**3. 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 carry out a specific task or series of tasks, considering a set of constraints that will depend basically on the tasks, the architecture of the robot and the environment where the robot has to move.

Sun et al. [7] set their sights on the path planning problem, 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, they propose an improved version of this method (Dynamic APF (DAPF)), which uses a dynamic window approach to avoid local minima regions. Additionally, they address the problem of dynamic obstacles avoidance by means of a danger index which does not only consider the relative distance between robot and obstacle but also their relative velocity. The experimental section proves the ability of the algorithm to find optimal paths that avoid both local minima and moving obstacles.

Zeng et al. [8] present a two-level hierarchical framework for robot navigation in dynamic environments in a continuous way, named JPS-IA3C (Jump Point Search Improved Asynchronous Advantage Actor-Critic). On the one hand, the global planner JPS+ (P), 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. On the other hand, 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). Additionally, IA3C builds a novel reward function framework, which 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. Bae et al. [9] propose 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 which performs independent actions or as a cooperative robot that collaborates with other robots. To address these issues, the proposal of this paper consists in 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.

Liu et al. [10] present a method for path planning oriented to Unmanned Surface Vehicles (USV), which takes into account the risk of water depth. This is a crucial factor for the safe navigation in shallow waters. With this aim, the authors study the stability of USV's in a variety of situations and calculate the minimum safe water depth. To plan the path, a Water Depth Risk Level A\* algorithm (WDRLA\*) 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.

Zhao et al. [11] focus their work on space robotics, which are designed to work in outer space in a variety of tasks, such as assembly and maintenance of space stations. In this kind of robots, the Multitask-based Trajectory-Planning Problem (MTTP) is of utmost importance, as it would enable 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 a parameter optimization, using an improved genetic algorithm to optimize the unknown parameters. Numerical simulations are carried out with a base spacecraft and a 7-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 (UAV). Majeed et al. [12] propose a flight path planning algorithm to find collision-free, minimum length and flyable paths for such vehicles in three-dimensional urban environments with fixed obstacles, for coverage missions. This problem consists in finding a low cost path that covers the free space of an area of interest with minimum 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. Simulation results prove the good performance of the algorithm in a variety of scenarios.

In the field of movement control of legged mobile robots, Yang et al. [13] aim attention at the problem of energy consumption, as it can be considered a performance index of quadruped robots. In their work, they model and analyze the energy consumption of the robot SCalf 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 which is the optimal choice of these relevant parameters, as far as energy consumption is concerned. To this purpose, the authors build the dynamics model of the robot, based on an analysis of the foot force distribution and derive a complete energy model which includes mechanical power and heat rate. Also, they use a foot trajectory based on cubic spline interpolation to describe the motions of the robot.

Finally, path planning is also a crucial problem in the field of industrial robotics. The work of Guo et al. [14] concentrates on the field of industrial manipulator robots, more concisely on machining and fabrication applications, among which deburring plays an important role. They develop a hybrid manipulator robot with five degrees of freedom. Also, they propose in the paper a deburring framework focusing on tool path planning (position and orientation) and 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 a deburring process.

**Funding:** This work was partially supported by the Spanish Government through the project DPI2016-78361-R (AEI/FEDER, UE) and the Generalitat Valenciana through the project AICO/2019/031.

**Acknowledgments:** This special issue would not have been possible without the valuable contributions of the authors, peer reviewers, and editorial team of Applied Sciences. We give our most sincere thanks to all the authors for their hard work, independently on the final decision about their submitted manuscripts. Also, all our gratitude to the peer reviewers for their help and fruitful feedback to authors. Finally, our warmest thanks to the editorial team for their untiring support and hard work during all the stages of development of this special issue and, in general, congratulations on the great success of the journal Applied Sciences.

**Conflicts of Interest:** The authors declare no conflicts of interest.
