Mathematical modelling of kinematics and control synthesis of a mobile robot with four steering and four independently driven wheels

Ovaj rad je fokusiran na razvoj regulatora za vođenje mobilnog robota duž zadane trajektorije. Robot je posebno opremljen sa četiri zakretna i neovisno pogonjena kotača. Uz određene pretpostavke, jednadžbe kinematike robota pretvaraju se u dvolančani format s trostrukim ulazom, s pojedinačnim generatorom u lancu. Zatim se provodi linearna aproksimacija ovih jednadžbi za slučaj malih odstupanja oko željene trajektorije. Ovaj pristup rezultira modelom vremenski promjenjivog sustava, koji je pogodan za sintezu vremenski promjenjivog linearnog zakona upravljanja temeljenog na principu kvadratne optimalnosti. Najučinkovitija verzija ovog zakona upravljanja pronađena je računalnim simulacijama provedenim u MATLAB-u (MathWorks, Natick, MA, SAD). Ovaj zakon upravljanja se zatim primjenjuje na stvarnom mobilnom robotu, razvijenom u Regionalnom centru izvrsnosti za robotske tehnologije (CRTA). Implementacija regulatora provedena je sustavom Robot Operating System (ROS), a njegova se izvedba procjenjuje kroz eksperimentalna mjerenja pomoću OptiTrack sustava.This master’s thesis is focused on developing a controller for guiding a mobile robot along the desired trajectory. The robot is uniquely equipped with four steerable and independently powered wheels. By making certain assumptions, equations of the robot kinematics are transformed into a format known as three-input, two-chain, single-generator chained form. A linear approximation of these equations is then performed for the case in which the perturbations around the desired trajectory are small. This approach results in a time-varying system model, which is suitable for the sinthesis of a time-varying linear control law based on the principle of quadratic optimality. The most effective version of this control law is identified through computer simulations conducted in MATLAB (MathWorks, Natick, MA, USA). This control law is then applied to a real-world mobile robot, developed at the Regional Center of Excellence for Robotic Technologies (CRTA). The implementation of the regulator is carried out by Robot Operating System (ROS), and its performance is assessed through experimental measurements using the OptiTrack system