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.

翻译：本文提出几何模型预测路径积分（GMPPI）方法，这是一种基于采样的控制器，能够在跟踪敏捷轨迹的同时规避障碍物。在每次迭代中，GMPPI生成大量候选展开轨迹，通过加权平均产生标称控制量以供受控无人机（UAV）执行。经典模型预测路径积分（MPPI）面临跟踪精度与避障性能的权衡：高噪声随机展开对轨迹跟踪效率低下，但却是碰撞规避的必要条件。为此，我们提出利用几何SE(3)控制生成部分GMPPI展开轨迹。为最大化其效益，我们设计了面向无人机的代价函数，以平衡轨迹跟踪与避障性能。所有生成的展开轨迹均投影至深度图像进行碰撞检测——据我们所知，这是首个在无人机MPPI控制回路中直接利用深度数据的方法。仿真结果表明，GMPPI在保持与无视障碍几何控制器相当跟踪误差的同时，其避障能力超越了当前最先进的规划器与基于学习的控制器。实物实验验证了该方法支持最高17米/秒的飞行速度，并在10米/秒速度下实现有效避障。