## 4 Experimental Results
### Basic Performance Test  
To test the basic performance of the iterative controller proposed in this paper, we conducted the first simulation experiment for various trajectory tracking tasks by directly driving the two wheels of the mobile robot shown in Figure 3. Four typical trajectory tracking tasks were used in the first simulation: circular trajectory, combination trajectory of arc and straight, cardioid-like trajectory, and spiral-like trajectory. **Trajectory 1:** The circular trajectory is a closed path composed of a single arc. The circle's center is \(P_{\mathrm{C1}}(0,0)\), the radius length is \(R_{1}=10\:\mathrm{m}\), and the initial point is \(P_{0}(0,10)\). The mobile platform needs to return to the initial position by rotating \(360^{\circ}\) in the counterclockwise direction of the circular trajectory, the total time of the trajectory is \(t_{\mathrm{s}}=2\:\mathrm{s}\), the sampling time is \(d_{t}=0.001\:\mathrm{s}\), and the initial position and posture of the mobile platform is \((0,10,\pi/2)\). **Trajectory 2:** The combination trajectory of arc and straight is also a closed path composed of two arcs and two straight lines. In this path, the center of first arc is \(P_{\mathrm{C1}}(0,0)\), and the radius is \(R_{1}=5\:\mathrm{m}\); the center of second arc is \(P_{\mathrm{C2}}(0,-10)\), the radius is \(R2=5\:\mathrm{m}\); the two straight lines connect the upper points and the lower points of the two arcs. The mobile platform needs to rotate \(360^{\circ}\) in the counterclockwise direction along the combination trajectory and return to the initial position. The time of each arc is \(t_{\mathrm{C1}}=t_{\mathrm{C2}}=0.5\:\mathrm{s}\), the time of each straight line is \(t_{\mathrm{L1}}=t_{\mathrm{L2}}=1\:\mathrm{s}\), the total time of the combination trajectory is \(t_{\mathrm{s}}=3\:\mathrm{s}\), the sampling time is \(d_{t}=0.001\:\mathrm{s}\), and the initial position and posture of the mobile platform are \((0,5,\pi/2)\). **Trajectory 3:** The cardioid-like trajectory is a closed path composed of multiple semi-circles. In this path, the center of the first semicircle is \(P_{\mathrm{C1}}(0,0)\), the radius is \(R_{1}=2.5\:\mathrm{m}\), and the starting point of the first semicircle is (2.5,0). The mobile platform arrives at the endpoint of the first semicircle trajectory by rotating \(180^{\circ}\) in the counterclockwise direction. The starting point of the second semicircle is set as the first endpoint, the center of the second semicircle is \(P_{\rm C2}(2.5,0)\), and the radius is \(R_{2}=5\) m. The mobile robot rotates \(180^{\circ}\) in the counterclockwise direction to the endpoint of the second semicircle trajectory. The starting point of the third semicircle is set as the second endpoint, the center of the third semicircle is \(P_{\rm C3}(5,0)\), and the radius is \(R_{3}=2.5\) m. The mobile robot returns to the initial position of the cardioid-like trajectory by rotating \(180^{\circ}\) in the counterclockwise direction. The duration for first and third semicircle is \(t_{\rm C1}=t_{\rm C3}=0.5\) s, the time of the second semicircle is \(t_{\rm C2}=1\) s, the total time is \(t_{\rm s}=2\) s, the sampling time is \(d_{t}=0.001\) s, and the initial position and posture of the mobile platform are \((2.5,0,\pi/2)\). **Trajectory 4:** The spiral-like trajectory is an open path composed of multiple semicircles. In this path, the center of the first semicircle is \(P_{\rm C1}(0,0)\), the radius is \(R_{1}=3\) m, and the starting point of first semicircle is \((2.5,0)\). The mobile platform arrives at the endpoint of the first semicircle trajectory by rotating \(180^{\circ}\) in the counterclockwise direction. The starting point of the second semicircle is set as the first endpoint, the center of the second semicircle is \(P_{\rm C2}(0.5,0)\), and the radius is \(R_{2}=3.5\) m. The mobile platform rotates \(180^{\circ}\) in the counterclockwise direction to the endpoint of the second semicircle trajectory.