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 ?

  • $\begingroup$ Maybe i don’t understand...you can already control all joints? I dont know how you nornally control your motors, but do you not have to give a position to them already? Can’t you simply choose the parameters and multiple them by the theta you already know? Please explain your current method of control, ie programming, some kind of interface, whatever and how you find the angles for each actuator already, then maybe i can help :) $\endgroup$ Aug 19, 2019 at 16:58
  • $\begingroup$ I'm having a hard time imagining what this setup looks like. It's simply 2 motors to 1 input? Why does the gripper have two motors? Power? space? cost? are the inputs not the same? $\endgroup$
    – tuskiomi
    Aug 19, 2019 at 16:58

1 Answer 1


I don’t think underactuated is the proper term. You are trying to control multiple actuators with a single DOF. That is redundancy resolution. I have used the Simplex Method to compute stable grasps for redundant finger devices - that method resolved the redundancy in a least-norm sense.

There are hundreds of research papers, going back to at least the 1980s (probably earlier) that discuss relative finger joint angles for different grasp types. For example, many papers describe human-preferred joint ratios for hands accomplishing “cylindrical grasps” of various sized cylinders. Others provide the same information for fingertip grasps, in which the normal vector from the surface of the fingertip is normal to the surface of the object.

You can search for keywords such as “grasp joint angle ratio finger” to find specific papers that postulate these ratios.

  • $\begingroup$ Rather than the term "redundancy", I would definitely favor the term "synergy". $\endgroup$ Jan 12, 2021 at 14:52

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