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

TL;DR

Geometric Model Predictive Path Integral (GMPPI) is a training-free, sampling-based controller for agile UAVs that enables online collision avoidance by integrating stereo depth perception with an SE(3) geometric controller inside MPPI. It employs dynamic rollout time steps, deterministic yaw control, and SE(3)-driven rollouts, running in parallel on a GPU to maximize throughput. The approach yields tracking accuracy close to a pure SE(3) controller while outperforming MPPI in cluttered environments, and achieves obstacle avoidance up to $10~\mathrm{m/s}$ in real-world flights and $13~\mathrm{m/s}$ in simulation, surpassing state-of-the-art obstacle-aware planners and several learning-based methods. The results demonstrate a practical, model-based navigation paradigm that reduces latency and broadens the speed-robustness trade-off for autonomous UAVs in cluttered environments.

Abstract

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 Unmanned Aerial Vehicle (UAV). We propose using geometric SE(3) control to generate part of the rollout trajectories, significantly increasing precision in agile flight. Furthermore, we introduce varying rollout simulation time step length and dynamic cost and noise parameters, vastly improving tracking performance of smooth and low-speed trajectories over an existing Model Predictive Path Integral (MPPI) implementation. Finally, we propose an integration of GMPPI with a stereo depth camera, enabling online obstacle avoidance at high speeds, a crucial step towards autonomous UAV flights in complex environments. The proposed controller can track simulated agile reference trajectories with position error similar to the geometric SE(3) controller. However, the same configuration of the proposed controller can avoid obstacles in a simulated forest environment at speeds of up to 13m/s, surpassing the performance of a state-of-the-art obstacle-aware planner. In real-world experiments, GMPPI retains the capability to track agile trajectories and avoids obstacles at speeds of up to 10m/s.

Figures (9)

• Figure 1: Visualisation of the real-world experiment verifying the obstacle avoidance capability of the proposed controller.
• Figure 2: Depth-camera image with the projection of the front four corners of the UAV collision box as defined in \ref{['eq:corners']} in each of the positions in the nominal trajectory $\boldsymbol{\mathbf{p}}^{\text{nom}}_j~\forall j \in (0, N+1)$, which is the result of applying the nominal control sequence $\boldsymbol{\mathbf{u}}^{\text{nom}}_j~\forall j \in (0, N)$ to the UAV in its current state.
• Figure 3: Illustration of the layout of the rollout states $\boldsymbol{\mathbf{x}}^k_j$ in time. Earlier steps are shorter to ensure precision, while later steps are longer and their length is dynamically adjusted to use the full range of the available depth sensor.
• Figure 4: Combination of geometric and random rollouts. A total of $K$ rollout sequences are simulated, of which $K - 32$ are random and $32$ use geometric control. All rollout commands are used to compute the next nominal command sequence $\boldsymbol{\mathbf{u}}^{\text{nom}}_j$ as well as the next set of rollout states $\boldsymbol{\mathbf{x}}^{k}_{j+1}$.
• Figure 5: GMPPI cost and noise parameters used in all experiments. A decrease in $c_j^p$, $c_j^q$ and $c_j^\omega$ promotes exploration. An increase in $c_j^v$ prevents unnecessary flight direction changes. Higher noise in the middle of rollouts promotes exploration.