hmpc

Submission

A reference implementation of the embedded MPC framework used in our submission Embedded Hierarchical MPC for Autonomous Navigation.
Paper: https://arxiv.org/pdf/2406.11506.
Video: https://youtu.be/0RnrKk6830I.

@article{benders2024embedded,
    title   = {Embedded Hierarchical MPC for Autonomous Navigation},
    author  = {Benders, Dennis and K{\"o}hler, Johannes and Niesten, Thijs and Babu{\v{s}}ka, Robert and Alonso-Mora, Javier and Ferranti, Laura},
    journal = {arXiv preprint arXiv:2406.11506},
    year    = {2024}
}

Summary

In this work, we propose a hierarchical MPC (HMPC) framework including the co-design of a planning MPC (PMPC) and tracking MPC (TMPC). The system diagram is given below:

In the offline phase, the terminal ingredients of the TMPC are computed. These ingredients implicitly encode the TMPC capabilities and include the terminal cost matrix $P$, terminal control matrix $K$, and positive constants $c_j^\mathrm{s}, j \in \mathbb{N}_{[1,n^\mathrm{s}]}$ and $c^\mathrm{o}$ to tighten the system and obstacle avoidance constraints, respectively. Based on a user-chosen minimum distance between trajectory and obstacles, the terminal set scaling $\alpha$ can be computed.

During online operation, the PMPC plans a dynamically feasible trajectory based on goal position $\boldsymbol{p}^\mathrm{g}$ and grid map $\mathcal{M}$. To construct this plan such that the TMPC is guaranteed to track it and take the TMPC capabilities into account, the system constraints are tightened by $c_j^\mathrm{s} \alpha, j \in \mathbb{N}_{[1,n^\mathrm{s}]}$ and the obstacle avoidance constraints are tightened by $c^\mathrm{o} \alpha$. The planned trajectory is tracked by the TMPC using state state feedback $\boldsymbol{x}$. The PMPC and TMPC use the same nonlinear model but operate at different frequencies, thus enabling the real-time implementation of the scheme using off-the-shelf nonlinear solvers on an onboard computer with limited computational resources.

🚀 HMPC has several advantages over a comparable single-layer MPC (SMPC) formulation that performs both planning and tracking in a single layer:

• HMPC allows to increase the prediction horizon by a minimum factor of 5, resulting in improved planning performance. In the case of our work, this results in a smoother trajectory and faster convergence to the goal position.
• HMPC allows to decouple the planning and tracking tasks, resulting in less sensitivity to model mismatch and better ability to maintain altitude.
• In contrast to SMPC, HMPC allows to prove obstacle avoidance and recursive feasibility of the complete framework. These are important properties to consider for safety-critical robotic applications.

✨ To avoid the obstacles, the PMPC and SMPC schemes leverage a novel and efficient obstacle avoidance constraint design method called I-DecompUtil. I-DecompUtil applies the DecompUtil convex decomposition algorithm applied per straight line segment between optimal PMPC states to construct convex obstacle-free regions per stage in the horizon.

The animation below shows the HMPC framework operating in the lab:

The quadrotor platform used for the lab experiments is based on the NXP HoverGames development kit:

How to get started?

Interested in reproducing our results and extending them for your own work? No problem!

This repository contains the code and documentation to reproduce the simple simulation, Gazebo simulation, and lab experiment results presented in our paper. This includes the modular MPC code framework used to implement all MPC schemes (PMPC, TMPC, and SMPC) and the I-DecompUtil obstacle avoidance constraints design method.

To get started, clone this repository by running:

git clone --recurse-submodules [email protected]:dbenders1/hmpc.git

and follow the instructions in the src README.

Contact information

Do you want to collaborate or do you have any questions? Feel free to reach out via https://github.com/dbenders1!