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in the workspace and then projected into the image space. The attractive potentials
are defined in the workspace to pull the robot towards the final desired configuration.
To account for field of view limits, repulsive potentials are defined in the image
space pushing the image trajectories away from the image boundary. Joint limits
are avoided by imposing repulsive potentials in the joint space of the robot. So, the
total force applied to the robot is a weighted sum of the individual forces computed
as the negated gradient of the above potentials. The image trajectories are obtained
in an iterative scheme by moving along the direction of the total force applied to
the robot. The discrete image trajectories are then time scaled and tracked using
an IBVS technique. The above strategy has been applied to targets with known
as well as unknown models. In the latter case, a scaled Euclidean reconstruction
is employed to obtain scaled camera paths in the workspace. Image local minima
are automatically avoided by updating the image Jacobian using the values of the
current desired image features along the time scaled feature trajectories.
As an inherent deficiency of potential field-based path-planning method, the
above strategy might lead to local minima. Although the authors reported no en-
counter of such local minima in their experiments, imposing physical constraints
such as collisions with obstacles and occlusions highly increase the chance of hav-
ing local minima in the overall potential field.
In [19] a potential field-based strategy is employed to account for workspace ob-
stacles, field of view limits, and robot's joint limits in a global planning framework.
To escape local minima generated by addition of the attractive and repulsive forces,
simulated annealing
[34] is employed in which proper tuning of the initial temper-
ature and the cooling rates are required to probabilistically ensure the method to
escape from local minima and converge to the global minimum. In the proposed
planning framework two different trajectory generation strategies are employed:
method A, where a trajectory for the end-effector is planned with respect to the
stationary target frame, and method B, where a trajectory for the target is planned
with respect to the current end-effector frame. The former results in a camera path
close to a straight line in the workspace, while in the latter the image trajectory of
the target's origin is constrained to move as close as possible to a straight line in
the image which lessens the chance of image features leaving the camera's field of
view. A local switching strategy is devised to switch from image-based control to
position-based control when closeness to image local minima and image singular-
ities are detected along the planned trajectories. This is done only once to avoid
instability due to repetitive switching, however there is no complete guarantee that
the field of view and joint limits are always ensured after the system is switched to
position-based control.
One of the main advantages of potential field-based approaches is the fast com-
putation of driving force which makes these approaches suitable for real-time appli-
cations such as visual servoing. For example, the above strategy can be employed
when tracking image trajectories to account for possible deviations from the planned
trajectory due to uncertainties in modeling and/or calibration (
e.g.
[12]).
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