Redes neurais como alternativas ao Jacobiano na solução iterativa da cinemática inversa

Abstract

The usage of robots has become a normal practice today thanks to large technological advances in recent decades. The planning of robots’ movements in the environment is one of the most important fundaments in the study of robotics. To complete tasks in the real world, the joints of the robot must move in such a way that the end-effector reach a given goal or follow a trajectory. The mapping from the movements made by the joints to positions in space is the problem called forward kinematics, while the inverse problem is called inverse kinematics. The inverse kinematics problem is generally very complex and many traditional solutions focus only on robots of specific topologies. The iterative method based on the Jacobian’s (pseudo)inverse matrix is a well-known, proven, and trusted generic approach that can be applied to many manipulators. However, it depends on linearizations that are valid only on a tight neighborhood around the current pose of the manipulator. This requires the robot to move only in small steps, intensely recalculating its trajectory along the way, making this approach inefficient in some applications. Neural networks, for their capacity of modeling non-linear systems, appear as an interesting alternative to solving this problem. Here, we show that neural networks indeed can be trained successfully to map displacements in the task space to angle increments of the joints, outperforming the method based in the Jacobian’s inverse when dealing with larger displacement increments and when near singularities. We validate the study through comparative results in simulated planar manipulators of 2-DOF and 3-DOF and it gives birth to a hybrid approach that has already been succesfully applied in real robots.