A Spatial Weight Error Control for a Class of Hyper-Redundant Robots

This paper treats the control problem of a class of hyper-redundant robots. The dynamic model of the arm is described by hyperbolic partial differential equations with uncertain components. By using a spatial weighted error control, the infinite dimensional system control becomes a finite-dimensional control problem. The stability analysis and the resulting controllers are obtained using the concept of boundary geometric control and a spatial weighted error control technique. A robust algorithm that is based on weighted error sliding mode control is discussed. The boundary tendon control determines the system evolution toward a prescribed switching surface, and in order to avoid the oscillations around the switching surface, a damping control determines a direct evolution, along the switching surface, toward the origin. Numerical simulations and experimental results are also provided to verify the effectiveness of the presented approach.