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Estimating precise metric depth and scene reconstruction from monocular endoscopy is a fundamental task for surgical navigation in robotic surgery. However, traditional stereo matching adopts binocular images to perceive the depth information, which is difficult to transfer to the soft robotics-based surgical systems due to the use of monocular endoscopy. In this paper, we present a novel framework that combines robot kinematics and monocular endoscope images with deep unsupervised learning into a single network for metric depth estimation and then achieve 3D reconstruction of complex anatomy. Specifically, we first obtain the relative depth maps of surgical scenes by leveraging a brightness-aware monocular depth estimation method. Then, the corresponding endoscope poses are computed based on non-linear optimization of geometric and photometric reprojection residuals. Afterwards, we develop a Depth-driven Sliding Optimization (DDSO) algorithm to extract the scaling coefficient from kinematics and calculated poses offline. By coupling the metric scale and relative depth data, we form a robust ensemble that represents the metric and consistent depth. Next, we treat the ensemble as supervisory labels to train a metric depth estimation network for surgeries (i.e., MetricDepthS-Net) that distills the embeddings from the robot kinematics, endoscopic videos, and poses. With accurate metric depth estimation, we utilize a dense visual reconstruction method to recover the 3D structure of the whole surgical site. We have extensively evaluated the proposed framework on public SCARED and achieved comparable performance with stereo-based depth estimation methods. Our results demonstrate the feasibility of the proposed approach to recover the metric depth and 3D structure with monocular inputs.