Error adaptive tracking for mobile robots

In mobile robots it is usual that the desired trajectory is memorized or previously generated. When following a trajectory, there are several possibilities attending to the way in which the actual robot state can be related with the whole trajectory. One of them is the extension of the servosystem approach, usually called "trajectory tracking". This is the only possibility if we need strict temporal deterministic requirements. But if not, other possibilities appear. One of them is called "path following", where the path\´s point to track is the "nearest" (under several conditions) to the actual robot\´s position. In this paper we present another method suitable for nondeterministic systems, which we may call "error adaptive tracking", because the tracking pace adapts to the errors. Its benefits and advantages are identified. Afterwards, we determine how to construct this method and we apply it to the case of SIRIUS, an advanced wheelchair. Then a control law that ensures asymptotic stability is extracted using the second Lyapunov method and under the error adaptive tracking approach. Finally, we show the benefits of the new method, comparing it with the trajectory tracking approach.