Custom Non-Linear Model Predictive Control for Obstacle Avoidance in Indoor and Outdoor Environments

TL;DR

A Non-linear Model Predictive Control (NMPC) framework for the DJI Matrice 100 is introduced, addressing challenges by using a dynamic model and B-spline interpolation for smooth reference trajectories, ensuring minimal deviation while respecting safety constraints.

Abstract

Navigating complex environments requires Unmanned Aerial Vehicles (UAVs) and autonomous systems to perform trajectory tracking and obstacle avoidance in real-time. While many control strategies have effectively utilized linear approximations, addressing the non-linear dynamics of UAV, especially in obstacle-dense environments, remains a key challenge that requires further research. This paper introduces a Non-linear Model Predictive Control (NMPC) framework for the DJI Matrice 100, addressing these challenges by using a dynamic model and B-spline interpolation for smooth reference trajectories, ensuring minimal deviation while respecting safety constraints. The framework supports various trajectory types and employs a penalty-based cost function for control accuracy in tight maneuvers. The framework utilizes CasADi for efficient real-time optimization, enabling the UAV to maintain robust operation even under tight computational constraints. Simulation and real-world indoor and outdoor experiments demonstrated the NMPC ability to adapt to disturbances, resulting in smooth, collision-free navigation.

Figures (8)

• Figure 1: Experimental flight of DJI Matrice 100 demonstrating non-linear model predictive control for obstacle avoidance at Gränsö 2024.
• Figure 2: Control System Architecture: On the left, a Vicon motion capture system with 16 cameras captures 6-DOF data, which is processed by a computer station running NMPC to generate control commands for the UAV. On the right, the outdoor system uses GPS tracking at Gränsö, with NMPC calculating control inputs based on GPS data. The figure illustrates the body-fixed frame $(x, y, z)$ and the rotational directions of the four propellers $(w_1, w_2, w_3, w_4)$, along with the axes of rotation $(\xi, \eta, \zeta)$.
• Figure 3: Desired and Actual Path Following in 3D with NMPC in the Hexagonal and Multiple Obstacle Scenario Simulations: The left image depicts a hexagonal path formed using a B-spline, the right image the multiple obstacle path, where the blue line represents the actual flight path, the yellow dashed line indicates the desired trajectory, and the red spheres depict the obstacles, surrounded by a yellow safety distance.
• Figure 4: Comparative Analysis of UAV Path Following with NMPC in the Hexagonal Path Scenario: In the upper left corner the yellow square outlines the Vicon system's operational limits, indicating the area prepared for indoor experiments, the green line is the desired trajectory, the blue line is the actual path taken by the UAV, the red line shows the prediction horizon, and the yellow line indicates the path being sent to the controller at the current time step. The control inputs for thrust, roll, pitch, and yaw rate are shown in the lower sections, alongside control error plots for the X, Y, and Z axes (This applies to Figs. \ref{['fig:combined_figure_multi_obstacle_4_simulator_results']}, \ref{['fig:nmpc_path_tracking_obstacle']}, and \ref{['fig:combined_figure_multi_obstacle_3']} as well).
• Figure 5: Comparative Analysis of UAV Path Following with NMPC in the Multiple Obstacle Scenario. The top-left image depicts in 3D, the desired path (blue dashed line) and the actual path (orange line), with the multiple obstacles illustrated by the green spheres (This applies to Figs. \ref{['fig:nmpc_path_tracking_obstacle']} and \ref{['fig:combined_multi_obstacle']}).