Asymmetric Constrained Control of a Cervical Orthotic Device Based on Barrier Sliding Modes

This work proposes a robust sliding mode controller to enforce the tracking trajectory of a cervical orthotic device subjected to asymmetric box constraints. The convergence analysis employs an asymmetric barrier Lyapunov function (ABLF), whose argument is a restricted sliding surface. The stability analysis demonstrates the finite-time convergence of the states towards the sliding surface and, therefore, the exponential stability of the system trajectories. The controller ensures the fulfillment of the restrictions imposed on the sliding surface and consequently over the states. Numerical simulations exhibit the performance of the proposed controller ensuring restricted movements for flexion and extension of a virtual orthotic cervical device. The restricted movements obey asymmetric constraints according to the therapies proposed by medical specialists.