Autonomous mobile robots are an important focus of current research due to the advantages they bring to the industry, such as performing dangerous tasks with greater precision than humans. An autonomous mobile robot must be able to generate a collision-free trajectory while avoiding static and dynamic obstacles from the specified start location to the target location. Machine learning, a sub-field of artificial intelligence, is applied to create a Long Short-Term Memory (LSTM) neural network that is implemented and executed to allow a mobile robot to find the trajectory between two points and navigate while avoiding a dynamic obstacle. The input of the network is the distance between the mobile robot and the obstacles thrown by the LiDAR sensor, the desired target location, and the mobile robot’s location with respect to the odometry reference frame. Using the model to learn the mapping between input and output in the sample data, the linear and angular velocity of the mobile robot are obtained. The mobile robot and its dynamic environment are simulated in Gazebo, which is an open-source 3D robotics simulator. Gazebo can be synchronized with ROS (Robot Operating System). The computational experiments show that the network model can plan a safe navigation path in a dynamic environment. The best test accuracy obtained was 99.24%, where the model can generalize other trajectories for which it was not specifically trained within a 15 cm radius of a trained destination position.