Modeling and Animating Human Figures - Computer Animation: Algorithms and Techniques - page 296

00 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15

Values indicate potentials
induced by obstacles 00 30 30 30 29 28 27 26 28 29 30 31 32 33 33 33 33

01 30 26 25 24 23 22 21 22 23 24 25 26 27 28 29 33

02 30 25 24 23 22 21 20 21 22 23 24 25 26 27 28 33

03 29 24 23 24 28 26 19 20 21 22 25 26 27 28 29 34

Polygons indicate
obstacles

04 28 23 22 28 28 19 18 19 20 29 30 31 32 34 30 34

05 27 22 21 26 19 18 17 16 17 24 21 02 06 34 03 34

Goal position for
end effector

06 26 21 20 25 18 17 16 15 16 17 02 01 02 01 02 07

07 25 20 19 18 17 16 15 14 05 12 11 15 01 02 03 00

08 24 19 18 17 16 15 14 13 12 11 10 05 04 03 04 00

09 25 20 19 18 17 16 15 12 11 10 09 06 05 04 05 10

10 25 21 20 19 18 15 14 13 12 11 06 07 06 05 06 15

Selected key frames from
path of arm computed by
genetic algorithm

11 25 25 25 24 23 16 15 14 13 12 09 08 09 10 11 16

12 26 26 26 25 24 17 18 15 16 22 12 11 10 11 12 17

13 27 22 21 20 19 18 17 18 17 18 13 12 11 12 13 18

14 27 23 22 21 20 19 18 17 16 15 14 13 12 13 14 18

Initial configuration
of arm

15 27 27 27 26 25 24 23 22 23 23 23 18 17 18 18 18

FIGURE 9.13
Path planning result [ 48 ] .

9.2.6 Strength
As anyone who has ever changed a spark plug in a car knows, avoiding all the obstacles and getting a
tool in the correct position is only half the battle. Once in position, the arm and hand must be in a con-
figuration in which there is enough strength available to actually dislodge the plug. To simulate more
realistic motions, strength criteria can be incorporated into the task planning [ 42 ]. As previously noted,
typical reaching motion problems are usually underconstrained, allowing for multiple solutions. The
solution space can be searched for a specific motion that is acceptable in terms of the amount of strain it
places on the figure.
When a specific motion is proposed by a kinematic planner, it can be evaluated according to the
strain it places on the body. The strain is determined by computing the torque necessary at each joint to
carry out the motion and rating the torque requirements according to desirability. Given the current
pose for the figure, the required joint accelerations, and any external forces, the torque required at each
joint can be calculated. For each joint, the maximum possible torque for both flexion and extension is
given as a function of the joint's angle as well as that of neighboring joints. A comfort metric can be
formed as the ratio of currently requested torque and maximum possible torque. The comfort level for
the figure is computed by finding the maximum torque ratio for the entire body. The most desirable
motions are those that minimize the maximum torque ratio over the duration of the motion.