Torque Vectoring (IJAT)

Kalman Filter Model

$$ X = \begin{bmatrix} V_x \\ V_y \\ \gamma \\ F_{yfl} \\ F_{yfr} \\ F_{yrl} \\ F_{yrr} \\ \end{bmatrix} \in{R^{7}} $$

$$ u = \begin{bmatrix} \frac{\delta_1 + \delta_2}{2} \\ T_{fl} = T_{dfl}-T_{bfl}\\ T_{fr} = T_{dfr}-T_{bfr}\\ T_{rl} = T_{drl}-T_{brl}\\ T_{rl} = T_{drl}-T_{brl}\\ \end{bmatrix}\in{R^{9}} $$

$$ z = h(X)+\textbf{V}=\begin{bmatrix} V_x \\ V_y \\ \gamma \\ a_x \\ a_y \\ \end{bmatrix}\in{R^{5}} $$

---

System model

$$ f(X) = \begin{bmatrix} \frac{1}{m} \left( \frac{1}{R}(u_2 + u_3) \cos(u_1) - (x_4 + x_5) \sin(u_1) + \frac{1}{R}(u_4 + u_5) - C_{av} x_1^2 \right) + x_2 x_3 \\ \frac{1}{m} \left( \frac{1}{R}(u_2 + u_3) \sin(u_1) + (x_4 + x_5) \cos(u_1) + (x_6 + x_7) \right) - x_1 x_3 \\ \frac{1}{m} \left( l_f \left( \frac{1}{R}(u_2 + u_3) \sin(u_1) + (x_4 + x_5) \cos(u_1) \right) + t \left( \frac{1}{R}(u_2 - u_3) \cos(u_1) + (-x_4 + x_5) \cos(u_1) + \frac{1}{R}(u_4 - u_5) \right) - l_r (x_6 + x_7) \right) \\ \frac{x_1}{\sigma} \left( -x_i + \overline{F}_{yj} \right) \\ \end{bmatrix} $$

where $i$=[4, 5, 6, 7], $j$=[fl, fr, rl, rr]

---

Mesurement model

$$ h(X) = \begin{bmatrix} x_1 \ (=V_x) \\ x_2 \ (=V_y) \\ x_3 \ (=\gamma) \\ \frac{1}{m}[\frac{(u_2+u_3)}{R}cos(u_1) - (x_4+x_5)sin(u_1)+\frac{(u_4+u_5)}{R}-C_{av}x_1^2] \\ \frac{1}{m}[\frac{(u_2+u_3)}{R}sin(u_1) + (x_4+x_5)cos(u_1)+x_6+x_7] \end{bmatrix}, where \ R \ is \ radius \ of \ tire $$

---

Optimization data

You can access the data for cornering stiffness optimization at the following link

https://drive.google.com/drive/folders/1Z1bGMPGGy64C2DSpo4TEib-w9FsFJz2Y?usp=sharing