TABLE I.

Examples of analytical expressions obtained using symbolic and the different polynomial regressions for one of the tendons of the robotic system.

Regression	Expressions
Symbolic	13.7sin(θ1 − 0.78) + 12.3θ2 + 8.48θ3 + 4.02θ3sin (θ3) + 14.5
Linear	9.26θ1 + 12.6θ2 + 11.8θ3 + 7.26
Quadratic	$\begin{array}{l}3.77{\theta }_1^2+0.89{\theta }_2^2+2.2{\theta }_3^2-0.338{\theta }_1{\theta }_2-0.457{\theta }_2{\theta }_3-\\ 0.142{\theta }_3{\theta }_1+8.35{\theta }_1+11.2{\theta }_2+9.7{\theta }_3+5.24\end{array}$
Cubic	$\begin{array}{l}-1.89{\theta }_1^3-2.05{\theta }_2^3-1.56{\theta }_3^3-0.438{\theta }_1^2{\theta }_2+\\ 0.258{\theta }_1{\theta }_2^2-0.0127{\theta }_1^2{\theta }_3+0.281{\theta }_3^2{\theta }_1-\\ 0.163{\theta }_2^2{\theta }_3+0.287{\theta }_3^2{\theta }_2+0.494{\theta }_3{\theta }_2{\theta }_1+4.8{\theta }_1^2+\\ 5.63{\theta }_2^2+5.02{\theta }_3^2-0.571{\theta }_2{\theta }_3-0.949{\theta }_1{\theta }_3-\\ 0.367{\theta }_1{\theta }_2+10.3{\theta }_1+8.88{\theta }_2+8.78{\theta }_3+4.83\end{array}$
Quartic	$\begin{array}{l}-1.26{\theta }_1^4+0.26{\theta }_2^4-0.0831{\theta }_3^4+0.208{\theta }_1^3{\theta }_2-\\ 0.635{\theta }_2^3{\theta }_1+0.756{\theta }_2^3{\theta }_3-0.222{\theta }_3^3{\theta }_2-0.26{\theta }_3^3{\theta }_1-\\ 0.159{\theta }_1^3{\theta }_3-0.0594{\theta }_1^2{\theta }_2^2+0.0947{\theta }_3^2{\theta }_1^2-\\ 0.824{\theta }_2^2{\theta }_3^2+0.0728{\theta }_3{\theta }_2^2{\theta }_1-0.112{\theta }_3^2{\theta }_2{\theta }_1-\\ 0.135{\theta }_3{\theta }_2{\theta }_1^2+1.08{\theta }_1^3-3.0{\theta }_2^3-0.903{\theta }_3^3+\\ 1.44{\theta }_2^2{\theta }_1+0.0506{\theta }_2{\theta }_1^2+0.109{\theta }_3{\theta }_1^2+\\ 0.516{\theta }_3{\theta }_2{\theta }_1+1.95{\theta }_3^2{\theta }_2+0.881{\theta }_3^2{\theta }_1-\\ 0.677{\theta }_3{\theta }_2^2+6.05{\theta }_1^2+6.64{\theta }_2^2+3.71{\theta }_3^2-\\ 1.26{\theta }_2{\theta }_1-1.54{\theta }_3{\theta }_2-1.11{\theta }_3{\theta }_1+9.72{\theta }_1+\\ 8.52{\theta }_2+9.44{\theta }_3+4.7\end{array}$