A Deep Learning Approach to Navigating the Joint Solution Space of Redundant Inverse Kinematics and Its Applications to Numerical IK Computations

As an increasing number of robotic manipulators possess seven or more degrees-of-freedom (DoF), solving inverse kinematic (IK) for kinematically redundant manipulators is becoming critical. Numerical optimizations are commonly used to solve the problem due to their generality and accuracy. Unfortunately, they typically only generate one joint solution at a time, despite the multiple joint configurations that redundant manipulators can provide to move the end-effector to a target position. The long iterative optimization process is also a concern, particularly if extra constraints such as obstacle avoidance have to be evaluated. In this paper, we show that numerical methods may be complemented by deep learning to overcome these limitations. Through deep learning, the solution space of redundant IK may be learned with neural networks (NNs), which allows multiple distinct joint solutions corresponding to a given target position to be obtained by navigating the solution space. The main challenge is to overcome the one-to-one functional mapping of NNs. This paper solves this problem with a novel probabilistic encoding of manipulator poses and their corresponding infinite number of joint solutions. Two examples are presented to demonstrate the application of the proposed method to facilitate numerical IK computations: (1) finding a good initial joint solution to bootstrap the numerical IK calculation, and (2) evaluating extra constraints, such as obstacle avoidance, off the optimization iterations. Experiments show that the proposed method can accelerate the execution of different numerical IK modules in the popular IKpy package up to 50% for a 7-DoF manipulator, depending on the accuracy required.