The problem of simultaneous position and internal force control is discussed with cooperative manipulators system under variable load and dynamic uncertainties in this study. A position synchronized sliding mode controller is proposed in the presence of variable load, as well as modeling uncertainties, joint friction, and external disturbances. To deal with the complex situation brought by variable load, virtual synchronization coupled errors are introduced for internal force tracking control and joint synchronization in the meantime. Dual feedforward neural networks are adopted, where a radial basis function-neural network based dynamic compensator and a radial basis function-neural network based internal force estimator are established, respectively, so that precise dynamic knowledge and force measurement are out of demand through their cooperation. Together with simulation studies and analysis, the position and internal force errors are shown to converge asymptotically to zero. Using Lyapunov stability approach, the proposed controller is proven to be robust in face of variable external load and the aforementioned uncertainties.
Asymptotic Prediction Error Variance for Feedforward Neural Networks
