Dynamic Modeling of a Skid-Steered Wheeled Vehicle with Experimental Verification Wei Yu, Oscar Chuy Jr., Emmanuel G. Collins Jr., and Patrick Hollis Abstract— Skid-steered vehicles are often used as outdoor mobile robots due to their robust mechanical structure and high maneuverability. Sliding along with rolling is inherent to general curvilinear motion, which makes both kinematic and dynamic modeling difficult. For the purpose of motion planning this paper develops and experimentally verifies dynamic models of a skid-steered wheeled vehicle for general planar (2D) motion and for linear 3D motion. These models are characterized by the coefficient of rolling resistance, the coefficient of friction, and the shear deformation modulus, which have terrain-dependent values. The dynamic models also include motor saturation and motor power limitations, which enable correct prediction of vehicle velocities when traversing hills. It is shown that the closed-loop system that results from inclusion of the dynamics of the (PID) speed controllers for each set of wheels does a much better job than the open loop model of predicting the vehicle linear and angular velocities. Hence, the closed-loop model is recommended for motion planning. I. INTRODUCTION Dynamic models of autonomous ground vehicles are needed to enable realistic motion predictions in unstructured, outdoor environments that have substantial changes in ele- vation, consist of a variety of terrain surfaces, and/or require frequent accelerations and decelerations. At least 4 different planning tasks can be accomplished using appropriate dy- namic models: 1) time optimal motion planning, 2) energy efficient motion planning, 3) planning in the presence of a fault, 4) reduction in the frequency of replanning. Ackerman steering, differential steering, and skid steering are the most widely applied steering mechanisms for wheeled and tracked vehicles. Ackerman steering has the advantage of good controllability [1], but has the disadvantages of low maneuverability and a complex steering subsystem [2]. Differential steering is popular because it provides high maneuverability with a zero turning radius and has a simple steering configuration [1]. However, it has limited mobility on outdoor terrains. Like differential steering, skid steering leads to high maneuverability [1], [3] and also has a simple and robust mechanical structure [4], [5]. In contrast, it has good mobility on a variety of terrains, which makes it suitable for all-terrain traversal. A skid-steered vehicle can be characterized by two fea- tures [1], [2]. First, the vehicle steering depends on control- ling the relative velocities of the left and right side wheels. Second, all wheels or tracks point to the longitudinal axis W. Yu, O. Chuy, E. Collins, and P. Hollis are with the Center for Intelligent Systems, Control and Robotics (CISCOR) and the Department of Mechanical Engineering, Florida A&M University-Florida State Uni- versity, Tallahassee, FL 32310, USA {yuwei,chuy,ecollins, hollis}@eng.fsu.edu of the vehicle and vehicle turning requires slippage of the wheels or tracks. Due to identical steering mechanisms, wheeled and tracked skid-steered vehicles share many prop- erties [2], [5], [6], [7]. Many of the difficulties associated with modeling and operating both classes of skid-steered vehicles arise from the complex wheel (or track) and terrain interaction [2], [7]. For Ackerman-steered or differential- steered vehicles, the wheel motions may often be accurately modeled by pure rolling, while for skid-steered vehicles in general curvilinear motion, the wheels (or tracks) roll and slide at the same time [2], [5], [7], [8]. This makes it difficult to develop kinematic and dynamic models that accurately describe the motion. Other disadvantages are that the motion tends to be energy inefficient, difficult to control [4], [9], and for wheeled vehicles, the tires tend to wear out faster. A kinematic model of a skid-steered wheeled vehicle maps the wheel velocities to the vehicle velocities and is an im- portant component in the development of a dynamic model. In contrast to the kinematic models for Ackerman-steered and differentially-steered vehicles, the kinematic model of a skid-steered vehicle is terrain-dependent [2], [10] and is dependent on more than the physical dimensions of the vehicle. In [2], [9] a kinematic model of a skid-steered vehicle was developed by assuming a certain equivalence with a kinematic model of a differential-steered vehicle. This was accomplished by experimentally determining the instantaneous centers of rotation (ICRs) of the sliding veloc- ities of the left and right wheels. An alternative kinematic model that is based on the slip ratios of the wheels has been presented in [6], [10]. This model takes into account the longitudinal slip ratios of the left and right wheels. The difficulty in using this model is the actual detection of slip, which cannot be computed analytically. Hence, developing practical methods to experimentally determine the slip ratios is an active research area [5], [6]. To date, there is very little published research on the experimentally verified dynamic models for general motion of skid-steered vehicles, especially wheeled vehicles. The main reason is that it is hard to model the tire (or track) and terrain interaction when slipping and skidding occur. (For each vehicle wheel, if the wheel velocity computed using the angular velocity of the wheel is larger than the actual linear velocity of the wheel, slipping occurs, while if the computed wheel velocity is smaller than the actual linear velocity, skidding occurs.) The research of [3] developed a dynamic model for planar motion by considering longitudinal rolling resistance, lateral friction, moment of resistance for the vehicle, and also the nonholonomic constraint for lateral The 2009 IEEE/RSJ International Conference on Intelligent Robots and Systems October 11-15, 2009 St. Louis, USA 978-1-4244-3804-4/09/$25.00 ©2009 IEEE 4212