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Recently I'm reading 《Morion Control of Rendundant Robots under Joint Constraints:Saturation in the Null Space》 and have a few questions. 1.In the end of Section 2, the author mentioned that they can obtain the largest possible reduncing factor s=0.9091 with their algorithm. I don't understand why they can get this result by using a null-space velocity vector Qndot=[-0.4913 0.8537 -0.6093 -0.9007]. 2.The pseudocode of SNS algorithm at the velocity level, how to choose or calculate an appropriate null-space velocity vector? What's the difference between this vector and several objective functions?

I'd like to appreciate so much if someone can help me to get through this part. It confused me a lot.

Actually, I think that one of the situation we have to use SNS algorithm is that when the robotic arm is close to the singular position, because singularity of Jacobian matrix may cause large velocity and over constraints. Is this thoughts correct?

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