Adaptive Neural Network Based Sliding Mode Control of Continuum Robots with Mismatched Uncertainties

Continuum robots are utilized in applications where a high-level accuracy and delicacy is desired, which in return demand a robust control design. However, due to their nonlinearity and elasticity, this task of robust control design presents a steep challenge. A challenge that is mostly simplified through restrictive modelling and operating assumptions. One common assumption used is the uncertainty matching condition, in which the controller is expected to have direct access to any affecting uncertainty. This assumption is difficult to justify in continuum robots as due to their high nonlinear dynamics, practical limitations, and congested operating environments. Uncertainties could affect continuum robots from any of their states and are not necessarily reachable by the controller. Here, we will solve this problem using the multi-surface sliding mode control technique in combination with RBF neural networks as our uncertainties approximators. First, Cosserat rod theory is used to derive the dynamic model of the continuum robot due to its generality. Then, we propose an adaptive RBF neural network based multi-surface sliding mode control to guarantee tracking stability. Simulation results are included to verify the effectiveness of the proposed control scheme.