Historically, trapezoidal velocity profiles have been widely used to control engines. Nevertheless, the evolution of robots and their uses has led to the need of using smoother profiles, due to the demand of high precision and delicate movements. It has been shown that this can be achieved by minimizing the change of acceleration and using s-curve profiles. Moreover, to provide a good control of the movement of a robot, it is necessary to ensure that it will meet the desired velocity profile. Therefore, a way to prevent how the wheels will react on the soil becomes highly useful, in order to adapt the supplied torque. This thesis suggests a model to define an appropriate s-curve velocity profile given the desired starting and ending kinematic states for a mobile robot. The study is then focused on a one-wheel system to define the interaction between the soil and a wheel. This interaction is modelled and extended in order to calculate the required torque, drawbar pull and power needed to fulfil the desired s-curve velocity profile. Finally, an introduction to unicycle robots is given as an example of how the proposed models could be applied in the motion planning of a mobile robot. Key words: terramechanics, s-curve, jerk, velocity profile

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