A Dataset and Benchmark for Learning the Kinematics of Concentric Tube Continuum Robots

Abstract

Concentric tube continuum robots utilize nested tubes, which are subject to a set of inequalities. Current approaches to account for inequalities rely on branching methods such as if-else statements. It can introduce discontinuities, may result in a complicated decision tree, has a high wall-clock time, and cannot be vectorized. This affects the behavior and result of downstream methods in control, learning, workspace estimation, and path planning, among others.In this paper, we investigate a mapping to mitigate branching methods. We derive a lower triangular transformation matrix to disentangle the inequalities and provide proof for the unique existence. It transforms the interdependent inequalities into independent box constraints. Further investigations are made for sampling, control, and workspace estimation. Approaches utilizing the proposed mapping are at least 14 times faster (up to 176 times faster), generate always valid joint configurations, are more interpretable, and are easier to extend.

Data augmentation for design of concentric tube continuum robots by generative adversarial networks

“…The problem of path planning or control is addressed by the inverse relation with similar methods [12,[14][15][16]. Such approaches rely on a densely sampled and valid data set of high measurement accuracy, which is time-consuming to establish [17]. For that reason, some authors stick with learning other physical models [14][15][16].…”

“…Kuntz et al are using a combination of measurements and simulation data [13]. Measurements are typically carried out by photogrammetry [3,7,9], electromagnetic tracking systems [11,17], or fiber optical systems [18], whereas only photogrammetry is able to measure the backbone instead of just the tip.…”

“…However, the number of measurement points along the fiber path is limited, which affects the spatial resolution of shape estimation. Similarly, electromagnetic tracking systems can be used to measure the tip's position only [2], [20], [21], [22], [23], while determination of the backbone's total shape is not possible with this approach.…”

Sim2Real Transfer of Reinforcement Learning for Concentric Tube Robots

“…can transform extensions to the interval [0, 1]. Extensions can be further transformed to the interval [−1, 1] with a system of linear equations [11]…”

“…Although CTRs have several advantages over traditional rigid robots for minimally invasive surgery (MIS) including increased flexibility and maneuverability, controlling these robotic systems is challenging. Learningbased approaches for kinematics, shape estimation, and dynamics have shown promise and deep learning-based forward kinematics and shape estimation for CTRs have been shown to be more accurate than traditional methods by training on a large data set of training data [9], [10], [11], [12], [13]. In terms of simulation data effectiveness, Sim2Real learning-based methods [14] can aid neural networks and reinforcement learning (RL) policies to adapton-the-fly to changing CTR hardware systems.…”