Determining the graspable range of a robot arm

Question

I have a 6 DOF robot arm, and I want to do some object grasping experiments. Here, the robot is rigidly mounted to a table, and the object is placed on a different adjacent table. The robot must pick up the object with its gripper parallel to the normal of the object's table, such that it is pointing directly downwards at the point of grasping.

Now, the two tables have adjustable heights. For any given height difference between them. there will be a fixed range of positions over which the robot arm can achieve this perpendicular pose. What I am trying to figure out, is what the optimum relative distance of the tables is such that this range of positions is maximum.

Is there a way to compute this analytically given the robot arm kinematics? Or is there a solution which applies to all robot arms (e.g. it is optimum when the tables are at the same height)?

If it is important, the arm is the Kinova MICO: https://www.youtube.com/watch?v=gUrjtUmivKo.

Thanks!

Answer 1

I think this is fundamentally a question of maximizing manipulability of a closed kinematic chain (the chain is closed by the object being grasped).

The good news is that others have asked and tried to answer this question. The bad news is that it's far from trivial and there's no easy analytic solution. This paper came to mind when I read the question: https://dx.doi.org/10.1115/1.2829312. (You can find a pdf if you search online.)

Since you're not choosing any other kinematic parameters other than table height, it'd probably be easiest to just find a good spot with some trial and error.