## 4 Simulation and Analysis
### Simulation Results  
MMS steering angle simulation results with distribution and coupling control are shown in Figure 9. In CM, IR, DM, and SM, the switching time in coupling control is shorter than that used in distribution control. The mode switching times for CM, IR, DM, and SM are respectively 4.9 s, 3.4 s, 3.3 s, and 4.2 s, respectively, under coupling control. Under distribution control, the mode switching times are 6.1 s, 4.8 s, 5.1 s, and 5.5 s, respectively. Of these four motions, the IR mode switching time is the shortest whether coupling or distribution control is used. This is primarily due to the small, symmetrical rotation angles of the four OSMs. The average steering angle errors of the four OSMs are 0.4\({}^{\circ}\), 0.3\({}^{\circ}\), 0.6\({}^{\circ}\), and 0.6\({}^{\circ}\) for CM, IR, DM, and SM, respectively, under coupling control. Under distribution control, their respective errors are 1.4\({}^{\circ}\), 1.1\({}^{\circ}\), 1.7\({}^{\circ}\), and 1.6\({}^{\circ}\). In addition, Figure 9d shows that the relationships between the two front and two rear wheels are better maintained under coupling control than under distribution control. The results demonstrate that there is good steering angle symmetry and uniformity among the four OSMs during coupling control mode switching. Overall, the four OSM steering angles exhibit better synchronization under the proposed control methodology than under distribution control. Angular velocity distribution and coupling control MMS simulation results are shown in Figure 10. In all motion modes, the angular velocity first increases and then decreases smoothly. All modes exhibit maximum angular velocity. Under distribution control, the angular velocity responses are slower than under coupling control. The maximum angular velocities are all smaller as well. The maximum angular  
Figure 9: Steering angle curves of four off-center arms during motion mode switching: (**a**) cross motion; (**b**) in-place rotation; (**c**) diagonal motion; (**d**) steering motion. velocities of the four OSMs do not maintain good symmetry under distribution control. For example, in CM, the maximum angular velocities are all nearly 0.74 rad\(\cdot\) s\({}^{-1}\) but only 0.63 rad\(\cdot\) s\({}^{-1}\), 0.61 rad\(\cdot\) s\({}^{-1}\), 0.60 rad\(\cdot\) s\({}^{-1}\), and 0.62 rad\(\cdot\) s\({}^{-1}\) for the left front, right front, left rear, and right rear OSMs, respectively, under distribution control. Results from the other three motion modes are similar to those from CM. The CM, IR, and SM time differences are all above 1 s. The biggest mode switching time difference between coupling and distribution control occurs during DM. The time difference for this motion can reach approximately 2 s. One can speculate that the angular velocities of the four OSMs under coupling control show better synchronicity than those under the proposed control methodology. The OSM CE curves for all motion modes are shown in Figure 11. We take the CE between wheel 1 and wheel 2 as an example for analysis. Obviously, the CEs are greater under distribution control than under coupling control. The respective absolute maximum angular velocity CEs during CM, IR, DM, and SM are 0.008 rad\(\cdot\) s\({}^{-1}\), 0.006 rad\(\cdot\) s\({}^{-1}\), 0.011 rad\(\cdot\) s\({}^{-1}\), and 0.007 rad\(\cdot\) s\({}^{-1}\) under distribution control. The respective average CEs are 0.002 rad\(\cdot\) s\({}^{-1}\), 0.001 rad\(\cdot\) s\({}^{-1}\), 0.003 rad\(\cdot\) s\({}^{-1}\), and 0.003 rad\(\cdot\) s\({}^{-1}\) for these four motions. In coupling tests, the maximum CEs are 0.004 rad\(\cdot\) s\({}^{-1}\), 0.002 rad\(\cdot\) s\({}^{-1}\), 0.006 rad\(\cdot\) s\({}^{-1}\), and 0.003 rad\(\cdot\) s\({}^{-1}\), respectively, and the average CEs are 0.0008 rad\(\cdot\) s\({}^{-1}\), 0.0004 rad\(\cdot\) s\({}^{-1}\), 0.001 rad\(\cdot\) s\({}^{-1}\), and 0.0009 rad\(\cdot\) s\({}^{-1}\), respectively. Clearly, the CEs change randomly throughout MMS during distribution control tests.