YouMyNerfHerder
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- Nov 25, 2019
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Hi all, first time posting. The quick and dirty: I'm a PhD student studying neuroscience, but some calculus has recently come up in one of my studies. Any help in clarification would be greatly appreciated.
Basics of the study: We had people grasp a robotic handle that was interfaced with a computer display. The computer monitor would show both a moving target (imagine a circle moving around a figure-of-eight path) as well as a circle corresponding to the position of the participant's hand. Participants were instructed to overlay their circle (denoting their hand position) with the target circle. We were interested in calculating tracking error with a few different metrics (I'll only discuss 2 here).
Longitudinal component: Determines whether the hand is ahead of or behind the target. Positive value denotes ahead, negative denotes behind.
Normal component: Determines whether the hand is to the right or the left of the target, relative to the trajectory of the target. I.e. if the target is moving left-to-right, left of target would be up, right of target would be down.
My confusion is how the longitudinal and normal components are calculated. I've attached a screenshot of a previous study that used the same formulas that we're using, as well as a diagram to explain some things.
Legend:
PH -> Position of the hand
PT -> Position of the target
Ul -> Longitudinal vector
Un -> Normal vector
Delta -> Tracking error (hypotenuse of x and y positional error)
Deltal -> Longitudinal error
Deltan -> Normal erorr
So for the first equation, I'm a little lost as to what's going on. From what I understand, the vector Ul (of the target) is calculated by the inversion of the hypotenuse in the velocity domain (derivates of x and y). And then it's multiplied by a matrix of the derivate of x and y? Why? And then this equals the velocity of x and the velocity of y represented in a matrix?
I'm totally out to lunch for the second equation.
The rest is fairly straight forward. Deltal is calculated from the positional error multiplied by Ul and Deltan is calculated by the positional error multiplied by Un. Again, I don't quite understand what Ul or Un mean or why we calculate them with these formula.
Thanks in advance!
Basics of the study: We had people grasp a robotic handle that was interfaced with a computer display. The computer monitor would show both a moving target (imagine a circle moving around a figure-of-eight path) as well as a circle corresponding to the position of the participant's hand. Participants were instructed to overlay their circle (denoting their hand position) with the target circle. We were interested in calculating tracking error with a few different metrics (I'll only discuss 2 here).
Longitudinal component: Determines whether the hand is ahead of or behind the target. Positive value denotes ahead, negative denotes behind.
Normal component: Determines whether the hand is to the right or the left of the target, relative to the trajectory of the target. I.e. if the target is moving left-to-right, left of target would be up, right of target would be down.
My confusion is how the longitudinal and normal components are calculated. I've attached a screenshot of a previous study that used the same formulas that we're using, as well as a diagram to explain some things.
Legend:
PH -> Position of the hand
PT -> Position of the target
Ul -> Longitudinal vector
Un -> Normal vector
Delta -> Tracking error (hypotenuse of x and y positional error)
Deltal -> Longitudinal error
Deltan -> Normal erorr
So for the first equation, I'm a little lost as to what's going on. From what I understand, the vector Ul (of the target) is calculated by the inversion of the hypotenuse in the velocity domain (derivates of x and y). And then it's multiplied by a matrix of the derivate of x and y? Why? And then this equals the velocity of x and the velocity of y represented in a matrix?
I'm totally out to lunch for the second equation.
The rest is fairly straight forward. Deltal is calculated from the positional error multiplied by Ul and Deltan is calculated by the positional error multiplied by Un. Again, I don't quite understand what Ul or Un mean or why we calculate them with these formula.
Thanks in advance!
