Generalization for Deep Reinforcement Learning for Inverse Kinematics of Concentric Tube Robots

Abstract

Concentric tube robots (CTRs) are a class of continuum robot that depend on the interactions between neigh- bouring, concentrically aligned tubes to produce the curvilinear shapes of the robot backbone [1]. The main application of these unique robots is that of minimally invasive surgery (MIS), where most of the developments for CTRs have been focused. Due to the confined workspaces and resulting extended learning times for surgeons in MIS, dexterous, compliant continuum robots such as CTRs have been under development in prefer- ence to the mechanically rigid and limited degrees-of- freedom (DOF) robots used in interventional medicine today. The precurved tubes in CTRs, sometimes referred to as active cannulas or catheters, are manufactured from super-elastic materials like Nickel-Titanium alloys with each tube nested concentrically. From the base, the individual tubes can be actuated through extension and rotation, which results in the bending and twisting of the backbone as well as access to the surgical site through the channel and robot tip. Clinically, CTRs are motivated for use in brain, cardiac, gastric surgery as well other procedures [2]. Due to tube interactions, modelling and control is non- trivial. Position control for CTRs has relied on model development, and although a balance between compu- tation and accuracy has been reached in the literature [1], there remain issues such as performance in the presence of tube parameter discrepancies and the impact of unmodelled physical phenomena such as friction and permanent plastic deformation. This motivates the devel- opment of an end-to-end model-free control framework for CTRs. We extend our previous model-free deep reinforcement learning (deepRL) method [3] with an initial proof of concept for generalization. The task we give the agent then is to control the end-effector Cartesian robot tip position by means of actions that represent changes in joint values to reach a desired position in the robot workspace whilst considering a specific CTR system.