On modeling and control of omnidirectional wheels

Mobile robots are more and more commonly used for everyday automated transportation and logistics tasks; they carry goods, parts and even people. When maneuvers in cluttered environments are executed with expensive loads the need for reliable, safe and efficient movement is paramount. This dissertation is written with the goal of solving some problems related to a special class of mobile transport robots. Omnidirectional wheels are well known in the robotics community, their exceptional maneuvering capabilities attract a lot of robot builders and several industrial applications are known as well. To fully exploit the advantages of these special wheels sophisticated mechanics and control methods are required. Since modern engineering uses simulation wherever possible, to eliminate design errors early in the development, the first objective of my research was to create an easy to use, yet realistic model in simulation for the general omnidirectional wheel. To create this model I used empirical tire models created for automotive simulation – to make advantage of the knowledge accumulated in this domain – and modified them to generate forces like an omnidirectional wheel, in essence transforming the longitudinal force component in the direction of the rollers. I created two embodiments as an example in Dymola environment and verified their functionality using kinematic equations and simple lumped robot models. Omnidirectional wheels have no side-force generating capabilities, this is the very attribute that allows them to generate holonomic movement. Due to this characteristic omnidirectional platforms do not keep their direction of movement when braked intensively, instead they tend to swerve around the most loaded wheel. My second goal was to try and eliminate the swerving effect when braking. The braking problem involves a nonlinear MIMO system with uncertain parameters, since for example the ground-wheel contact depends nonlinearly on the unknown wheel load, ground and wheel material characteristics. I created a sliding mode controller that takes wheel center velocity vectors as input and actuates the brakes according to the given wheels’ capability to reduce unwanted platform motion i.e. swerving. I also incorporated a factor to tune braking distance. I verified the performance of the controller in simulation, it showed high tolerance against structured and unstructured uncertainties in the platform model. The control law only uses knowledge on the kinematics of the robot, yet it works well with robots with dynamic properties. To be able to control an omnidirectional platform, feedback of the motion is essential. Due to the special movement, traditional, wheel rotation based methods are highly inaccurate; therefore I directed my research towards optical feedback, using an image detector facing the ground and correlation. The method itself is not new most people know it from optical mice. There are many similar solutions in the literature, but they are not suited to movements up to several tens of m/s. To enhance the range of the sensor I investigated the possibility of using line scan cameras. They offer high speed and resolution in a single dimension. To verify whether movements off the main axis make measurements impossible I created a simulator in Matlab and made several experiments with a virtual sensor. My results show that by careful choice of parameters and processing, a line scan camera can be made insensitive to off axis movements and high speed one dimensional measurement is possible while moving in two dimensions. The results of my research were evaluated in simulation and an early prototype of the speed sensor was incorporated in student projects.