A Mutivariable Methodology for Fast Visual Servoing of Flexible Manipulators Moving in a Restricted Workspace

Abstract

High-speed visual servoing of manipulators including flexibilities is considered. In the proposed methodology, a model taking into account all the dynamics of the system is identified from the measurements usually available in visual servoing. This model is valid around the working position of the arm and can be easily recomputed after camera displacement. Two multivariable strategies are proposed for controlling the position of the end-effector: generalized predictive control and control. Comparative simulation and experimental results on a 2-degrees of freedom planar manipulator are given. A robustness evaluation step shows that the available working space is quite large.

Keywords:

• flexible arms
• multivariable control
• robotic manipulators
• model identification
• vision-based control

Acknowledgement

This work was supported by a Ph.D. grant from the Alsace Regional Council and the French National Center for Scientific Research (CNRS).

Notes

1. ‘High bandwidth’ is rather subjective. Herein, we aim at increasing the bandwidth as much as possible, therefore making the flexible modes of the structure become effective.

2. See Isidori for the definition [30]. For a LTI system, this is equivalent to be minimum phase, i.e. to have all zeros with negative imaginary part.

3. This limitation is very common when considering segment deformations.

4. As reported by Ferretti et al., a high bandwidth of the local joint velocity loop can make the control of the end-effector position more difficult [36]. However, in the current case, the bandwidth of the inner velocity loop is maximized in order to maximize the potential bandwidth of the outer loop. The complexity of the tuning of the outer loop will be handled by high-order multivariable controllers.

5. Notice that these quasi-static assumption is only used for the determination of the Jacobian matrix without limitation of the validity of the global model.

6. A bistable system is stable and has a stable inverse.

7. The motion of the heart has very sharp transients near from step displacements due to the high acceleration of the myocardium at each heart beat.

8. The inverse of the modulus margin is equal to the norm of .

9. Singular values are the input/output amplification ratios in the different eigen directions, in the sense of the norm on signals.

10. Notice that a different camera position was chosen compared to the experiments presented in the previous section. Therefore, the control signals significantly differ.