efficiently search out collision-free paths and to avoid obstacles in motion. In this field, [PERSON] et al. [1] propose an efficient algorithm (Canonical Ordering Dynamic Brushfire (CODB)) to incrementally update the cell values when cell states are changed (due to changes in the environment). It requires fewer cell visits and computation costs than previous algorithms. They also propose an algorithm to compute DM-based subgoal graphs which are able to provide high-level collision-free roadmaps for the mobile robot. Finally, they verify that optimal trajectories can be obtained with these subgoal graphs and a real-time search algorithm. [PERSON] et al. [2] focus their study on multilegged walking robots. Their redundant limb structure usually confers them good stability and maneuverability even in complex environments. However, their ability to perceive the surrounding environment impacts upon their autonomous mobile ability. One of the critical issues is the accurate terrain identification. The authors propose an image infilling method for terrain classification based on a Bag-of-Words (BoW) approach, Speeded-Up Robust Features and Binary Robust Invariant Scalable Keypoints (SURF-BRISK) and Support Vector Machine (SVM). In broad lines, the obstacle regions are infilled by surrounding terrain to improve the classification accuracy, a super-pixel image infilling method for mixed terrain is developed and multiple labels can be given to complex terrains. Their experiments show the validity of the approach in mixed terrains and terrains with obstacles. The exploration problem is closely related to the mapping problem. It tries to discover unknown areas of the environment to add them to the map so that the robot can have a more complete knowledge of the surroundings. [PERSON] et al. [3] develop a method to explore unknown indoor environments, with the purpose of building a model of them. They approach the problem as a multiple-objective exploration, using the Multi-Objective Grey Wolf Optimizer (MOGWO) algorithm, which employs static waypoints in the process, promoting the efficient exploration of indoor environments. The philosophy of this exploration process is to optimize both the search of unexplored areas and the accuracy of the map. The simulation results show the ability of the approach to build complete maps, comparing to deterministic and hybrid stochastic exploration algorithms. As far as mapping and localization are concerned, hierarchical models play an important role. They arrange the information of the environment into several layers with different levels of granularity, which permit solving the localization problem efficiently. [PERSON] et al. [4] concentrate on this topic, and propose an algorithm to compress topological models in order to create the high-level layer of the map, by means of a clustering approach. They use omnidirectional images and global appearance descriptors. The experiments show the efficiency of the algorithm to create compact hierarchical models and to solve the problem of visual place recognition with a good balance between computation time and localization accuracy. Continuing with the localization problem, another relevant issue in mobile robotics is the incremental estimation of egomotion from the exteroceptive sensors the robot is equipped with, typically visual sensors. This problem is commonly known as visual odometry (VO). In this regard, the work by [PERSON] et al. [5] presents a Visual-Inertial Odometry approach, based on the cubature information filter and \(H_{\infty}\) filter, namely, \(MCH_{\infty}IF-VIO\), which uses a raw intensity-based measurement model for the camera. On the one hand, the measurements from the IMU (Inertial Measurement Unit), and the camera are fused by means of a hybrid information filter, which applies two cubature rules in the time-update and the measurement-update phases, to guarantee numerical stability.