5. Conclusions
In contrast with the previous indirect image-based visual servoing approaches proposed up to now to perform the guidance of FFSMR, this paper presents a new direct image-based visual servoing system that takes into account the system kinematics and dynamics. The proposed controller allows the robot not only to achieve a given location from an initial one, but also to perform the tracking of a desired image trajectory. The proposed approach considers the optimization of the motor commands with respect to a specified metric defined by the user. Additionally, a chaos compensator is integrated in the proposed controller to improve the joint behavior during the tracking. Three different experiments with three different scenarios were developed, and the proposed controller worked properly for all of them. The first experiment illustrated the tracking of a nonrepetitive image trajectory. The second one illustrated the tracking of a circular trajectory performed by the end-effector, where the chaotic movement of the joints was avoided by using the chaos compensator. Even though movements in 3D Cartesian space of the end-effector were very similar, when studying the torque applied to the joints, and thus, the evolution of the positions of the links, a great improvement was achieved, avoiding high fuel consumption due to sudden, fast, chaotic movements of the links. In the third experiment, the tracking of an abrupt trajectory was examined with the optimal control strategy with chaos compensation but with different values of the weight matrix.
