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To tackle the over-actuated and highly nonlinear characteristics that four-wheel-independent-steering and four-wheel-independent -driving (4WIS/4WID) vehicles exhibit when tracking aggressive trajectory, a hierarchical controller with layers of computation-intensive modules is commonly adopted. The high-level linear motion controller commands the desired state derivatives of the vehicle to meet the overall trajectory tracking objectives. Then the system dynamic is inversed by the mid-level control allocation layer and the low-level wheel control layer to map the target state derivatives to steering angle and motor torque commands. However, this type of controller is difficult to implement on the embedded hardware onboard since the nonlinear dynamic inversion is typically solved by nonlinear programming.

During the engaging process of sleeve and teeth ring in mechanical transmissions, their rotational speed and position differences cause multiple engaging ways and trajectories, and casual impacts between them will delay the engaging process and cause a long power off time for a gear shift. In order to reveal the engaging mechanism of the sleeve and the teeth ring, it is essential to build a high-fidelity model to cover all of their engaging ways and capture their speed changes for an impact. In this work, our contribution is that their impact process is modeled as a precise, continuous and nonlinear damping model, and then a hybrid automaton model is built to connect the system dynamics in different mechanical coupling relationships.