Modelling of mobile vehicles for simulation and control

The goal of the thesis is to realize a dynamic model of the differential drive robot Agilino. Dynamic models are fundamental in all the robot design phases. Both mechanical design and control software design phases need a model to proceed. Of course different design goals need different models to be used. The last statement lays on the awareness that a general model including all the robot dynamical aspects can be diffcult to realize and also useless with respect to the effort needed to find it. Of course, more general the model is, better it is but also more complex. Therefore, some dynamical aspects are usually simplified or neglected depending on the purpose of the model. In this thesis three models for three different purposes are researched: 1. The first model goal is to be as general as possible in order to be used as the real wheeled mobile robot until the first prototype is realized. To take into account many dynamical aspects in an easy and intuitive way the multi body programme Adams was chosen to realize this model. The following two mathematical models will be refined using this first one as the reference. 2. The second model is less general than the previous one because it is built computing the robot dynamic equations. It is needed to translate into mathematical equations the first model results in order to get a better understanding of the robot. It will be used in the motors choice and to plan safe trajectories for the robot. Safe trajectories stand for trajectories where the non-sliding and non-slipping constraints are respected at the robot driving wheels. 3. The third and last model is a mathematical model as the second one but simpler since its purpose is the realization of a control algorithm to drive the motors. All the dynamical aspects that will be neglected will be considered as disturbances and the control algorithm should be robust enough to deal with them. Therefore, the thesis purpose is to control the robot motion so that it follows the desired trajectories. The control of the robot motion can be divided into two actions. The first action follows the common sense rule that prevention is better than cure. Indeed, it consists in finding the velocities and accelerations limits of the trajectories to avoid both the longitudinal slip and the lateral slide. This action is performed offine so that the controller will never provide a trajectory that for sure cannot be travelled by the robot. The second action is the online control of the robot driving motors. The robot trajectory is described by the time evolution of the driving wheels angular velocities. The controller compares the ideal angular velocities with the ones measured by the encoders at the motors shaft and tries to null the error between them as quick as possible. The controller action is fundamental indeed it drives the robot motors to make the robot follow the desired trajectory taking care also of the unexpected situations as can be the reduction of the friction coeffcient at the wheel-ground contact point. In these cases, the controller recover the longitudinal slip or lateral slide that occur due to events that are not predictable a priori.