HCR - Lecture 10

HCR - Green Robots

Robot covered in green screen to be used in the metaverse for moving real objects, the green screen allows an easy replacement of the robot image, it can be invisible to the eye of the beholder (wearing a VR headset).

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• Ideas:
  • Metaverse with physical interactions (enabled by robotics) then you can get many new ideas of paradigms of interactions

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HCR - Calculating the Controlled Forces

${\vec{W}}_c=\overline{\stackrel{ˉ}{G}}\cdot \left[\begin{array}{l}{F}_{c1}\\ F_{c1}\end{array}\right]$Where:

• $W_c$ is in the columns space of $\overline{\stackrel{ˉ}{G}}$.NOT_SURE_ABOUT_THIS What does it mean?
  ⇒ G has max rank so it has $1$ or $\infty$ solutions.
  ⇒ ($\infty$ solutions $\iff$ $N(G)\ne \{0\}$)

Then:$\overline{\stackrel{ˉ}{F_c}}={\overline{\stackrel{ˉ}{G}}}^{\#}\cdot {\vec{W}}_c+N_G\cdot \xi$Where:

• ${\overline{\stackrel{ˉ}{G}}}^{\#}$ : pseudo-inverse
• $N_G$ : free parameter vector ($N_G=N(G)$)
• ${\overline{\stackrel{ˉ}{G}}}^{\#}\cdot {\vec{W}}_c$ : solution of the linear system
• ==Among all the $\xi$ we chose one such that $\overline{\stackrel{ˉ}{F_c}}=[F_{c1},F_{c2}]$ belongs to the friction cones==.

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• ~ Ex.:
  • Given an object and some contact points:
    
    We want to calculate: ${\vec{W}}_c=\overline{\stackrel{ˉ}{G}}\cdot {\left[{\vec{F}}_{c1},{\vec{F}}_{c2},{\vec{F}}_{c2}\right]}^T$So:
    1. Compute $\overline{\stackrel{ˉ}{G}}$ :
       
    2. Calculate the nullspace of $G$ : $N(G)$
       
    3. Find $\xi$ such that:
       

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