PUBLISHED IN THE PROCEEDINGS OF CLAWAR’06: INT. CONF. ON CLIMBING AND WALKING ROBOTS, SEPT 2006. 1 Model-based Control of a fast Rover over natural Terrain D. Lhomme-Desages * , Ch. Grand * , J-C. Guinot * * Laboratoire de Robotique de Paris Route du Panorama, 92260 Fontenay-aux-Roses email: lhomme@robot.jussieu.fr, grand@robot.jussieu.fr, guinot@robot.jussieu.fr Abstract — A model-based control for fast autonomous four-wheel mobile robots on soft soils is developed. This control strategy takes into account slip and skid effects to extend the mobility over planar granular soils. Each wheel is independently actuated by an electric motor. The overall objective is to follow a path roughly at rel- atively high speed. Some results obtained in dynamic simulation are presented. Keywords — rover, slip control, skid-steering, wheel-soil interaction I. Introduction Many popular controllers for wheeled mobile robots assume that wheels roll without slipping [1]. This leads to a nonholonomic constraint added to the kinematic or dynamic model. This assumption is quite legitimate for usual applications such as autonomous cars over hard terrains or slow indoor exploration. However, it is no longer adequate for many applications where wheel slip cannot be neglected [2], especially for traveling over nat- ural soils at high speed [3]. Therefore, a new control scheme is required. In this paper, a model-based control method for fast autonomous mobile robots on soft soils is developed. On such a type of terrain (sand for instance), slip and skid phenomena may be significant. The control strategy takes into account these effects to extend the mobility of the vehicles over planar natural soils. A non-linear model-based control of wheel slippage is studied, using a semi-empirical wheel-soil interaction model. A higher-level control is applied to a four wheel skid-steering vehicle which can travel at relatively high speed (several meters per second). Each wheel is inde- pendently actuated by an electric motor. The control frame is developed for a four-wheel mo- bile robot. The overall objective is to follow a path at relatively high speed. This controller implies a low-level control method that aims to regulate the slip rate of one wheel, since the traction force generated by the rotation of the wheel at the contact patch depends on the wheel slip. We indicate the limits and the sensors required to apply this strategy. Finally, some results obtained in dynamic simulation are presented. We compare different kinematic struc- tures (pure skid-steering and directional wheels). A comparison is also carried out with a classical kinematic control. II. Wheel-soil contact model Several modeling frameworks can be used to calculate the efforts involved in the wheel-soil interaction process. We use an extended version of the terramechanic model introduced by Bekker ([4],[5]). We assume a rigid wheel over a soft soil (Figure 1). θ 1 θ w w R r F t F l F n ω R R D z z l v Fig. 1. Model of a rigid wheel v is the velocity of the center of the wheel. ω is the angular velocity of the wheel. In this model, the efforts depend on the slip rate s, which is defined as: s =  1 − v ω.R if Rω ≥ v 1 − ω.R v if Rω<v (1) for v> 0 and ω> 0. This definition can be extended to every (v,ω) ∈ℜ 2 , as it is shown on Figure 2. Fig. 2. slip rate as a function of v and Rω v is the linear velocity of the center of the wheel. ω is the angular velocity of the wheel. According to Bekker theory [4], the normal force de- pends on the sinkage z through: F n = 1 3  w w  k c b + k φ  (3 − n) √ Dz 2n+1 2  (2)