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Tendon-driven continuum robot kinematic models are frequently computationally expensive, inaccurate due to unmodeled effects, or both. In particular, unmodeled effects produce uncertainties that arise during the robot’s operation that lead to variability in the resulting geometry. We propose a novel solution to these issues through the development of a Gaussian mixture kinematic model. We train a mixture density network to output a Gaussian mixture model representation of the robot geometry given the current tendon displacements. This model computes a probability distribution that is more representative of the true distribution of geometries at a given configuration than a model that outputs a single geometry, while also reducing the computation time. We demonstrate uses of this model through both a trajectory optimization method that explicitly reasons about the workspace uncertainty to minimize the probability of collision and an inverse kinematics method that maximizes the likelihood of occupying a desired geometry. 

Tendon-driven continuum robots have been gaining popularity in medical applications due to their ability to curve around complex anatomical structures, potentially reducing the invasiveness of surgery. However, accurate modeling is required to plan and control the movements of these flexible robots. Physics-based models have limitations due to unmodeled effects, leading to mismatches between model prediction and actual robot shape. Recently proposed learning-based methods have been shown to overcome some of these limitations but do not account for hysteresis, a significant source of error for these robots. To overcome these challenges, we propose a novel deep decoder neural network that predicts the complete shape of tendon-driven robots using point clouds as the shape representation, conditioned on prior configurations to account for hysteresis. We evaluate our method on a physical tendon-driven robot and show that our network model accurately predicts the robot's shape, significantly outperforming a state-of-the-art physics-based model and a learning-based model that does not account for hysteresis. 

Robotic surgical subtask automation has the potential to reduce the per-patient workload of human surgeons. There are a variety of surgical subtasks that require geometric information of subsurface anatomy, such as the location of tumors, which necessitates accurate and efficient surgical sensing. In this work, we propose an automated sensing method that maps 3D subsurface anatomy to provide such geometric knowledge. We model the anatomy via a Bayesian Hilbert map-based probabilistic 3D occupancy map. Using the 3D occupancy map, we plan sensing paths on the surface of the anatomy via a graph search algorithm, A * search, with a cost function that enables the trajectories generated to balance between exploration of unsensed regions and refining the existing probabilistic understanding. We demonstrate the performance of our proposed method by comparing it against 3 different methods in several anatomical environments including a real-life CT scan dataset. The experimental results show that our method efficiently detects relevant subsurface anatomy with shorter trajectories than the comparison methods, and the resulting occupancy map achieves high accuracy. 

Tendon-driven continuum robot kinematic models are frequently computationally expensive, inaccurate due to unmodeled effects, or both. In particular, unmodeled effects produce uncertainties that arise during the robot’s operation that lead to variability in the resulting geometry. We propose a novel solution to these issues through the development of a Gaussian mixture kinematic model. We train a mixture density network to output a Gaussian mixture model representation of the robot geometry given the current tendon displacements. This model computes a probability distribution that is more representative of the true distribution of geometries at a given configuration than a model that outputs a single geometry, while also reducing the computation time. We demonstrate one use of this model through a trajectory optimization method that explicitly reasons about the