3D Collision-Free Motion Based on Collision Index

A collision-free motion planning method for mobile robots moving in three-dimensional workspace is proposed in this article. To simplify the mathematical representation and reduce the computation complexity for collision detection, objects in the workspace are modeled as ellipsoids. By means of applying a series of coordinate and scaling transformations between the robot and the obstacles in the workspace, intersection check is reduced to test whether the point representing the robot falls outside or inside the transformed ellipsoids representing the obstacles. Therefore, the requirement of the computation time for collision detection is reduced drastically in comparison with the computational geometry method, which computes a distance function of the robot segments and the obstacles. As a measurement of the possible occurrence of collision, the collision index, which is defined by projecting conceptually an ellipsoid onto a three-dimensional Gaussian distribution contour, plays a significant role in planning the collision-free path. The method based on reinforcement learning search using the defined collision index for collision-free motion is proposed. A simulation example is given in this article to demonstrate the efficiency of the proposed method. The result shows that the mobile robot can pass through the blocking obstacles and reach the desired final position successfully after several trials.