The two previous sections give us the basic tools to build
an uncalibrated visual control system. Assume that our initial
visual state is
and our goal is
.
One could directly apply one of the control laws in
Section 3.1 to try to move to
as
quickly as possible. For reasons of stability and convergence
(to be explored later in Chapter 5) it
makes sense to divide the distance between
and
into a sequence of p subgoals:
The robot is then moved towards each of the subgoals in order by:
To achieve the final goal
step 1 to 3 of the above procedure
is repeated until convergence. The algorithm is best started
with a rough estimate of the true Jacobian, which can be obtained
by, for instance, a very rough model, or by executing one set
of test movements along the motor coordinate axes and form one initial
finite difference approximation. In Chapter 5
we will show how to modify the algorithm so it is stable even
for random initial Jacobians.
We call the set of subgoals way points, which are essentially additional
visual goals describing the visual situation at intermediate points.
In a bare bones visual servoing system it is usually enough to
generate the way points at equidistant points along a line, such
as in eq. 3.8. When solving real manipulation tasks
the way points are generated in conjunction with trajectory planning.
This is described in Section 5.2 and Chapter 7.
By requiring a system to pass near or through such way points,
drift from the desired trajectory can be eliminated.
Dividing the transition between
and
into
several subsegments, with intermediate visual goals along the straight
line between them also allows us to bring the manipulator back onto the
desired trajectory as soon as possible in the event of a deflection,
by servoing on the nearest subgoal between the current pose and the
goal. This is illustrated in Fig. 3.2. This
behavior also reflects how the human arm reacts to a deflection.
Figure 3.2: Planning intermediate way points in visual space reduces
trajectory error compared to pure servoing on the goal.