Robust Control of Robot Arms via Quasi Sliding Modes and Neural NetworksAdvances and Applications in Sliding Mode Control systems

This chapter presents a control approach for robotic manipulators based on a discrete-time sliding mode control which has received much less coverage in the literature with respect to continuous time sliding-mode strategies. This is due to its major drawback, consisting in the presence of a sector, of width depending on the available bound on system uncertainties, where robustness is lost because the sliding mode condition cannot be exactly imposed. For this reason, only ultimate bound-edness of trajectories can be guaranteed, and the larger the uncertainties affecting the system are, the wider is the bound on trajectories which can be guaranteed. As a possible solution to this problem, in this chapter a discontinuous control law has been proposed, employing a controller inside the sector based on an estimation, as accu-rate as possible, of the overall effect of uncertainties affecting the system. Different solutions for obtaining this estimate have been considered and the achievable per-formances have be compared using experimental data. The first approach consists in estimating the uncertain terms by a well established method which is an adap-tive on-line procedure for autoregressive modeling of non-stationary multivariable time series by means of a Kalman filtering. In the second solution, radial basis neural networks are used to perform the estimation of the uncertainties affecting the system. The proposed control system is evaluated on the ERICC robot arm. Experimental evi-dence shows satisfactory trajectory tracking performances and noticeable robustness in the presence of model inaccuracies and payload perturbations