We have an allegro hand in our robot, and it is in actuated behavior. In other words, each joint is controlled one or more than one actuator, that is motor. There are 3 actuators for each finger, since each finger has 3 joints. Since there are 4 fingers in allegro hand, it has totally 12 actuators.
However, we want to control the hand in under-actuated manner. Namely, movement of each finger must be controlled by only one actuator, not three actuators. To accomplish this, we think that we can parametrize other 2 actuators of a finger based on first actuator of the finger:
f$_1(\theta) = \theta \rightarrow joint \,\, 1$
f$_2(\theta) = 0.43\theta \rightarrow joint \,\, 2$
f$_3(\theta) = 0.25\theta \rightarrow joint \,\, 3$
The angle $\theta$ is total rotation of first joint. Rotation of second and third joint will be parameterized based on rotation of first joint. I aim to generate such a under-actuated system.
How can I do that ?
How can I determine these 3 functions and their coefficients like 0.43 and 0.25 ?