Learning the Inverse Kinematics of a 6-DOF Concentric Tube Robot through a Generative Adversarial Network

Concentric tube robots (CTR’s) are a highly complex robotic system due to a combination of both joint and transitional spaces as well as having high degrees of freedom. Due to their advantages in having a small form factor, ability to navigate in constrained spaces, there is a great need for a robust control system. Analytical inverse kinematics (IK) offer one such approach, but suffer from numerical problems and instabilities in its Jacobian. Furthermore, redundancy is not addressed in such solutions. Neural Networks offer an opportunity to approximate the inverse kinematics, as well as offer advantages that numerical solution cannot offer. In particular, we approach inverse kinematics through a simulation intensive method by bootstrapping the Jacobian to generate data to simulate both the Jacobian and the forward kinematics with a shallow feed-forward neural network. We then perform a standard optimisation of the positional error through feedback to solve for IK. Furthermore, to tackle the issue of redundancy and generate starting configurations, we explore utilising an ensemble Generative Adversarial Network to generate a variety of robot configurations such that the end-effector is close to the target point. By comparing with standard inverse kinematic approaches, from a pure function approximation from target end poses to robot configuration spaces, to a data-driven lookup process, we show that our mixture of Jacobian Learning + GAN offer relatively high accuracy (2.5% of total robot length) as well as low computational time (1 1.5 s/point), a significant improvement over literature values of 10% of total robot length for neural network based implementations.