Corrections to “Micropositioning and Control of an Underactuated Platform for Microscopic Applications”

1. In [1], there is an error in Equation (20). ${\mathbf{G}}_{\theta }=[\frac{C_{\theta }{K}_1}{H},\frac{C_{\theta }{K}_2}{H}]$, a 1×2 matrix with full row rank, should have a right inverse instead of the left inverse in Equation (20). Hence, Equation (20) in [1] has been corrected

   From:

   $${\mathbf{u}}_{rot}={({\mathbf{G}}_{\theta }^T{\mathbf{G}}_{\theta })}^{-1}{\mathbf{G}}_{\theta }^T{\stackrel{.}{\theta }}_d+k_{rot}{[1,1]}^{T}sgn(s_1)$$ (20)
   To:

   $${\mathbf{u}}_{rot}={\mathbf{G}}_{\theta }^T{({\mathbf{G}}_{\theta }{\mathbf{G}}_{\theta }^T)}^{-1}{\stackrel{.}{\theta }}_d+k_{rot}{[1,1]}^{T}sgn(s_1)$$ (20)
2. Additionally, there was a typographical error in the last part of the sentence in [1] after Equation (24), where ‘slop’ was mentioned in the sentence, instead of ‘slope’. The following correction has been made:

   • In Section IV-A, the sentence, “The desired sliding line in the $XY$ plane that consists of a set of points $\{(x,y)\}=(x_O^W,y_O^W)\mid J_c=J_d\}$ can be defined as

     $$y=a(x-{(x_O^W)}_d)+{(y_O^W)}_d$$ (24)
     where $a$ is the slop of the sliding line.” has been corrected to “The desired sliding line in the $XY$ plane that consists of a set of points $\{(x,y)\}=(x_O^W,y_O^W)\mid J_c=J_d\}$ can be defined as

     $$y=a(x-{(x_O^W)}_d)+{(y_O^W)}_d$$ (24)
     where $a$ is the slope of the sliding line.”