Collision computation of moving bodies
The collision problem is a topic which focuses the attention of all the scientists involved in robotics studies. Just because the past methods can find the collision between two moving objects but they have difficulties in extending their application to collision of several moving bodies, the authors developed an explicit mathematical representation of \(n\)-dimensional bodies moving in translation along general trajectories. The paper is organized as follows: Section 2 gives an explicit algebraic representation (which applies to objects moving along arbitrary trajectories) of a translating object on \(\mathbb{R}^n\). Several cases of linear and piecewise linear trajectories are also considered. The special case of translating polytopes is described in the next section. This is followed by algorithms for the collision problem of moving bodies and by an integer program for the case of several moving bodies. Finally, a simulation study to compare the proposed integer programming model and the current approach is presented.
scientific article; zbMATH DE number 1358219