3D Collision-Free Trajectory Planning for Mobile Robot Based on Quadric Modeling
Kao‐Shing Hwang, Ming‐Dar Tsai, Ming-Yi Ju · 1998
Abstract A 3-D collision-free trajectory planning method for a mobile robot is proposed in the paper. The geometric shapes of the objects in the workspace are modeled as ellipsoids of 3-D quadric model for simple mathematical representation and easy geometric approximation. By a series of coordinate transformations between the mobile robot and obstacles, the collision detection problem in trajectory planning is reduced to test a point falling outside or inside the transformed ellipsoids, which models obstacles geometrically. Finally, the collision probability, which is defined by projecting the quadric ellipsoid onto a 3-D Gaussian distribution contour, plays a very significant role in search the optimal path through the defined objective function.