## 6 Comments on the Proposed Algorithm Using IQV  
The proposed control algorithm was developed for the diagonalized equations of dynamics, which were obtained from the decomposition of a symmetric inertia matrix. However, the algorithm in a simplified version is also suitable for trajectory tracking when the vehicle is described by a model with a diagonal inertia matrix. In the control strategies of recent years, it is very common that the inertia matrix is diagonal. This means that dynamic couplings are compensated by the controller. Information about the couplings is then not available. To guarantee good performance of the controller, combinations of different methods are also used. For example, the use of the following control methods can be given:  
1. SMC [9,10] or SMC and backstepping [16];
2. NN based controllers [26] (with SMC), [16,17,23,37] (with SMC and backstepping), [31] (and event-triggered control);
3. Observer-based control schemes [30] (event-triggered dynamic surface control), [28] (using fuzzy logic), [40] (line-of-sight (LOS) adaptive trajectory tracking controller with terminal sliding mode control);
4. Nonlinear model predictive control (NMPC) strategy [22];
5. Controllers with prescribed performance [33]. The proposed controller based on IQV uses SMC and backstepping methods, but also velocity transformation. Thus, it is a slightly different combination than the methods in Group 1. In NN-based methods (Group 2), additional knowledge (about NN) is required,which can improve the performance of the controller, but at the same time the control scheme is more complicated. Control strategies based on observer (Group 2) allow the use of inaccessible signals. However, the dynamics of the system with an observer also changes, which distorts the information about the dynamics of the system itself (i.e., without an observer). The IQV controller only takes into account the vehicle model. In [22], additional optimization was used, and such a mechanism is not included in the developed IQV algorithm. In the prescribed performance based methods as in [33], it is necessary to guarantee that the signals run within certain limits, while the IQV controller does not have to meet this condition. It is worth recalling some control strategies suitable for asymmetric vehicles because the proposed algorithm belongs to this group. However, one should point out the differences between it and selected controllers developed in recent years and performing the same task. 1. SMC [39];
2. Controllers using NN [34], ref. [36] (disturbance observer, backstepping, prescribed performance);
3. Observer-based approaches [41] (prescribed performance), ref. [44] (Lyapunov approach), ref. [43] (Lyapunov and backstepping control methods);
4. Input-output linearization [42];
5. Controllers with prescribed performance [64]. The differences between the proposed algorithm and the previously mentioned control methods have already been indicated. However, the methods for vehicle models with asymmetry serve the same purpose as the proposed algorithm. The method described in [42] uses the transformation of coordinates and for this reason it was chosen for comparison in the simulation test. This article focuses on showing the operation of the control scheme using IQV, but ignores its other important property known in the literature. The dynamical equations denoted can also be used to study vehicle dynamics (e.g., coupling estimation), as shown for fully actuated vehicles in [49]. An identical possibility is not provided by the aforementioned control strategies for asymmetric vehicles, because, although the model equations can be transformed so that the accelerations are independent, e.g., in [36; 42; 64], the inertial couplings are only transformed (the diagonalizing method of the acceleration equations is not used). In addition, the authors of these papers did not indicate that their proposed strategies can be used to analyze vehicle dynamics, while the offered controller can be used for this purpose during the trajectory tracking task.