FPGA Implementation of the Interior-Point Algorithm with Applications to Collision Detection

The interior-point algorithm is a powerful method for solving a linear program (LP). A variety of optimization problems can be formulated as LPs. Often times the limiting factor of deploying an algorithm to solve LPs in a high performance system is the run-time efficiency. In this paper, we present the FPGA implementation of an affine interior-point algorithm that is designed to solve LPs. Specifically, we present the application of this algorithm to solving the LP for the real-time collision detection. The most important feature that distinguishes this particular algorithm from other collision detection methods is its superior ability to perform detection between pairs of objects undergoing fast rotational and translational motions.