model name.

python src/model_fitting/ --model_name simple_sim_gp --model_version <git_hash>

Fitting an RDRv model

Similarly, we train the RDRv model with the following one-line command. This script trains all three dimensions simultaneously and provides a plot of the fitting result. The model is similarly saved under the directory ros_gp_mpc/results/model_fitting/<git_hash>/ with the given name (e.g.: simple_sim_rdrv).

python src/model_fitting/ --model_name simple_sim_rdrv --x 7 8 9

Model comparison experiment

To compare the trained models, we provide an automatic script for the Simplified Simulation. Running the following command will compare the specified models with the "Ideal" and the "Nominal" scenarios by default, and produce several results plots in the directory: results/images/. Using the --fast argument will run the script faster with less velocity samples.

python src/experiments/ --model_version <git_hash_1 git_hash_2 ...> --model_name <name_1 name_2 ...> --model_type <type_1 type_2> --fast

For example:

python src/experiments/ --model_version 42b8650b 42b8650b --model_name simple_sim_gp simple_sim_rdrv --model_type gp rdrv --fast


Gazebo simulator

In this section, we demonstrate how to use our repository on the Gazebo Simulator.

Preparing the simulation environment

First, follow the installation guide for the rpg_quadrotor_package if you didn't do it previously.

Then, run an empty world simulation, and enable the command override function. Due to the increased computational demand of running the Gazebo simulator in parallel to the controller, the following launchfile runs the gazebo simulator at 50% speed:

roslaunch ros_gp_mpc quadrotor_empty_world.launch enable_command_feedthrough:=True

Finally, click Connect and Arm Bridge on the RPG Quadrotor GUI.

Dataset recording, model fitting & evaluation in Gazebo

Run the following script to execute several random trajectories on the Gazebo Simulator and compile a dataset of the measured errors.

roslaunch ros_gp_mpc gp_mpc_wrapper.launch recording:=True dataset_name:=gazebo_dataset environment:=gazebo flight_mode:=random n_seeds:=10

Leave the script running until it outputs the following message:

[INFO] [1612101145.957326, 230.510000]: No more references will be received

Update the ModelFitConfig class from config/ file to point the training scripts to the new dataset:

# ## Dataset loading ## #
ds_name = "gazebo_dataset"
ds_metadata = {
    "gazebo": "default",

Train a new GP (or RDRv) model as before:

python src/model_fitting/ --n_points 20 --model_name gazebo_sim_gp --x 7 --y 7
python src/model_fitting/ --n_points 20 --model_name gazebo_sim_gp --x 8 --y 8
python src/model_fitting/ --n_points 20 --model_name gazebo_sim_gp --x 9 --y 9

We don't provide an automatic script to compare models in the Gazebo environment. However, you can do it manually by following the next steps:

Run a Circle trajectory without correction:

Run the following launch file. Set plot:=True for displaying a plot of the trajectory that will be executed beforehand, and the tracking performance after finishing the run. Close the plot and the tracking will start automatically:

roslaunch ros_gp_mpc gp_mpc_wrapper.launch environment:=gazebo flight_mode:=loop plot:=True

Should result in an a verage tracking error of 0.2m when the maximum reference axial velocity is 10 m/s. Note that the drone does not reach this velocity because of the aerodynamic effects modeled in Gazebo:

[INFO] [1607523334.300131, 925.860000]: Tracking complete. Total RMSE: 0.20400 m. Max axial vel: 9.415. Mean optimization time: 7.938 ms

Run a Circle trajectory with correction

roslaunch ros_gp_mpc gp_mpc_wrapper.launch environment:=gazebo flight_mode:=loop plot:=True model_version:=<git_hash> model_name:=gazebo_sim_gp model_type:=gp

Will improve the tracking performance by around 50%, resulting in an average tracking error of 0.1m at the same speed:

[INFO] [1607523961.356929, 1239.280000]: Tracking complete. Total RMSE: 0.09487 m. Max axial vel: 9.714. Mean optimization time: 11.019 ms

Final notes

  • Trajectory types

    The user can also run a lemniscate trajectory by setting: flight_mode:=lemniscate. It is also possible to edit the reference trajectories of the circle and lemniscate by modifying the file: config/circle_and_lemniscate_options.yaml

  • Thrust level control

    Even though the MPC model operates at thrust level control, currently the ROS node sends total thrust + body rate commands. To switch to single thrust level control, edit the following line from the MPC ros interface file:

    From (body rate control):

    next_control.control_mode = 2

    Instead switch to (thrust level control):

    next_control.control_mode = 4