Solving inverse kinematics by fully automated planar curves intersecting

This paper presents a new method for solving the Inverse Kinematics Problem of general 6-DOF serial manipulators. This problem has been a fundamental research area for the last 4 decades as it has numerous applications. Granted, many methods have been developed, but none of them is at the same time fast, accurate, numerically stable for an arbitrary end-effect or pose and capable of finding all solutions to the problem. The inverse kinematics problem can be reduced to finding intersections between planar curves, as it was shown by Jorge Angeles. Here we present a new way of transforming those curves into bivariate polynomials without the application of half-tan substitution and then of finding their intersections numerically using Bernstein elimination. It is achieved without any human interaction, so the method is fully automated, thus suitable for applications.