Page 67 - Sensing, Intelligence, Motion : How Robots and Humans Move in an Unstructured World

42 A QUICK SKETCH OF MAJOR ISSUES IN ROBOTICS

system. In the task in Figure 2.9 the motion will be planned in two stages:

1. A guarded motion in the y direction will be used for the part of the path in
free space, namely from the arm initial position (Figure 2.9a) to grasping
the object A (Figure 2.9b) to the position when object A contacts surface
T (Figure 2.9c). Only position control will be used at this stage. (Since
object A is immobile during the grasping operation, let us assume that
such control will suffice for grasping.)
2. Compliant motion control will be done during the part of motion where
object A is in continuous contact with table T , between positions shown in
Figures 2.9c and 2.9d. Both position and force control will be used at this
stage: position control in the direction x and force control in direction y.

Here is why this control is called compliant. During this part of the path the
control system will only attempt to maintain a set force pressure in the y direction.
If a little bump is encountered on the table, the arm’s attempt to maintain the
same y coordinate as before will instantaneously develop a stronger reaction
force from the table. As the arm’s control measures and reacts to forces in this
y direction, it will then comply, gently raising the arm enough to keep the same
action/reaction forces in the y direction. As the bump is passed, the reaction force
will quickly decrease, and the arm’s control will move the arm endpoint a notch
down, just to maintain the force at the set value.
This hybrid controller therefore has two feedback loops (see Figure 2.10): one
for position control and one for force control. (Each loop may of course have its
own complications; for example, each can be built as a PID controller shown in
Figure 2.8.)
Remember that the controller shown in Figure 2.10 can provide a successful
compliance control only specifically along the y axis, which is what is needed for
the task in Figure 2.9. In reality the direction of the compliance line may differ
from case to case, so for the general case a more general scheme is needed.
The controller shown in Figure 2.11 can handle such cases. Its main difference
from the controller in Figure 2.10 is that instead of specific matrices M 1 and M 2
in Figure 2.10, a generalized constraint frame 2 × 2rotationmatrix Q is used.
Matrix Q describes orientation of the constraint axes. Other inputs in the scheme
are as follows:
Axis s specifies the position versus control differentiation of axes,

1, where s i = 1if axis i of constraint frame is position-controlled
s i =
0, where s i = 0if axis i of constraint frame is force-controlled
p d = (x d ,y d ) is the desired position vector.
f d = (f xd ,f yd ) is the desired force vector.
R is the coordinate transformation of the force control loop.
T is the coordinate transformation of the position control loop.