Visual Servoing via Nonlinear Predictive Control - Visual Servoing via Advanced Numerical Methods - page 380

are still kept even if visibility constraints ( − 0 . 29 < u < 0 . 29 , − 0 . 4 < v < 0 . 4) are

considered (see Figure 20.16).

20.5 Conclusions

In this chapter, we have shown that an alternative approach of IBVS can be the VPC
strategy. The visual servoing task is then formulated into a nonlinear optimization
problem over a prediction horizon. The advantage of this formulation is the capabil-
ity of easily dealing with visibility constraints and 3D constraints. The optimization
procedure can be compared to an on-line implicit and optimal constrained path-
planning of features in the image plane. The choice of the image prediction model
has been discussed. The approximated local model can be less efficient than the
global model for difficult configurations but no 3D data are required. On the other
hand, if 3D data are available, VPC GM gives satisfying results for any initial con-
figuration and motion to achieve. The VPC setting parameters, i.e. , the prediction
horizon and the weighted matrix, play a crucial role in terms of camera and visual
feature trajectories. Simulation results highlight the efficiency of VPC. Finally, this
strategy is very flexible and can be used whatever the robotic system (mobile robot
or robot arm) and the camera (perspective or catadioptric).

References

[1] Allibert, G., Courtial, E., Toure, Y.: Visual predictive control. In: IFAC Workshop on
Nonlinear Predictive Control for Fast Systems, Grenoble, France (2006)
[2] Allibert, G., Courtial, E., Toure, Y.: Real-time visual predictive controller for image-
based trajectory tracking of mobile robot. In: 17th IFAC World Congress, Seoul, Korea
(2008)
[3] Allibert, G., Courtial, E., Toure, Y.: Visual predictive control for manipulators with
catadioptric camera. In: IEEE Int. Conf. on Robotics and Automation, Pasadena, USA
(2008)
[4] Chaumette, F.: Potential problems of stability and convergence in image-based and
position-based visual servoing. In: Kriegman, D., Hager, G., Morse, A. (eds.) The Con-
fluence of Vision and Control. LNCIS, vol. 237, pp. 66-78. Springer, Heidelberg (1998)
[5] Chaumette, F., Hutchinson, S.: Visual servo control, part i: Basic approaches. IEEE
Robotics and Automation Magazine 13(4), 82-90 (2006)
[6] Chaumette, F., Hutchinson, S.: Visual servo control, part ii: Advanced approaches.
IEEE Robotics and Automation Magazine 14(1), 109-118 (2007)
[7] Chesi, G.: Visual servoing path planning via homogeneous forms and lmi optimiza-
tions. IEEE Trans. Robotics and Automation 25(2), 281-291 (2009)
[8] Chong, E., Zak, S.H.: An Introduction to Optimization, 2nd edn. John Wiley & Sons
Inc., Chichester (2001)
[9] Danes, P., Bellot, D.: Towards an lmi approach to multicriteria visual servoing in
robotics. European Journal of Control 12(1), 86-110 (2006)
[10] Durola, S., Danes, P., Coutinho, D., Courdesses, M.: Rational systems and matrix in-
equalities to the multicriteria analysis of visual servos. In: IEEE Int. Conf. on Robotics
and Automation, Kobe, Japan (2009)