This paper describes continuous-space methodologies to estimate the collision
probability, Euclidean distance and gradient between an ellipsoidal robot model
and an environment surface modeled as a set of Gaussian distributions.
Continuous-space collision probability estimation is critical for
uncertainty-aware motion planning. Most collision detection and avoidance
approaches assume the robot is modeled as a sphere, but ellipsoidal
representations provide tighter approximations and enable navigation in
cluttered and narrow spaces. State-of-the-art methods derive the Euclidean
distance and gradient by processing raw point clouds, which is computationally
expensive for large workspaces. Recent advances in Gaussian surface modeling
(e.g. mixture models, splatting) enable compressed and high-fidelity surface
representations. Few methods exist to estimate continuous-space occupancy from
such models. They require Gaussians to model free space and are unable to
estimate the collision probability, Euclidean distance and gradient for an
ellipsoidal robot. The proposed methods bridge this gap by extending prior work
in ellipsoid-to-ellipsoid Euclidean distance and collision probability
estimation to Gaussian surface models. A geometric blending approach is also
proposed to improve collision probability estimation. The approaches are
evaluated with numerical 2D and 3D experiments using real-world point cloud
data.

该论文描述了使用连续空间方法估计椭球形机器人模型与将环境表面建模为一组高斯分布之间的碰撞概率、欧几里得距离和梯度。