High-speed Visual Feedback Control for Grasping and Manipulation - Visual Servoing via Advanced Numerical Methods - page 38

(a) SW mode (b) HT mode

Fig. 3.1 Hybrid trajectory [10]

Object
trajectory

Desired
joint angle

Command
torque

Trajectory
generator

Manipulator
Dynamics

Stereo
Vision

f

Controller

- q d

+ p o

t

Time

Joint
angle

q

Fig. 3.2 Block diagram

the function of the time variable t , and it makes easy to design a controller. We call
this motion the “SW” mode. Then, the hitting motion is the tracking of the change
of a ball trajectory, and this motion is necessary to hit a ball precisely. This motion
can be achieved by mapping the trajectory of the manipulator to the ball position
directly. This motion is represented as the function of the object position p 0 .We
call this motion the “HT” mode.
By integrating the two modes, the desired trajectory of the joint angle vector of
the manipulator q d ∈ R

n

is defined as

n

q d = f ( p 0 , t ) ∈ R , (3.1)

where f is an appropriate nonlinear function, and n is the number of joints. The joint
angle vector q is controlled so as to track q d using an appropriate controller. Figure
3.2 shows the block diagram.

3.2.2 System Configuration

Figure 3.3 shows the high-speed robot system. A human throws a ball toward the
manipulator from 2 5 m distance. The manipulator hits the ball toward an objective

point. Figure 3.4(b) shows a photo of the system.

.