Neural Network as an Alternative to the Jacobian for Iterative Solution to Inverse Kinematics

The inverse kinematics problem is generally very complex and many traditional solutions are targeted only to robots of certain specific topologies. The iterative method based on the (pseudo) inverse of the Jacobian matrix is a well-known, proven and reliable general approach that can be applied to a wide variety of manipulators. However, it relies on linearizations that are only valid within a very tight neighborhood around the current pose of the manipulator. This requires the robot to move at very short steps, intensively recalculating its trajectory along the way, making this approach inefficient for certain applications. Neural networks, for their known capacity of modelling highly non-linear systems, appear as an interesting alternative. In this paper we demonstrate that neural networks can indeed be successfully trained to map task space displacements into joint angle increments, outperforming the method based on the inverse of the Jacobian when dealing with larger displacement increments. We validate our study showing comparative results for hypothetical 2-DOF and 3-DOF planar manipulators.