Closed-Form Analytical Model of Binding Force for Wheeled Mobile Robots with Skid-Steering Mechanism Running on Sandy Terrains

Wheeled mobile robot (WMR) with skid-steering mechanism is popular due to its simplicity and robust performance. Dynamic models of skid-steering systems are very important to their control, and binding force is one essential component of the dynamic models. Integrating the bulldozing resistance force determined using Hegedus's theory along the wheel side face to estimate the binding force is a common way. However, due to the complexity of Hegedus's equations, it is hard to use the binding force model online. To solve this problem, the equivalent wheel sinkage is utilized to compute the bulldozing resistance force, which can then be used to develop a closed-form analytical expression of binding force. The analytical model is used to compute the binding force based on the experimental results obtained using a six-wheeled mobile robot running on a sandy terrain UM-LSS1 and the measured terrain mechanical parameters. Under the specific experimental conditions described in this paper, the binding force exerted on the wheel side face can be neglected for the cases with light vehicle and low forward velocity.