Deriving equation for partial derivatives in LOCAL frame #2588
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Hi, I was reading article about partial derivatives in rigid body dynamics: but different for In |
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Replies: 3 comments
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Please have a look to https://m.roboticsproceedings.org/rss14/p38.pdf which is where I explain everything related to analytical derivatives of rigid body dynamics algorithms. As I also often explain, there is some tricks implemented in Pinocchio to avoid useless computations or accelerate computations. It is hard to list all of them in a single peace of research article. Unfortunately, the paper you mentioned is just a replicate of our work published at R:SS 2018 without real novelty as the code of Pinocchio was already implementing the computational tricks. |
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I use WORLD convention to store the quantities in a common frame to really avoid useless computations, facilitating the writing of rigid body dynamics derivatives. In case you write derivatives of WORLD or LOCAL expressed quantities, deriving the quantities depends of the frame in which you work. Please have a look to https://hal.science/hal-03758989/file/HUMANOIDS_2022_FINAL.pdf For the LOCAL context, you have to account for the partial between the current joint and the end effector. Which explains the set of computations you have extracted in your initial form. |
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Hi, Thank you very much for feedback. I did derive equation just like in source code thanks to your linked papers, but I'm still confused about partial derivatives of spatial vectors. Does partial derivatives behave same as other spatial vectors? Considering that to map acceleration vector from one frame to another you only need to use transform action like in picture below (equation (1)): Does equation (1) apply for partial derivatives? It seems like partial derivative is only "apparent derivative viewed by observer in LOCAL frame" like in equation (2) in picture, rather than full partial derivative like for time derivative (3). I am also confused about frames used in pinocchio. Is LOCAL frame a moving frame, or is it stationary frame that happen to coincide with moving one, like in Featherstone's book? |
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I use WORLD convention to store the quantities in a common frame to really avoid useless computations, facilitating the writing of rigid body dynamics derivatives.
In case you write derivatives of WORLD or LOCAL expressed quantities, deriving the quantities depends of the frame in which you work. Please have a look to https://hal.science/hal-03758989/file/HUMANOIDS_2022_FINAL.pdf
For the LOCAL context, you have to account for the partial between the current joint and the end effector. Which explains the set of computations you have extracted in your initial form.