Virtual trajectory in tracking control of mobile robots

During trajectory tracking, it is highly likely that a mobile robot has to perform other functions such as obstacle avoidance, map correction, posture corrections, and etc. If the mobile robot must track its original reference trajectory after finishing some of these functions, exact time trajectory tracking is difficult due to large distance error. And planning a new trajectory on each event is not efficient and has some drawbacks. So, in this paper, we propose a virtual trajectory whose time scale is the only parameter that is different from the original trajectory. We also show its convergence to the original trajectory and the effectiveness of the algorithm by simulating the virtual trajectory design with a backstepping controller. Simulation results show that the virtual trajectory gives a stable and advanced performance for the case that the mobile robot must perform other functions during trajectory tracking. And due to the time and position convergence characteristics, the virtual trajectory is helpful to any delayed tracking problem. The proposed virtual trajectory can be adapted not only mobile robot, but also any system which track a reference trajectory.