## 1 Introduction
### Related Work  
#### 1.1.1 Detection and Estimation of Articulated Objects  
Recent methods for the detection of articulated objects utilize RGB-D images and neural networks. [PERSON] et al. [3] proposed an RGB-D-image-based approach for estimating articulated objects like cabinets and drawers. The method uses a pair of RGB-D images, assuming that the object state changes while the robot remains stationary. The SSD object detector [4] is employed to detect object positions in the input image. The parameters of the joint are determined by extracting a point cloud from the bounding box area and removing static points. Initial joint parameters are estimated using the RANSAC algorithm and then optimized using Particle Swarm Optimization. This approach effectively explains data in both images based on the input hypothesis [3]. The method presented in [3] successfully determines the position and configuration of articulated joints and objects. It was validated using the RBO dataset [5], which includes sequences of interactions with articulated objects. However, the method has limitations, such as incomplete object visibility, noisy depth data, or object occlusion, which influences accurate state estimation. Additionally, the system requires robot interaction with the object to estimate its model, which introduces time requirements and potential risk of object damage. In this work, we are focused on estimating the information about articulated objects from a single view only. Object interactions provide an alternative approach for building environment models with articulated objects, as discussed by [PERSON] et al. [1]. This method involves sensor fusion, combining object tracking from a vision system and measurements from the robot manipulator's sensors to reduce uncertainty in the articulated object model and parameters. The authors present a graph probabilistic model of robot interaction that includes the articulated object model, its parameters, measurements of the object's position with six degrees of freedom, measurements from the manipulator's sensors, and the action taken. The vision system uses noisy measurements, which are projected onto the evaluated model using inverse kinematics. The estimated configuration is relative to the original observation and lies on the model's surface. A simple kinematics function is employed to determine the position corresponding to the assumed configuration. The sensor model is approximated by a two-dimensional normal distribution centered at a zero vector, depending on the translational and rotational distance between the model projection and the observations. The manipulator sensor model is based on short translational movements, measured in binary to indicate successful execution. The authors compare two approaches for selecting actions that reduce model uncertainty: entropy reduction and information gain. The study findings indicate that greedily minimizing entropy after each step is not the optimal method to reduce the entropy of the proposed models and their parameters. Instead, the information gain approach, using Kullback-Leibler divergence, is more effective. The environment model can be built using a coefficient graph (factor graph) proposed by [PERSON] et al. [6]. This method addresses computational complexity in algorithms based on particle filters. The authors use a graph to reduce complexity, taking a 3D point cloud and a geometric model as input. The problem is represented as an undirected graph MRF (Markov Random Field), inferring hidden variables to maximize joint probability. Inference involves message exchange between variables until convergence. The best estimate determines the positions of object parts, forming the overall position estimates. The Pull Message Passing for Nonparametric Belief propagation (PMPNBP) algorithm is used for inference, evaluating samples, and approximating mixtures efficiently [6]. In [2], the robot acquires two point clouds. The first point cloud is obtained before the interaction of the robot with the object.