Image-based Visual Servo Control Design with Multi-Constraint Satisfaction - Visual Servoing via Advanced Numerical Methods - page 281

(a) (b)

Fig. 15.6 (a) Robot trajectory; and (b) visual feature evolution

(a) (b)

Fig. 15.7 (a) Kinematics screw evolution; and (b) zoom on the control

of the second task. The components of the camera's kinematics screw vary strongly
at the transition but remain bounded. This condition ensures that the velocity vector
q ( t ) remains continuously differentiable during the complete motion. Now, consid-
ering the right picture of Figure 15.7, one can observe that the control components
remain bounded, insuring that the limitation on the acceleration of the camera is sat-
isfied. Such a guarantee could not be obtained with a simple second order dynamics
as proposed in [19]. As it can be seen in Figure 15.7 (right picture), one of the con-
trol component saturates for a while at the beginning of the task. However, as this
saturating condition has been considered in the control synthesis, the stability of the
closed-loop system remains guaranteed.

15.6 Concluding Remarks and Perspectives

Techniques that allow to design a multicriteria image-based controller in order to
track moving targets with square integrable velocity were proposed in this chapter.