Deformable object manipulation (DOM) with point clouds has great potential as non-rigid 3D shapes can be measured without detecting and tracking image features. However, robotic shape control of deformable objects with point clouds is challenging due to: the unknown point-wise correspondences and the noisy partial observability of raw point clouds; the modeling difficulties of the relationship between point clouds and robot motions. To tackle these challenges, this paper introduces a novel modal-graph framework for the model-free shape servoing of deformable objects with raw point clouds. Unlike the existing works studying the object's geometry structure, our method builds a low-frequency deformation structure for the DOM system, which is robust to the measurement irregularities. The built modal representation and graph structure enable us to directly extract low-dimensional deformation features from raw point clouds. Such extraction requires no extra point processing of registrations, refinements, and occlusion removal. Moreover, to shape the object using the extracted features, we design an adaptive robust controller which is proved to be input-to-state stable (ISS) without offline learning or identifying both the physical and geometric object models. Extensive simulations and experiments are conducted to validate the effectiveness of our method for linear, planar, tubular, and solid objects under different settings.

Shape control of deformable objects is a challenging and important robotic problem. This paper proposes a model-free controller using novel 3D global deformation features based on modal analysis. Unlike most existing controllers using geometric features, our controller employs a physically-based deformation feature by decoupling 3D global deformation into low-frequency mode shapes. Although modal analysis is widely adopted in computer vision and simulation, it has not been used in robotic deformation control. We develop a new model-free framework for modal-based deformation control under robot manipulation. Physical interpretation of mode shapes enables us to formulate an analytical deformation Jacobian matrix mapping the robot manipulation onto changes of the modal features. In the Jacobian matrix, unknown geometry and physical properties of the object are treated as low-dimensional modal parameters which can be used to linearly parameterize the closed-loop system. Thus, an adaptive controller with proven stability can be designed to deform the object while online estimating the modal parameters. Simulations and experiments are conducted using linear, planar, and solid objects under different settings. The results not only confirm the superior performance of our controller but also demonstrate its advantages over the baseline method.

The computation of anatomical information and laparoscope position is a fundamental block of robot-assisted surgical navigation in Minimally Invasive Surgery (MIS). Recovering a dense 3D structure of surgical scene using visual cues remains a challenge, and the online laparoscopic tracking mostly relies on external sensors, which increases system complexity. In this paper, we propose a learning-driven framework, in which an image-guided laparoscopic localization with 3D reconstructions of complex anatomical structures is hereby achieved. To reconstruct the 3D structure of the whole surgical environment, we first fine-tune a learning-based stereoscopic depth perception method, which is robust to the texture-less and variant soft tissues, for depth estimation. Then, we develop a dense visual reconstruction algorithm to represent the scene by surfels, estimate the laparoscope pose and fuse the depth data into a unified reference coordinate for tissue reconstruction. To estimate poses of new laparoscope views, we realize a coarse-to-fine localization method, which incorporates our reconstructed 3D model. We evaluate the reconstruction method and the localization module on three datasets, namely, the stereo correspondence and reconstruction of endoscopic data (SCARED), the ex-vivo phantom and tissue data collected with Universal Robot (UR) and Karl Storz Laparoscope, and the in-vivo DaVinci robotic surgery dataset. Extensive experiments have been conducted to prove the superior performance of our method in 3D anatomy reconstruction and laparoscopic localization, which demonstrates its potential implementation to surgical navigation system.