Planejamento e controle de trajetória aplicado à navegação de um robô móvel diferencial

Abstract

The main objective of this academic work is to study and implement a navigation architecture for a differential mobile robot, integrating trajectory planning strategies and kinematic control. The ability to coordinate obstacle-free path generation with precise motion execution is a central theme in mobile robotics, as it ensures that the robot moves autonomously, safely, and feasibly, even in the face of nonholonomic constraints and complex scenarios. Initially, the kinematics of the differential robot is presented, describing the equations that relate linear and angular velocities to planar motion. Subsequently, a control law based on Least Squares optimization is implemented, minimizing the error between the desired velocity and the velocity executable by the robot, while respecting its nonholonomic constraints. For trajectory planning and obstacle avoidance, the Artificial Potential Fields technique was adopted. This approach was chosen due to its combination of computational simplicity and ability to generate continuous trajectories, where an attractive field guides the robot to the destination and repulsive fields steer it away from collision regions. The integration between the kinematic controller and the reactive planner was evaluated in two simulation environments. In MATLAB, tests were conducted in two-dimensional scenarios to validate the controller's behavior regarding different obstacle configurations. Subsequently, the algorithm was validated in the three-dimensional environment of CoppeliaSim, using a Pioneer robot model equipped with a LiDAR sensor and controlled via a Python API. The results demonstrated that the system was capable of guiding the robot to the destination with satisfactory precision, performing smooth and effective avoidance maneuvers, thus validating the proposed approach for autonomous navigation applications.