Control of differentially flat mechanical systems in the presence of uncertainty

Considers the problem of controlling differentially flat nonholonomic mechanical systems in the presence of system model uncertainty. Note that, despite the importance of the effects of uncertainty on control system performance, very few results are available for controlling uncertain flat systems. It is proposed that a simple and effective solution to this problem can be obtained by combining: a trajectory generation algorithm for the flat outputs with an adaptive tracking controller for a set of reducing outputs. The reducing outputs are a subset of the configuration coordinates and are readily obtained from the system description; the tracking controller for these outputs is developed by employing a performance-based adaptive control methodology. This approach is shown to ensure accurate motion control without knowledge of the system dynamic model, and to be generalizable to provide compensation for uncertainty in the system kinematic model as well