**Preface to "Mobile Robots Navigation"**

The presence of mobile robots in diverse scenarios is considerably increasing to solve a variety of issues. Among them, many developments have occurred in the fields of ground, underwater, and flying robotics.

Independent of the environment in which they move, navigation is a fundamental ability of mobile robots so that they can complete autonomously high-level tasks in a specific environment. This problem can be efficiently addressed through the following actions: First, the environment in which the robot has to move must be perceived, and some relevant information must be extracted from it (mapping problem). Second, the robot must be able to estimate its position and orientation within this environment (localization problem). With this information, a trajectory toward the target points must be planned (path planning), and the vehicle has to be reactively guided along this trajectory considering either possible changes or interactions with the environment or with the user (control).

To perceive the environment, some kinds of onboard sensors can be used, such as laser rangefinders, visual systems, or RGB-D platforms. This perception task can be conducted either beforehand or once the navigation task has started while the robot moves through the environment, and the result is a model or map of the environment. The localization task must be designed considering several issues: the available sensors, the structure of the map, and the movement constraints of the robot (i.e., trajectories in 3D or 6D). Integrated exploration systems jointly consider all these issues and they achieve trajectory planning and control while a model of the environment is obtained, and the robot estimates its position and orientation. Finally, the availability of versatile tools to simulate any new development in mobile robots navigation is crucial to quickly testing and comparing navigation algorithms.

Given this information, this book presents current frameworks in these fields and, in general, approaches to any problem related to the navigation of mobile robots. The chapters can be classified into two main groups: (a) map building and localization and (b) path planning and motion control.

The first group of chapters addresses the problems of map building and/or localization. In most applications, mobile robots have to move through a priori unknown environments. Therefore, either a partial knowledge of the surroundings of the robot or building a more complete model or map of this environment that can be used is necessary to subsequently estimate the position and orientation of the robot and to plan optimal trajectories to the target points so that the robot can autonomously move and perform the task for which it has been designed.

Occupancy grids are a traditional and efficient mechanism used to represent the environment. Distance maps (DMs) are a tool widely used to encode the search space in robotics path planning and obstacle avoidance as they can provide the robot with a certain safety radius to efficiently search for collision-free paths and to avoid obstacles in motion. In this field, Chapter 1 proposes 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. CODB requires fewer cell visits and computation costs than previous algorithms. The authors also propose an algorithm to compute DM-based subgoal graphs that 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.

Chapter 2 focuses on multilegged walking robots. Their redundant limb structure usually

confers good stability and maneuverability, even in complex environments. However, their ability to perceive the surrounding environment impacts their autonomous mobile ability. One of the critical issues is 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). Broadly, 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 terrain and terrain 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 more completely know the surroundings. Chapter 3 outlines a method for exploring and modelling unknown indoor environments . The authors approach the problem as a multiple-objective exploration, using the multi-objective grey wolf optimizer (MOGWO) algorithm, which employs static waypoints in the process that promote the efficient exploration of indoor environments. This exploration process works by optimizing 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 in comparison with deterministic and hybrid stochastic exploration algorithms.

In mapping and localization, hierarchical models play an important role. They are used to arrange the information of the environment into several layers with different levels of granularity, which permit solving the efficient solving of the localization problem. Chapter 4 concentrates on this topic, and proposes an algorithm to compress topological models to create the high-level layer of the map by means of a clustering approach. The authors use omnidirectional images and global appearance descriptors. The experiments show the efficiency of the algorithm for creating 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 with which the robot is equipped, typically visual sensors. This problem is commonly known as visual odometry (VO). Chapter 5 presents a visual-inertial odometry approach based on the cubature information filter and H<sup>∞</sup> filter, namely MCH<sup>∞</sup> IF-VIO, which uses a raw intensity-based measurement model for the camera. The measurements from the inertial measurement unit (IMU) and the camera are fused by means of a hybrid information filter that applies two cubature rules in the time update and the measurement update phases to guarantee numerical stability. The H<sup>∞</sup> filter is used in the measurement update phase to achieve robustness against non-Gaussian noises in the camera measurements. The authors validate their proposal experimentally with a publicly available outdoors dataset, comparing its performance to other previously reported approaches.

Finally, versatile tools that enable researchers to quickly test and compare navigation algorithms in real operation conditions are key in autonomous mobile robotics. In this field, in chapter 6, a framework is developed for fast experimental testing of navigation algorithms in autonomous robotics, which is based on the robot operating system (ROS). The authors provide a basic structure arranged into a number of abstraction levels, which allows researchers to implement and test their algorithms, focusing on any sub-problem of interest such as mapping or localization. The chapter proves the validity of the framework by showing how to implement the localization module of a ground robot that uses global navigation satellite system positioning and Monte Carlo localization with a Kalman filter, and is tested with large outdoor environments.

The second group of chapters address the problems of path planning and motion control. Once a local representation or a complete map of the environment is available, the robot can focus on the planning of optimal trajectories and the motion control to conduct a specific task or series of tasks considering a set of constraints that depend basically on the tasks, the architecture of the robot, and the environment within which the robot moves.

Chapter 7 focuses on the path planning problem, and more concisely, on artificial potential field (APF) approaches. They are an efficient alternative for motion planning in mobile robotics, but they are often limited by the presence of local minima in which the robot may get trapped. For this reason, the authors propose an improved version of this method (dynamic APF, DAPF) that uses a dynamic window approach to avoid local minima regions. They address the problem of dynamic obstacles avoidance by means of a danger index that considers the relative distance between robot and obstacle as well as their relative velocity. The experimental section proves the ability of the algorithm to find optimal paths that avoid both local minima and moving obstacles.

Chapter 8 presents a two-level hierarchical framework for continuous robot navigation in dynamic environments named jump point search improved asynchronous advantage actor-critic (JPS-IA3C). The JPS+ (P) global planner, which is a variant of JPS, efficiently computes a sequence of subgoals for the motion controller, which can eliminate first move lag and avoid local minima. The low-level motion controller IA3C learns the control policies of the robots' local motion to satisfy the kinematic constraints and adapt to changing environments (moving obstacles). IA3C builds a novel reward function framework that avoids learning inefficiencies dues to sparse reward. The authors perform a set of simulation experiments that prove that this hierarchy is able to cope with incomplete and noisy information and navigate robots in unseen and large environments with shorter path lengths and low execution time.

In some applications, the collaboration between the members of a team of robots can be of interest. Chapter 9 proposes a multi-robot path planning algorithm that tries to overcome some of the shortcomings of conventional methods, such as the adaptation to complex and dynamic systems and environments. In multi-robot navigation, depending on the situation of the mission, each robot can be seen either as a moving obstacle that performs independent actions or as a cooperative robot that collaborates with other robots. To address these issues, the authors propose a framework based on the use of deep q learning combined with convolutional neural networks, using visual information from the surrounding of the robots. The simulation results prove the flexible and efficient navigation provided by the method.

Chapter 10 presents a method for path planning for unmanned surface vehicles (USVs), which considers the risk of water depth. This is a crucial factor for safe navigation in shallow waters. With this aim, the authors study the stability of USVs in a variety of situations and calculate the minimum safe water depth. To plan the path, a water depth risk level A\* (WDRLA\*) algorithm is proposed and its performance is compared with the traditional A\* shortest path and safest path. The authors use the depth point of the electronic navigation chart (ENC) and a spline function interpolation algorithm to obtain a grid environment model considering water depth. The numerical simulations prove that the algorithm guarantees navigation safety in different conditions.

Chapter 11 focuses on space robotics that are designed to work in outer space in a variety of tasks, such as assembly and maintenance of space stations. In this kind of robot, the multitask-based trajectory-planning problem (MTTP) is of utmost importance, as it enables the robot to perform two or more tasks in each mission, what would suppose a save of energy. The authors use piecewise continuous sine functions to create the trajectories along the waypoints and transform this problem into parameter optimization, using an improved genetic algorithm to optimize the unknown parameters. Numerical simulations are conducted with a base spacecraft and a seven degrees of freedom manipulator in two simulation cases, and they prove the efficiency of the approach.

Trajectory planning is also a relevant technology for autonomous unmanned aerial vehicles (UAVs). Chapter 12 proposes a flight path planning algorithm to find collision-free, minimum length, and flyable paths for UAVs in three-dimensional urban environments with fixed obstacles for coverage missions. This problem consists of finding a low cost path that covers the free space of an area of interest with minimal overlapping. The authors address this problem based on a novel footprints' sweeps fitting method. They generate a sparse waypoint graph by connecting footprints' sweeps endpoints considering the obstacles, maneuverability constraints, and footprints' sweeps visiting sequence. The simulation results prove the performance of the algorithm in a variety of scenarios.

In the field of movement control of legged mobile robots, chapter 13 addresses the problem of energy consumption, since it can be considered a performance index of quadruped robots. In the chapter, the authors model and analyze the energy consumption of the SCalf robot with a trot gait, and they study the effect of different gait parameters, such as step length, gait cycle, step height, and duty cycle. The experiments show the optimal choice for these relevant parameters, as far as energy consumption is concerned. For this purpose, the authors build a dynamics model of the robot based on an analysis of the foot force distribution and derive a complete energy model that includes mechanical power and heat rate. They use foot trajectory based on cubic spline interpolation to describe the motions of the robot.

Finally, path planning is another important problem in the field of industrial robotics. Chapter 14 concentrates on the field of industrial manipulator robots, more concisely on machining and fabrication applications, among which deburring plays an important role. The authors develop a hybrid manipulator robot with five degrees of freedom. They propose a deburring framework focusing on tool path planning (position and orientation), robotic layered deburring planning, and a process parameter control based on fuzzy logic. A variety of experiments are performed to prove the dexterous manipulation and the orientation reachability of the manipulator and to verify the effectiveness of the two proposed methods in the deburring process.

> **Oscar Reinoso, Luis Pay´a** *Special Issue Editors*
