In this paper, a linear proportional derivative (PD) controller is designed for highly nonlinear and uncertain system by using robust factorization approach. To evaluate a linear PD methodology two type methodologies are introduced; sliding mode controller and fuzzy logic methodology. This research aims to design a new methodology to fix the position in continuum robot manipulator. PD method is a linear methodology which can be used for highly nonlinear system’s (e.g., continuum robot manipulator). To estimate this method, new parallel fuzzy sliding mode controller (PD.FSMC) is used. This estimator can estimate most of nonlinearity terms of dynamic parameters to achieve the best performance. The asymptotic stability of fuzzy PD control with first-order sliding mode compensation in the parallel structure is proven. For the parallel structure, the finite time convergence with a super-twisting second-order sliding-mode is guaranteed.

The increasing demand for multi-degree-of-freedom (DOF) continuum robot in presence of highly nonlinear dynamic parameters in a number of industries has motivated a flurry of research in the development of soft computing nonlinear methodology. This robot is capable of providing smooth and isotropic three-dimensional motion in each joint. Compared to conventional robotic manipulators that offer the same motion capabilities, the innovative spherical motor possesses several advantages. Not only can the spherical motor combine 3-DOF motion in a single joint, it has a large range of motion with no singularities in its workspace. This research contributes to the on-going research effort by exploring alternate methods for controlling the continuum robot manipulator. This research addresses two basic issues related to the control of a continuum robots; (1) a more accurate representation of the dynamic model of an existing prototype, and (2) the design of a robust feedback controller. The robust backstepping controller proposed in this research is used to further demonstrate the appealing features exhibited by the continuum robot. Robust feedback controller is used to position control of continuum robot in presence of uncertainties. Using Lyapunov type stability arguments, a robust backstepping controller is designed to achieve this objective. The controller developed in this research is designed in two steps. Firstly, a robust stabilizing torque is designed for the nominal continuum robot dynamics derived using the constrained Lagrangian formulation. Next, the fuzzy logic methodology applied to it to solution uncertainty problem. The fuzzy model free problem is formulated to minimize the nonlinear formulation of continuum robot. The eventual stability of the controller depends on the torque generating capabilities of the continuum robots.