Previously, we have seen stiffness control in work space, which was quite obvious in terms of interactions
happen in operational space.
But what happens if we try to apply stiffness control in joint space?
Would that give us additional benefits or it is totally useless and is additional pain?
Let's try to investigate that issue.
First, let's see dynamical model of robot manipulator.
Let's take the input control as PD plus gravity control method, but applied in drawing space.
As you can see, input control is much more easier in joint space than in workspace because of not involving
complex Jacobean terms.
Let's investigate what will happen in steady state conditions, namely, wind velocity and acceleration
terms becomes zero and gravity turns cancel each other.
Don't forget this is not true in practice because we cannot model gravity term.
Exactly.
We can write Equation 1.2 in the form 1.3.
As we have learned before, we can convert joint corners to workspace coordinates using analytical Jacobean.
Now let's combine equations 1.3 and 1.4 in order to get final equations, which defines that this steady
state error.
If you analyze Equation one point five, you will see that circle term is nothing but equal in compliance.
This also gives us definition of stiffness matrix because stiffness is nothing but inverse of compliance.
This stiffness is configuration dependent because Jacobins are configuration dependent.
So all in all, implementation of stiffness control is easier in joint space because analytical Jacobins
and there are inverse are not involved.
But the stiffness term becomes rather difficult because it changes depending on configuration, which
was not a problem in workspace stiffness control.