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The planned paths obtained based on only a nominal model of the camera and/or
robot may not be fully traversable by the robot without violating certain constraints.
In a recent work [9], Chesi proposed a planning approach to design a robust image
trajectory that satisfies the required constraints not only for the nominal model but
rather for a family of admissible models. In the proposed approach an uncertain
model has been considered for image correspondence between the initial and de-
sired images, and the camera's intrinsic parameters are assumed to be affected by
some unknown random errors with known bounds. Given the above uncertain mod-
els, there are different admissible camera poses and consequently different camera
trajectories rather than a common and robust one. A polynomial parametrization is
proposed through which each camera trajectory is parameterized by a possible cam-
era pose and by a design variable which is common to all admissible trajectories.
So, the robust trajectory is computed through an optimization problem determin-
ing the common design variable that satisfies field of view limits and maximizes
the distance of the image features from the boundary of image on all parameterized
trajectories.
Although the results obtained through the above approaches in taking calibra-
tion uncertainty and measurement errors into account seem promising, more re-
search needs to be done. Physical constraints, especially collisions and occlusions,
are highly affected by the uncertainties in the modeling of the environment. Robot
path-planning considering uncertainties in modeling, localization, and sensing has
been studied for decades within path-planning community [40] yielded a number of
promising approaches,
e.g.
[5], [30], [43], [48], [55]. Incorporating the research re-
sults achieved through these approaches into the visual servoing framework would
be a promising future direction. Moreover, planning robust trajectories for visual
servoing tasks in unknown or partially known environments remains an open re-
search problem.
11.5
Conclusions
We provided a comprehensive review of existing path-planning for visual servoing
techniques aimed at making the visual servoing more robust in complex scenar-
ios, especially in applications where the initial and desired views are distant. Con-
sidering the underlying path-planning approach, the existing techniques have been
divided into four categories: (1) image space path-planning, (2) optimization-based
path-planning, (3) potential field-based path-planning, and (4) global path-planning.
We reported on the previous works pertinent to each category and for each technique
we discussed the set of assumptions along with its benefits and drawbacks and its
integration with the reactive visual servo controllers.
Recent works (discussed in Section 11.4) demonstrated the effectiveness of ac-
counting for modeling/calibration uncertainties and measurement errors at the plan-
ning stage in generating robust trajectories for visual servoing scenarios where the
available data are affected by uncertainties. Towards that aim, incorporating the
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