## 5 Conclusions
\begin{tabular}{l l} MASSA & maximum absolute value of the side-slip angle over simulation horizon \\ MASSAR & maximum absolute value of side-slip angular rate over simulation horizon \\ MPC & model predictive control \\ MPCC & MPC with CTSAs \\ MPCN & MPC without CTSAs \\ RWS & rear wheel steering \\ SMC & sliding mode control \\ TFM & tire force margin derived from the friction circle (N) \\ VSC & vehicle stability control \\ WLS & weighted least square \\ \(C_{f}\), \(C_{r}\) & cornering stiffness of front and rear tires (N/rad) \\ \(e_{y}\), \(e_{g}\) & lateral offset error (m) and heading error (rad) \\ \(F_{x}\), \(F_{y}\), \(F_{z}\) & longitudinal, lateral and vertical tire forces of a tire (N) \\ \(F_{xi}\), \(F_{yi}\), \(F_{zi}\) & longitudinal, lateral and vertical tire forces of \(i\)-th wheel (N) \\ \(F_{yf}\), \(F_{yr}\) & front and rear lateral tire forces in the 2-DOF bicycle model (N) \\ \(F_{y,max}\) & maximum lateral tire force of a tire at \(\alpha=\alpha_{m}\) (N) \\ \(\mathbf{z}\) & matrix used for the constraint on RWS and 4 WS in WLS based method \\ \(l_{z}\) & yaw moment of inertial (kg\(\cdot\)m\({}^{2}\)) \\ \(l_{i}\) & LQ cost function for the input configuration \(IC\#i\) \\ \(\mathrm{K}_{\mathrm{LQR},i}\) & gain matrix of LQR for input configuration \(IC\#i\) \\ \(k_{v}\) & velocity gain for preview distance (s\({}^{-1}\)) \\ \(L_{p}\) & preview distance (m) \\ \(l_{r}\), \(l_{r}\) & distance from a center of gravity to front and rear axles (m) \\ \(M_{X}\), \(M_{Y}\) & differences between x- and y-positions at the peak points of the target path (m) \\ \(M_{DX}\), \(M_{SX}\) & response and settling delays of vehicle trajectory with respect to target path (m) \\ \(M_{OS}\) & percentage overshoot along y-direction in the lower lane of the target path \\ \(N\) & prediction horizon of MPC \\ \(m\) & vehicle total mass (kg) \\ \(\mathbf{q}\) & vector of tire forces as a solution of WLS based method \\ \(T_{Bi}\), \(T_{Di}\) & braking and traction torques generated at \(i\)-th wheel from \(\Delta M_{z}\) (N\(\cdot\)m) \\ \(T_{s}\) & sampling interval of discrete-time system (s) \\ \(t_{r}\), \(t_{r}\) & half of track widths of front and rear axles (m) \\ \(v_{x}\), \(v_{y}\) & longitudinal and lateral velocities of CoG of a vehicle (m/s) \\ \(\alpha\) & tire slip angle (rad) \\ \(a_{m}\) & tire slip angle where the maximum lateral tire force comes out (rad) \\ \(\alpha_{f}\), \(a_{r}\) & tire slip angles of front and rear wheels (rad) \\ \(\beta\) & side-slip angle of CoG of a vehicle (rad) = tan\({}^{-1}(v_{y}/v_{x})\approx(v_{y}/v_{x})\) \\ \(\delta_{f}\), \(\delta_{r}\) & front and rear steering angles as a control input in LQR and MPC (rad) \\ \(\Delta F_{yr}\) & control lateral tire force of rear wheels generated by an actuator (N) \\ \(\Delta F_{xi}\) & control longitudinal tire force at \(i\)-th wheel, generated by an actuator (N) \\ \(\Delta M_{z}\) & control yaw moment as a control input in LQR and MPC (N\(\cdot\)m) \\ \(\eta\) & tuning parameter on relaxation term of equality constraint \\ \(\gamma\), \(\gamma_{d}\) & real and reference yaw rates (rad/s) \\ \(\chi\) & curvature at a particular point on a target path (m\({}^{-1}\)) \\ \(\kappa_{i}\) & virtual weight on the longitudinal and lateral tire forces \\ \(\kappa\) & the vector of virtual weights \\ \(\xi_{i}\) & the maximum allowable value of \(i\)-th term in LQ cost function \\ \(\varphi\) & heading angle of a vehicle (rad) \\ \(\varphi_{d}\) & desired heading angle obtained at preview point (rad) \\ \(\mu\) & tire-road friction coefficient \\ \(\rho_{i}\) & weight on \(i\)-th term in LQCF \\ \(\Theta\) & weighting matrix of WLS based method \\ \(\zeta\) & the product of \(\mu\) and \(F_{z}=\mu F_{z}\) \\ \end{tabular}