Kinematics, Dynamics, and Control of Robot Manipulators

—Continuum manipulators are a rapidly emerging class of robots. However, due to the complexity of their mathematical models and modeling inaccuracies, the development of effective control systems is a particularly challenging task. This paper presents the first attempt on kinematic control of continuum manipulators using a fuzzy-model-based approach. A fuzzy controller is proposed for autonomous execution of end-effector trajectory tracking tasks for a continuum manipulator. Particularly, membership functions are employed to combine the linearized state-space models, to achieve, overall, a fuzzy model. The fuzzy model can help design the fuzzy controller; in our approach, this process is supported by a thorough stability analysis. This control methodology enables a solution with low computational requirements to this motion control problem— there is no need to continuously update the Jacobian of the continuum manipulator. The superior performance of this controller is validated in MATLAB simulations and compared with those of classical controllers found in the literature. The experiments on a rapid-prototyped continuum manipulator further verify the feasibility and the advantages of this fuzzy controller in the presence of modeling discrepancies and hardware inaccuracies.

Design a nonlinear controller for second order nonlinear uncertain dynamical systems is one of
the most important challenging works. This paper focuses on the design of a chattering free
mathematical error-based tuning sliding mode controller (MTSMC) for highly nonlinear dynamic
robot manipulator, in presence of uncertainties. In order to provide high performance nonlinear
methodology, sliding mode controller is selected. Pure sliding mode controller can be used to
control of partly known nonlinear dynamic parameters of robot manipulator. Conversely, pure
sliding mode controller is used in many applications; it has an important drawback namely;
chattering phenomenon which it can causes some problems such as saturation and heat the
mechanical parts of robot manipulators or drivers.
In order to reduce the chattering this research is used the switching function in presence of
mathematical error-based method instead of switching function method in pure sliding mode
controller. The results demonstrate that the sliding mode controller with switching function is a
model-based controllers which works well in certain and partly uncertain system. Pure sliding
mode controller has difficulty in handling unstructured model uncertainties. To solve this problem
applied mathematical model-free tuning method to sliding mode controller for adjusting the sliding
surface gain (λ ). Since the sliding surface gain (λ) is adjusted by mathematical model free-based
tuning method, it is nonlinear and continuous. In this research new λ is obtained by the previous λ
multiple sliding surface slopes updating factor α. Chattering free mathematical error-based
tuning sliding mode controller is stable controller which eliminates the chattering phenomenon
without to use the boundary layer saturation function. Lyapunov stability is proved in
mathematical error-based tuning sliding mode controller with switching (sign) function. This controller has acceptable performance in presence of uncertainty (e.g., overshoot=0%, rise
time=0.8 second, steady state error = 1e-9 and RMS error=1.8e-12).

In this study, a mathematical tunable gain model free PID-like sliding mode fuzzy controller (GTSMFC) is designed to rich the best performance. Sliding mode fuzzy controller is studied because of its model free, stable and high performance. Today, most of systems (e.g., robot manipulators) are used in unknown and unstructured environment and caused to provide sophisticated systems, therefore strong mathematical tools (e.g., nonlinear sliding mode controller) are used in artificial intelligent control methodologies to design model free nonlinear robust controller with high performance (e.g., minimum error, good trajectory, disturbance rejection). Non linear classical theories have been applied successfully in many applications, but they also have some limitation. One of the best nonlinear robust controller which can be used in uncertainty nonlinear systems, are sliding mode controller but pure sliding mode controller has some disadvantages therefore this research focuses on applied sliding mode controller in fuzzy logic theory to solve the limitation in fuzzy logic controller and sliding mode controller. One of the most important challenging in pure sliding mode controller and sliding mode fuzzy controller is sliding surface slope. This paper focuses on adjusting the gain updating factor and sliding surface slope in PID like sliding mode fuzzy controller to have the best performance and reduce the limitation.