Geometric Model Predictive Path Integral for Agile UAV Control with Online Collision Avoidance

In this letter, we introduce Geometric Model Predictive Path Integral (GMPPI), a sampling-based controller capable of tracking agile trajectories while avoiding obstacles. In each iteration, GMPPI generates a large number of candidate rollout trajectories and then averages them to create a nominal control to be followed by the controlled Unmanned Aerial Vehicle (UAV). Classical Model Predictive Path Integral (MPPI) faces a trade-off between tracking precision and obstacle avoidance; high-noise random rollouts are inefficient for tracking but necessary for collision avoidance. To this end, we propose leveraging geometric SE(3) control to generate a portion of GMPPI rollouts. To maximize their benefit, we introduce a UAV-tailored cost function balancing tracking performance with obstacle avoidance. All generated rollouts are projected onto depth images for collision avoidance, representing, to our knowledge, the first method utilizing depth data directly in a UAV MPPI loop. Simulations show GMPPI matches the tracking error of an obstacle-blind geometric controller while exceeding the avoidance capabilities of state-of-the-art planners and learning-based controllers. Real-world experiments demonstrate flight at speeds up to 17 m/s and obstacle avoidance up to 10 m/s.