Purpose Concentric tube robots are composed of multiple concentric, pre-curved, super-elastic, telescopic tubes that are compliant and have a small diameter suitable for interventions that must be minimally invasive like fetal surgery. Combinations of rotation and extension of the tubes can alter the robot's shape but the inverse kinematics are complex to model due to the challenge of incorporating friction and other tube interactions or manufacturing imperfections. We propose a model-free reinforcement learning approach to form the inverse kinematics solution and directly obtain a control policy. Method Three exploration strategies are shown for deep deterministic policy gradient with hindsight experience replay for concentric tube robots in simulation environments. The aim is to overcome the joint to Cartesian sampling bias and be scalable with the number of robotic tubes. To compare strategies, evaluation of the trained policy network to selected Cartesian goals and associated errors are analyzed. The learned control policy is demonstrated with trajectory following tasks. Results Separation of extension and rotation joints for Gaussian exploration is required to overcome Cartesian sampling bias. Parameter noise and Ornstein-Uhlenbeck were found to be optimal strategies with less than 1 mm error in all simulation environments. Various trajectories can be followed with the optimal exploration strategy learned policy at high joint extension values. Our inverse kinematics solver in evaluation has 0.44 mm extension and 0.3 • rotation error.
ConclusionWe demonstrate the feasibility of effective model-free control for concentric tube robots. Directly using the control policy, arbitrary trajectories can be followed and this is an important step towards overcoming the challenge of concentric tube robot control for clinical use in minimally invasive interventions.
Optical ultrasound, where ultrasound is both generated and received using light, can be integrated in very small diameter instruments making it ideally suited to minimally invasive interventions. One-dimensional information can be obtained using a single pair of optical fibres comprising of a source and detector but this can be difficult to interpret clinically. In this paper, we present a robotic-assisted scanning solution where a concentric tube robot manipulates an optical ultrasound probe along a consistent trajectory. A torque coil is utilised as a buffer between the curved nitinol tube and the probe to prevent torsion on the probe and maintain the axial orientation of the probe while the tube is rotating. The design and control of the scanning mechanism are presented along with the integration of the mechanism with a fibre-based imaging probe. Trajectory repeatability is assessed using electromagnetic tracking and a technique to calibrate the transformation between imaging and robot coordinates using a known model is presented. Finally, we show example images of 3D printed phantoms generated by collecting multiple OpUS A-scans within the same 3D scene to illustrate how robot-assisted scanning can expand the field of view.
Concentric Tube Robots (CTRs) are promising for minimally invasive interventions due to their miniature diameter, high dexterity, and compliance with soft tissue. CTRs comprise individual pre-curved tubes usually composed of NiTi and are arranged concentrically. As each tube is relatively rotated and translated, the backbone elongates, twists, and bends with a dexterity that is advantageous for confined spaces. Tube interactions, unmodelled phenomena, and inaccurate tube parameter estimation make physical modeling of CTRs challenging, complicating in turn kinematics and control. Deep reinforcement learning (RL) has been investigated as a solution. However, hardware validation has remained a challenge due to differences between the simulation and hardware domains. With simulation-only data, in this work, domain randomization is proposed as a strategy for translation to hardware of a simulation policy with no additionally acquired physical training data. The differences in simulation and hardware forward kinematics accuracy and precision are characterized by errors of 14.74±8.87 mm or 26.61±17.00 % robot length. We showcase that the proposed domain randomization approach reduces errors by 56 % in mean errors as compared to no domain randomization. Furthermore, we demonstrate path following capability in hardware with a line path with resulting errors of 4.37 ± 2.39 mm or 5.61 ± 3.11 % robot length.
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