Algorithm for Trajectory Optimization of a Mobile Robot that Takes into Account Velocity and Acceleration Constraints

Model gibanja robota s diferencijalnim pogonom uključuje njegov položaj u prostoru te translacijske i rotacijske brzine i ubrzanja kojima se robot giba. Riješen je optimizacijski problem gibanja mobilnog robota u prostoru od početne do zadane pozicije uzimajući u obzir ograničenja brzina i ubrzanja robota te izbjegavajući prepreke. Kriterij optimalnosti može biti kombinacija utrošene energije i vremena gibanja, u kojem slučaju govorimo o vremenski optimalnom gibanju robota. Problem je zbog svoje visoke dimenzionalnosti i nelinearnosti teško riješiti u stvarnom vremenu. Prikazana je usporedba optimizacijskih metoda prema dobivenim brzinama robota i trajektorijama te vremenu utrošenom za dobivanje optimalnog rješenja.Motion model of a differential drive mobile robot includes its position in space and translational and rotational velocities and accelerations. The optimization problem of a mobile robot motion from its initial position to a goal position without colliding with obstacles and taking into account velocity and acceleration constraints has been solved. Optimization criteria can be a combination of energy efficiency and time spent, in this case we are talking about time-optimal robot motion. Because of its high dimensionality and nonlinearity, the problem is hard to solve in real-time. A comparison between the optimization methods is presented according to the obtained velocities and robot trajectories as well as the time spent to find the optimal solution