The main contribution of this paper is the design of a robust model reference fuzzy sliding mode observation technique to control multi-input, multi-output (MIMO) nonlinear uncertain dynamical robot manipulators. A fuzzy sliding mode controller was used in this study to control the robot manipulator in the presence of uncertainty and disturbance. To address the challenges of robustness, chattering phenomenon, and error convergence under uncertain conditions, the proposed sliding mode observer was applied to the fuzzy sliding mode controller. This theory was applied to a six-degrees-of-freedom (DOF) PUMA robot manipulator to verify the power of the proposed method.

System Identification is used to build mathematical models of a dynamic system based on measured data. To design the best controllers for linear or nonlinear systems, mathematical modeling is the main challenge. To solve this challenge conventional and intelligent identification are recommended. System identification is divided into different algorithms. In this research, two important types algorithm are compared to identifying the highly nonlinear systems, namely: Auto-Regressive with eXternal model input (ARX) and Auto Regressive moving Average with eXternal model input (Armax) Theory. These two methods are applied to the highly nonlinear industrial motor.

In this research, intelligent adaptive backstepping control is presented as robust control for continuum robot. The first objective in this research is design a Proportional-Derivative (PD) fuzzy system to compensate the system model uncertainties. The second objective is focused on the design tuning gain adaptive methodology according to high quality partly nonlinear methodology. Conventional backstepping controller is one of the important robust controllers especially to control of continuum robot manipulator. The fuzzy controller is used in this method to system compensation. In real time to increase the system robust fuzzy logic theory is applied to backstepping controller. To approximate a time-varying nonlinear dynamic system, a fuzzy system requires a large amount of fuzzy rule base. The adaptive laws in this algorithm are designed based on the Lyapunov stability theorem. This method is applied to continuum robot manipulator to have the best performance.

The minimum rule base Proportional Integral Derivative (PID) Fuzzy hybrid guidance Controller for three dimensions spherical motor is presented in this research. A three dimensions spherical motor is well equipped with conventional control techniques and, in particular, various PID controllers which demonstrate a good performance and successfully solve different guidance problems. Guidance control in a three dimensions spherical motor is performed by the PID controllers producing the control signals which are applied to systems torque. The necessary reference inputs for a PID controller are usually supplied by the system's sensors based on different data. The popularity of PID Fuzzy hybrid guidance Controller can be attributed to their robust performance in a wide range of operating conditions and partly to their functional simplicity. PID methodology has three inputs and if any input is described with seven linguistic values, and any rule has three conditions we will need 343 rules. It is too much work to write 343 rules. In this research the PID-like fuzzy controller can be constructed as a parallel structure of a PD-like fuzzy controller and a conventional PI controller to have the minimum rule base. Linear type PID controller is used to modify PID fuzzy logic theory to design hybrid guidance methodology. This research is used to reduce or eliminate the fuzzy and conventional PID controller problem based on minimum rule base fuzzy logic theory and modified it by PID method to control of spherical motor system and testing of the quality of process control in the simulation environment of MATLAB/SIMULINK Simulator.

The main four objectives to design controllers are: stability, robust, minimum error and reliability. Linear PID controller is model-free controller and this controller is not reliable. One of the robust nonlinear controller to control of nonlinear systems is sliding mode controller (SMC). Sliding mode controller (SMC) is robust conventional nonlinear controller in a partly uncertain dynamic system’s parameters. Sliding mode controller is divided into two main sub parts: discontinues controller(τ_dis) and equivalent controller(τ_eq). Discontinues controller is used to design suitable tracking performance based on very fast switching. Fast switching or discontinuous part have essential role to achieve to good trajectory following, but it is caused system instability and chattering phenomenon. Chattering phenomenon is one of the main challenges in conventional sliding mode controller and it can causes some important mechanical problems such as saturation and heats the mechanical parts of robot manipulators or drivers. To reduce or eliminate the chattering two methods are used in many researches which these methods are: boundary layer saturation method and artificial intelligence based method. In this research fuzzy switching methodology is used to eliminate the chattering in presence of uncertainty to increase the robust of this controller with application to three dimensions of spherical motor.

This research is focused on proposed adaptive fuzzy sliding mode algorithms with the adaptation laws derived in the Lyapunov sense. The stability of the closed-loop system is proved mathematically based on the Lyapunov method. Adaptive MIMO fuzzy compensate fuzzy sliding mode method design a MIMO fuzzy system to compensate for the model uncertainties of the system, and chattering also solved by new adaption method. Since there is no tuning method to adjust the premise part of fuzzy rules so we presented a scheme to online tune consequence part of fuzzy rules. Classical sliding mode control is robust to control model uncertainties and external disturbances. A sliding mode method with a switching control low guarantees the stability of the certain and/or uncertain system, but the addition of the switching control low introduces chattering into the system. One of the main targets in this research to reduce or eliminate chattering is to insert online tuning method. Classical sliding mode control method has difficulty in handling unstructured model uncertainties. One can overcome this problem by combining a sliding mode controller and artificial intelligence (e.g. fuzzy logic). To approximate a time-varying nonlinear dynamic system, a fuzzy system requires a large amount of fuzzy rule base. This large number of fuzzy rules will cause a high computation load. The addition of an adaptive law to a fuzzy sliding mode controller to online tune the parameters of the fuzzy rules in use will ensure a moderate computational load. The adaptive laws in this algorithm are designed based on the Lyapunov stability theorem. Asymptotic stability of the closed loop system is also proved in the sense of Lyapunov. This method is applied to continuum robot manipulator to have the best performance.

Spherical three Degree-of- Freedom (DOF) is controlled by model-base fuzzy computed torque controller. The spherical motor has three revolute joints allowing the corresponding parts to move horizontally and vertically. When developing a controller using conventional control methodology (e.g., feedback linearization methodology), a design scheme has to be produced, usually based on a system’s dynamic model. The work outline in this research utilizes soft computing applied to new conventional controller to address these methodology issues. Computed torque controller (CTC) is influential nonlinear controllers to certain systems which this method is based on compute the required arm torque using nonlinear feedback control law. When all dynamic and physical parameters are known, CTC works superbly; practically a large amount of systems have uncertainties and fuzzy feedback Inference Engine (FIS) is used to reduce this kind of limitation. Fuzzy logic provides functional capability without the use of a system dynamic model and has the characteristics suitable for capturing the approximate, varying values found in a MATLAB based area. Based on this research model- base fuzzy computed torque controller applied to spherical motor is presented to have a stable and robust nonlinear controller and have a good result compared with conventional and pure fuzzy logic controllers.

This research is focused on proposed minimum rule base PID computed torque algorithms with application to continuum robot manipulator. The stability of the closed-loop system is proved mathematically based on the Lyapunov method. Classical Computed Torque Controller (CTC) is robust to control model partly uncertainties and external disturbances. This controller is one of the significant nonlinear methodologies; according to the nonlinear dynamic formulation. One of the main targets in this research is increase the robustness based on the artificial intelligence methodology. Classical computed torque control has difficulty in handling unstructured model uncertainties. One can overcome this problem by combining a computed torque controller and artificial intelligence (e.g. fuzzy logic). To approximate a time-varying nonlinear dynamic system, a fuzzy system requires a large amount of fuzzy rule base. This large number of fuzzy rules will cause a high computation load. To reduce the number of rule base this research is focused on the PD like fuzzy plus integral methodology. This method is applied to continuum robot manipulator to have the best performance.

The minimum rule base Proportional Integral Derivative (PID) Fuzzy Computed Torque Controller is presented in this research. The popularity of PID Fuzzy Computed Torque Controller can be attributed to their robust performance in a wide range of operating conditions and partly to their functional simplicity. The process of setting of PID Fuzzy Computed Torque Controller can be determined as an optimization task. Over the years, use of intelligent strategies for tuning of these controllers has been growing. PID methodology has three inputs and if any input is described with seven linguistic values, and any rule has three conditions we will need 343 rules. It is too much work to write 343 rules. In this research the PID-like fuzzy controller can be constructed as a parallel structure of a PD-like fuzzy controller and a PI controller to have the minimum rule base. However computed torque controller is work based on cancelling decoupling and nonlinear terms of dynamic parameters of each link, this controller is work based on manipulator dynamic model and this technique is highly sensitive to the knowledge of all parameters of nonlinear robot manipulator’s dynamic equation. This research is used to reduce or eliminate the computed torque controller problem based on minimum rule base fuzzy logic theory to control of flexible robot manipulator system and testing of the quality of process control in the simulation environment of MATLAB/SIMULINK Simulator.

The minimum rule base Proportional Integral Derivative (PID) Fuzzy Computed Torque Controller with application to spherical motor is presented in this research. The popularity of PID Fuzzy Computed Torque Controller can be attributed to their robust performance in a wide range of operating conditions and partly to their functional simplicity. PID methodology has three inputs and if any input is described with seven linguistic values, and any rule has three conditions we will need 343 rules. It is too much work to write 343 rules and have lots of problem to design embedded control system e.g., Field Programmable Gate Array (FPGA). In this research the PID-like fuzzy controller can be constructed as a parallel structure of a PD-like fuzzy controller and a conventional PI controller to have the minimum rule base and acceptable trajectory follow disturbance to control of spherical motor. However computed torque controller is work based on cancelling decoupling and nonlinear terms of dynamic parameters for each direction of three degree of freedom spherical motor, this controller is work based on motor dynamic model and this technique is highly sensitive to the knowledge of all parameters of nonlinear spherical motor’s dynamic equation. This research is used to reduce or eliminate the computed torque controller problem based on minimum rule base fuzzy logic theory to control of three degrees of freedom spherical motor system and testing of the quality of process control in the simulation environment of MATLAB/SIMULINK Simulator.

In this paper the development, modeling and high precision robust control of an electro-mechanical continuum robot manipulator is presented. In this paper main controller is a Sliding Mode Controller which modified by modified PD methodology based on the boundary derivative methodology. Parallel fuzzy logic theory is used to compensate the system dynamic uncertainty controller based on sliding mode theory. Sliding mode controller (SMC) is a significant nonlinear controller under condition of partly uncertain dynamic parameters of system. This controller is used to control of highly nonlinear systems especially for continuum robot manipulator, because this controller is robust and stable in presence of partly uncertainties. PD partly switching nonlinear SMC by modified PD boundary derivative method is used to achieve a stable tracking, while the parallel fuzzy-logic optimization added intelligence to the control system through an automatic tuning of the PD modified partly switching sliding mode methodology uncertainties. Adaptive methodology is used to on-line tuning the sliding surface slope and gain updating factor of this methodology. Simulation results demonstrated the validity of the Mamdani parallel fuzzy-optimization control with asymptotic and stable tracking at different position inputs. This compensation demonstrated a well synchronized control signal at different excitation conditions.

In various dynamic parameters systems that need to be training on-line adaptive control methodology is used. In this paper fuzzy model-base adaptive methodology is used to tune the linear Proportional Integral Derivative (PID) controller. The main objectives in any systems are; stability, robust and reliability. However PID controller is used in many applications but it has many challenges to control of continuum robot. To solve these problems nonlinear adaptive methodology based on model base fuzzy logic is used. This research is used to reduce or eliminate the PID controller problems based on model reference fuzzy logic theory to control of flexible robot manipulator system and testing of the quality of process control in the simulation environment of MATLAB/SIMULINK Simulator.

Continuum robot manipulators are optimized to meet best trajectory requirements. Closed loop control is a key technology that is used to optimize the system output process to achieve this goal. In order to conduct research in the area of closed loop control, a control oriented cycle-to-cycle continuum robot model, containing dynamic model information for each individual continuum robot manipulator, is a necessity. In this research, the continuum robot manipulator is modeled according to information between joint variable and torque, which is represented by the nonlinear dynamic equation. After that, a multi-input-multi-output baseline computed torque control scheme is used to simultaneously control the torque load of system to regulate the joint variables to desired levels. One of the most important challenge in control theory is on-line tuning therefore fuzzy supervised optimization is used to tune the modified baseline and computed torque control coefficient. The performance of the modified baseline computed torque controller is compared with that of a baseline proportional, integral, and derivative (PID) controller.

The minimum rule base Proportional Integral Derivative (PID) Fuzzy Sliding Mode Controller (SMC) with application to spherical motor is presented in this research. The popularity of PID Fuzzy Sliding Mode Controller can be attributed to their robust performance in a wide range of operating conditions and partly to their functional simplicity. The process of setting of PID Fuzzy Sliding Mode Controller can be determined as an optimization task. Over the years, use of intelligent strategies for tuning of these controllers has been growing especially in nonlinear and uncertain systems. Proportional Integral Derivative methodology has three inputs and if any input is described with seven linguistic values, and any rule has three conditions, we will need 343 rules. It is too much work to write 343 rules and have lots of problem to design embedded control system e.g., Field Programmable Gate Array (FPGA). In this research the PID-like fuzzy controller can be constructed as a parallel structure of a PD-like fuzzy controller and a conventional PI controller to have the minimum rule base and good trajectory follow disturbance to control of spherical motor. However Sliding Mode Controller is work based on cancelling decoupling and nonlinear terms of dynamic parameters for each direction of three degree of freedom spherical motor, this controller is work based on motor dynamic model and this technique is highly sensitive to the knowledge of all parameters of nonlinear spherical motor’s dynamic equation which caused to challenge in uncertain system. This research is used to reduce or eliminate the Sliding Mode Controller problem based on minimum rule base fuzzy logic theory to control of three degrees of freedom spherical motor system and testing of the quality of process control in the simulation environment of MATLAB/SIMULINK Simulator.

Fuzzy logic controller (FLC) is an important nonlinear controller in an uncertain dynamic system’s parameters. This controller is used to control of nonlinear dynamic systems particularly for spherical motor, because it has a suitable control performance and it is a stable. Conversely pure fuzzy logic controller is a high-quality intelligent nonlinear controller; it has two important problems; reliability and robustness in uncertain dynamic parameter. To increase the reliability and robustness, this research is focused on applied feedback linearization method in pure fuzzy logic controller. In this research the nonlinear equivalent dynamic (equivalent part) formulation problem in uncertain condition is also solved by combine pure fuzzy logic control and feedback linearization method. In this method feedback linearization theorem is applied to fuzzy logic controller to increase the stability, reliability and robustness, which it is based on nonlinear dynamic formulation. To achieve this goal, the dynamic-based formulation feedback linearization method is design. This method is robust and model-based nonlinear control therefore can reduce the nonlinearity term of system and reduce the effect of coupling. In this research MAMDANI fuzzy inference system is used as a main controller. It has minimum rule base to practical implementation. This technique was employed to obtain the desired control behavior with a number of information about dynamic model of system and a feedback linearization control was applied to reinforce system performance.

Stability, robust and reliability are the main objectives to design a controller for highly nonlinear spherical motor. Most of linear and nonlinear controllers are stable, model-base controllers are reliable but in this group sliding mode controller is a robust controller. Therefore in this research sliding mode controller is used to design stable, robust and reliable controller. For intelligence part, the minimum rule base Proportional Integral Derivative (PID) Fuzzy hybrid guidance Controller for three dimensions spherical motor is presented in this research. Guidance control in a three dimensions spherical motor is performed by the robust sliding mode controllers producing the control signals which are applied to systems torque. Sliding mode controller has an important problem, namely chattering. In this research, chattering-free sliding mode controller is design as a robust guidance controller to their robust performance in a wide range of operating conditions. In this research the PID-like fuzzy controller can be constructed as a parallel structure of a PD-like fuzzy controller and a PI-like controller to have the minimum rule base. Nonlinear type robust sliding mode controller is used to modify PID fuzzy logic theory to design robust and reliable hybrid guidance methodology. This research is used to reduce or eliminate the fuzzy and conventional sliding mode controller problem based on minimum rule base fuzzy logic theory and modified it by sliding mode method to control of spherical motor system.

Sliding mode controller (SMC) is a significant nonlinear controller under condition of partly uncertain dynamic parameters of system. This controller is used to control of highly nonlinear systems especially for robot manipulators, because this controller is a robust and stable. Conversely, pure sliding mode controller is used in many applications; it has two important drawbacks namely; chattering phenomenon, and nonlinear equivalent dynamic formulation in uncertain dynamic parameter. The nonlinear equivalent dynamic formulation problem and chattering phenomenon in uncertain system can be solved by using artificial intelligence theorem. However fuzzy logic controller is used to control complicated nonlinear dynamic systems, but it cannot guarantee stability and robustness. In this research parallel fuzzy logic theory is used to compensate the system dynamic uncertainty.

This research focuses on the basic concepts of continuum robot manipulator and control methodology. OCTARM Continuum robot manipulator is a 6 DOF serial robot manipulator. From the control point of view, robot manipulator divides into two main parts i.e. kinematics and dynamic parts. The dynamic parameters of this system are highly nonlinear. To control of this system nonlinear control methodology (computed torque controller and sliding mode controller) is introduced. Computed torque controller (CTC) is an influential nonlinear controller to certain systems which it is based on feedback linearization and computes the required arm torques using the nonlinear feedback control law. When all dynamic and physical parameters are known computed torque controller works superbly; practically a large amount of systems have uncertainties and sliding mode controller reduce this kind of limitation. Sliding mode controller (SMC) is a significant nonlinear controller under condition of partly uncertain dynamic parameters of system. This controller is used to control of highly nonlinear systems especially for robot manipulators, because this controller is a robust and stable. Comparative study between computed torque controller and sliding mode controller is introduced in this research.

The minimum rule base Proportional Integral Derivative (PID) Fuzzy backstepping Controller is presented in this research. The popularity of PID Fuzzy backstepping controller can be attributed to their robust performance in a wide range of operating conditions and partly to their functional simplicity. The process of setting of PID Fuzzy backstepping controller can be determined as an optimization task. Over the years, use of intelligent strategies for tuning of these controllers has been growing. PID methodology has three inputs and if any input is described with seven linguistic values, and any rule has three conditions we will need 7 × 7 × 7 = 343 rules. It is too much work to write 343 rules. In this research the PID-like fuzzy controller can be constructed as a parallel structure of a PD-like fuzzy controller and a PI-like controller to have the minimum rule base. However backstepping controller is work based on cancelling decoupling and nonlinear terms of dynamic parameters of each link, this controller is work based on manipulator dynamic model and this technique is highly sensitive to the knowledge of all parameters of nonlinear robot manipulator’s dynamic equation. This research is used to reduce or eliminate the backstepping controller problem based on minimum rule base fuzzy logic theory to control of flexible robot manipulator system and testing of the quality of process control in the simulation environment of MATLAB/SIMULINK Simulator.

Classical sliding mode controller is robust to model uncertainties and external disturbances. A sliding mode control method with a switching control low guarantees asymptotic stability of the system, but the addition of the switching control law introduces chattering in to the system. One way of attenuating chattering is to insert a saturation function inside of a boundary layer around the sliding surface. Unfortunately, this addition disrupts Lyapunov stability of the closed-loop system. Classical sliding mode control method has difficulty in handling unstructured model uncertainties. One can overcome this problem by combining a sliding mode controller and fuzzy system together. Fuzzy rules allow fuzzy systems to approximate arbitrary continuous functions. To approximate a time-varying nonlinear system, a fuzzy system requires a large amount of fuzzy rules. This large number of fuzzy rules will cause a high computation load. The addition of an adaptive law to a fuzzy sliding mode controller to online tune the parameters of the fuzzy rules in use will ensure a moderate computational load. Refer to this research; tuning methodology can online adjust both the premise and the consequence parts of the fuzzy rules. Since this algorithm for is specifically applied to a robot manipulator.

This research is focused on proposed Proportional-Integral (PI) like fuzzy adaptive backstopping fuzzy algorithms based on Proportional-Derivative (PD) fuzzy rule base with the adaptation laws derived in the Lyapunov sense. Adaptive SISO PI like fuzzy adaptive backstopping fuzzy method has two main objectives; the first objective is design a SISO fuzzy system to compensate for the model uncertainties of the system, and the second objective is focused on the design PI like fuzzy controller based on PD method as an adaptive methodology. Classical backstopping control is robust to control model uncertainties and external disturbances and is a main controller in this research. The fuzzy controller is used in this method to system compensation. To increase the robust of this controller adaptive PI like fuzzy controller is introduced and applied to backstopping fuzzy controller. Classical backstopping control method has difficulty in handling unstructured model uncertainties. One can overcome this problem by combining a backstopping controller and artificial intelligence (e.g. fuzzy logic). To approximate a time-varying nonlinear dynamic system, a fuzzy system requires a large amount of fuzzy rule base. This large number of fuzzy rules will cause a high computation load. The addition of an adaptive law to a backstopping fuzzy controller to online tune the coefficients in use will ensure a moderate computational load. The adaptive laws in this algorithm are designed based on the Lyapunov stability theorem. This method is applied to continuum robot manipulator to have the best performance.

Refer to this research, a position modified parallel error-based fuzzy Proportional Derivative (PD) gravity controller is proposed for continuum robot manipulator. The main problem of the pure conventional nonlinear controller was equivalent dynamic formulation in uncertain systems. The main challenge of linear controllers is linearization techniques and the quality of performance. The nonlinear equivalent dynamic problem in uncertain system is solved by applied fuzzy logic theory to modified PD gravity. To estimate the continuum robot manipulator system’s dynamic, proportional plus modified derivative with 7 rules Mamdani inference system is design and applied to modified PD gravity methodology. The proportional coefficient of controller is tuned by new methodology in limitation uncertainties. The results demonstrate that the proposed controller is a partly model-free controllers which works well in certain and partly uncertain system.

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. The robust backstopping 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 backstopping controller is designed to achieve this objective. The controller developed in this research is designed into two steps. Firstly, a robust stabilizing torque is designed for the nominal continuum robot dynamics derived using the constrained Lagrangian formulation based on modified PD backstopping controller. Next, the fuzzy logic methodology applied to it to solution uncertainty problem. The fuzzy model free problem is formulated to estimate the nonlinear formulation of continuum robot. The eventual stability of the controller depends on the torque generating capabilities of the continuum robots.

In this research, manage the Internal Combustion (IC) engine modeling and a multi-input-multi-output artificial intelligence baseline chattering free sliding mode methodology scheme is developed with guaranteed stability to simultaneously control fuel ratios to desired levels under various air flow disturbances by regulating the mass flow rates of engine PFI and DI injection systems. Modeling of an entire IC engine is a very important and complicated process because engines are nonlinear, multi inputs-multi outputs and time variant. One purpose of accurate modeling is to save development costs of real engines and minimizing the risks of damaging an engine when validating controller designs. Nevertheless, developing a small model, for specific controller design purposes, can be done and then validated on a larger, more complicated model. Analytical dynamic nonlinear modeling of internal combustion engine is carried out using elegant Euler-Lagrange method compromising accuracy and complexity. A baseline estimator with varying parameter gain is designed with guaranteed stability to allow implementation of the proposed state feedback sliding mode methodology into a MATLAB simulation environment, where the sliding mode strategy is implemented into a model engine control module (“software”). To estimate the dynamic model of IC engine fuzzy inference engine is applied to baseline sliding mode methodology. The fuzzy inference baseline sliding methodology performance was compared with a well-tuned baseline multi-loop PID controller through MATLAB simulations and showed improvements, where MATLAB simulations were conducted to validate the feasibility of utilizing the developed controller and state estimator for automotive engines. The proposed tracking method is designed to optimally track the desired FR by minimizing the error between the trapped in-cylinder mass and the product of the desired FR and fuel mass over a given time interval.

The Proportional Integral Derivative (PID) Fuzzy Sliding Mode Controller (FSMC) is the most widely used control strategy in the Industry (control of robotic arm). The popularity of PID FSMC controllers can be attributed to their robust performance in a wide range of operating conditions and partly to their functional simplicity. The process of setting of PID FSMC controller can be determined as an optimization task. Over the years, use of intelligent strategies for tuning of these controllers has been growing. Biologically inspired evolutionary strategies have gained importance over other strategies because of their consistent performance over wide range of process models and their flexibility. This paper analyses the modified PID FSMC controllers based on minimum rule base for flexible robot manipulator system and test the quality of process control in the simulation environment of MATLAB/SIMULINK Simulator.

Refer to this research, a position parallel error-based fuzzy inverse dynamic plus gravity controller is proposed for continuum robot manipulator. The main problem of the pure inverse dynamic controller was equivalent dynamic formulation in certain and uncertain systems. The nonlinear equivalent dynamic problem in uncertain system is solved by using fuzzy logic theory. To estimate the continuum robot manipulator system’s dynamic, 49 rules Mamdani inference system is design and applied to inverse dynamic plus gravity methodology. This methodology is based on applied fuzzy logic in equivalent nonlinear dynamic part to estimate unknown parameters. The results demonstrate that the error-based parallel fuzzy inverse dynamic plus gravity controller is a partly model-free controllers which works well in certain and partly uncertain system.

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 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 back stepping 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 back stepping controller is designed to achieve this objective. The controller developed in this research is designed into 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.

Both fuzzy logic and sliding mode can compensate the steady-state error of proportional-derivative (PD) method. This paper presents parallel sliding mode optimization for fuzzy PD management. The asymptotic stability of fuzzy PD management with first-order sliding mode optimization in the parallel structure is proven. For the parallel structure, the finite time convergence with a super-twisting second-order sliding-mode is guaranteed.

In this research, an artificial chattering free adaptive fuzzy modified sliding mode control design and application to continuum robotic manipulator has proposed in order to design high performance nonlinear controller in the presence of uncertainties. Regarding to the positive points in sliding mode controller, fuzzy logic controller and online tuning method, the output improves. Each method by adding to the previous controller has covered negative points. The main target in this research is design of model free estimator on-line sliding mode fuzzy algorithm for continuum robot manipulator to reach an acceptable performance. Continuum robot manipulators are highly nonlinear, and a number of parameters are uncertain, therefore design model free controller by both analytical and empirical paradigms are the main goal. Although classical sliding mode methodology has acceptable performance with known dynamic parameters such as stability and robustness but there are two important disadvantages as below: chattering phenomenon and mathematical nonlinear dynamic equivalent controller part. To solve the chattering fuzzy logic inference applied instead of dead zone function. To solve the equivalent problems in classical sliding mode controller this paper focuses on applied on-line tuning method in classical controller. This algorithm works very well in certain and uncertain environment. The system performance in sliding mode controller is sensitive to the sliding function. Therefore, compute the optimum value of sliding function for a system is the next challenge. This problem has solved by adjusting sliding function of the on-line method continuously in real-time. In this way, the overall system performance has improved with respect to the classical sliding mode controller. This controller solved chattering phenomenon as well as mathematical nonlinear equivalent part by applied modified PID supervisory method in modified fuzzy sliding mode controller and tuning the sliding function.

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.

Refer to this research, a gradient descent optimization methodology for position fuzzy- model based computed torque controller (GDFCTC) is proposed for highly nonlinear continuum robot manipulator. The main problem of the pure computed torque controller (CTC) was equivalent problem in uncertain systems. The simulation results exhibit that the CTC works well in certain system. To eliminate the continuum robot manipulator system’s dynamic; Mamdani fuzzy inference system is design and applied to CTC. This methodology is based on applied fuzzy logic in equivalent nonlinear dynamic part to estimate unknown parameters. This relatively controller is more plausible to implement in an actual real-time when compared to other techniques of nonlinear controller methodology of continuum arms. Based on the gradient descent optimization method, the PD-gain updating factor has been developed in certain and partly uncertain continuum robots. The new techniques proposed and methodologies adopted in this paper supported by MATLAB/SIMULINK results represent a significant contribution to the field of design an optimized nonlinear computed torque controller for continuum robots.

This paper studies the use of Modified Proportional-Integral-Derivative Sliding Mode Controller (MPIDSMC) control used to control a flexible manipulator. The control gain in the MPIDSMC controller has been determined in an empirical way so far. It is a considerable time-consuming process because the control performance depends not only on the control gain but also on the other parameters such as the payload, references and PID joint servo gains. Hence, the control gain must be tuned considering the other parameters. In order to find the optimal control gain for the MPIDSMC controller, a fuzzy logic approach is proposed in this paper. The proposed fuzzy logic scheme finds an optimum control gain that minimizes the tip vibration for the end effector of the flexible manipulator. Tuned gain response results are compared to results for other types of gains. The effectiveness of using the fuzzy logic appears in the reduction of the computational time and the ability to tune the gain with different loading condition and input parameters.

This paper examines single input single output (SISO) chattering free variable structure control (VSC) which controller coefficient is on-line tuned by fuzzy backstepping algorithm to control of continuum robot manipulator. Variable structure methodology is selected as a framework to construct the control law and address the stability and robustness of the close loop system based on Lyapunove formulation. The main goal is to guarantee acceptable error result and adjust the trajectory following. The proposed approach effectively combines the design technique from variable structure controller is based on Lyapunov and modified Proportional plus Derivative (P+D) fuzzy estimator to estimate the nonlinearity of undefined system dynamic in backstepping controller. The input represents the function between variable structure function, error and the modified rate of error. The outputs represent joint torque, respectively. The fuzzy backstepping methodology is on-line tune the variable structure function based on adaptive methodology. The performance of the SISO VSC based on-line tuned by fuzzy backstepping algorithm (FBSAVSC) is validated through comparison with VSC. Simulation results signify good performance of trajectory in presence of uncertainty joint torque load.

In this paper, a PD-serial fuzzy based robust nonlinear estimator for a robot manipulator is proposed by using robust factorization approach. That is, considering the uncertainties of dynamic model consisting of measurement error and disturbances, a PD with fuzzy estimator variable structure nonlinear feedback control scheme is designed to reduce effect of uncertainties. This research aims to design a new methodology to fix the position in robot manipulator. PD method is a linear methodology which can be used for highly nonlinear system’s (e.g., robot manipulator). To estimate this method, new serial fuzzy variable structure method (PD.FVSM) is used. This estimator can estimate the parameters to have the best performance.

Refer to this research, an intelligent robust fuzzy parallel feedback linearization estimator for Proportional-Integral-Derivative (PID) controller is proposed for highly nonlinear continuum robot manipulator. In the absence of robot knowledge, PID may be the best controller, because it is model-free, and its parameters can be adjusted easily and separately. And it is the most used in robot manipulators. In order to remove steady-state error caused by uncertainties and noise, the integrator gain has to be increased. This leads to worse transient performance, even destroys the stability. The integrator in a PID controller also reduces the bandwidth of the closed-loop system. Model-based compensation for PD control is an alternative method to substitute PID control. Feedback linearization compensation is one of the nonlinear compensator. The first problem of the pure feedback linearization compensator (FLC) was equivalent problem in certain and uncertain systems. The nonlinear equivalent dynamic problem in uncertain system is solved by using parallel fuzzy logic theory. To eliminate the continuum robot manipulator system’s dynamic; Mamdani fuzzy inference system is design and applied to FLC. This methodology is based on design parallel fuzzy inference system and applied to equivalent nonlinear dynamic part of FLC. The results demonstrate that the model free fuzzy FLC estimator works well to compensate linear PID controller in presence of partly uncertainty system (e.g., continuum robot).

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.

Computed torque controller (CTC) is a significant nonlinear controller under condition of partly uncertain dynamic parameters of system. This controller is used to control of highly nonlinear systems especially for robot manipulators, because this controller is a robust and stable. Conversely, computed torque controller is used in many applications; it has an important drawback namely; nonlinear equivalent dynamic formulation in uncertain dynamic parameter. The nonlinear equivalent dynamic formulation problem in uncertain system can be solved by using artificial intelligence theorem. However fuzzy logic controller is used to control complicated nonlinear dynamic systems, but it cannot guarantee stability and robustness. In this research parallel fuzzy logic theory is used to compensate the system dynamic uncertainty in computed torque controller.

The Proportional Integral Derivative (PID) Fuzzy hybrid (switching mode computed torque sliding mode) Controller is presented in this research. The popularity of PID FHC controllers can be attributed to their robust performance in a wide range of operating conditions and partly to their functional simplicity. The process of setting of PID FHC controller can be determined as an optimization task. Over the years, use of intelligent strategies for tuning of these controllers has been growing. Biologically inspired evolutionary strategies have gained importance over other strategies because of their consistent performance over wide range of process models and their flexibility. This paper analyses the manual tuning techniques and compares the same with Gradient Descent tuning methods for tuning PID FHC controllers for flexible robot manipulator system and testing of the quality of process control in the simulation environment of MATLAB/SIMULINK Simulator.

This research involved developing a surgical robot assistant using an articulated PUMA robot running on a linear or nonlinear axis. The research concentrated on studying the artificial intelligence based switching computed torque controller to localization of an endoscopic tool. Results show that the switching artificial nonlinear control algorithm is capable to design a stable controller. For this system, error was used as the performance metric. Positioning of the endoscopic manipulator relative to the world coordinate frame was possible to within 0.05 inch. Error in maintaining a constant point in space is evident during repositioning however this was caused by limitations in the robot arm.

In this research, model reference fuzzy based control is presented as robust controls for IC engine. The objective of the study is to design controls for IC engines without the knowledge of the boundary of uncertainties and dynamic information by using fuzzy model reference PD plus mass of air while improve the robustness of the PD plus mass of air control. A PD plus mass of air provides for eliminate the mass of air and ultimate accuracy in the presence of the bounded disturbance/uncertainties, although this methods also causes some oscillation. The fuzzy PD plus mass of air is proposed as a solution to the problems crated by unstability. This method has a good performance in presence of uncertainty.

Both fuzzy logic and computed fuel ratio can compensate the steady-state error of proportional-derivative (PD) method. This paper presents parallel computed fuel ratio compensation for fuzzy plus PID control management with application to internal combustion (IC) engine. The asymptotic stability of fuzzy plus PID control methodology with first-order computed fuel ratio estimation in the parallel structure is proven. For the parallel structure, the finite time convergence with a super-twisting second-order sliding-mode is guaranteed.

This paper describes the design and implementation of robust nonlinear sliding mode control strategies for robot manipulators whose dynamic or kinematic models are uncertain. Therefore a fuzzy sliding mode tracking controller for robot manipulators with uncertainty in the kinematic and dynamic models is design and analyzes. The controller is developed based on the unit quaternion representation so that singularities associated with the otherwise commonly used three parameter representations are avoided. Simulation results for a planar application of the continuum or hyper-redundant robot manipulator (CRM) are provided to illustrate the performance of the developed adaptive controller. These manipulators do not have rigid joints, hence, they are difficult to model and this leads to significant challenges in developing high-performance control algorithms. In this research, a joint level controller for continuum robots is described which utilizes a fuzzy methodology component to compensate for dynamic uncertainties.

Refer to this research, an intelligent fuzzy parallel switching Proportional-Derivative (PD) plus gravity controller is proposed for highly nonlinear continuum robot manipulator. Design a nonlinear controller for second order nonlinear uncertain dynamical systems is one of the most important challenging works. In order to provide high performance in nonlinear systems, switching partly sliding mode plus gravity controller is selected. Pure switching partly sliding mode plus gravity controller can be used to control of partly known nonlinear dynamic parameters of continuum robot manipulator. Conversely, this method is used in many applications; it must to solve chattering phenomenon which it can cause some problems such as saturation and heat the mechanical parts of continuum robot manipulators or drivers. In order to solve the chattering phenomenon, implement easily and avoid mathematical model base controller, Mamdani’s performance/error-based fuzzy logic methodology with two inputs and one output and 49 rules is parallel applied to pure switching partly sliding mode plus gravity controller. The results demonstrate that this method is a model-free controllers which works well in certain and partly uncertain system.

One of the best nonlinear robust controllers which can be used in uncertain nonlinear systems is sliding mode controller (SMC), but pure SMC results in chattering in a noisy environment. This effect can be eliminated by optimizing the sliding surface slope. This paper investigates a novel methodology in designing a SMC by a new heuristic search, so called "colonial competitive algorithm "in order to tune the sliding surface slope and the switching gain of the discontinuous part in SMC structure. This process decreases the integral of absolute errors which results in tracking the desired inputs by the outputs in designing a controller for robot manipulator. Simulation results prove that the optimized performance obtained through CCA significantly reduces the chattering phenomena and results in better trajectory tracking compared to typical trial and error methods.

Both fuzzy logic and sliding mode can compensate the steady-state error of proportional-derivative (PD) control. This paper presents parallel sliding mode compensations for fuzzy PD controllers. 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.

Design a nonlinear controller for second order nonlinear uncertain dynamical systems (e.g., internal combustion engine) is one of the most important challenging works. This paper focuses on the comparative study between two important nonlinear controllers namely; computed torque controller (CTC) and sliding mode controller (SMC) and applied to internal combustion (IC) engine in presence of uncertainties. In order to provide high performance nonlinear methodology, sliding mode controller and computed torque controller are selected. Pure SMC and CTC can be used to control of partly known nonlinear dynamic parameters of IC engine. Pure sliding mode controller and computed torque controller have difficulty in handling unstructured model uncertainties. To solve this problem applied linear error-based tuning method to sliding mode controller and computed torque controller for adjusting the sliding surface gain (λ ) and linear inner loop gain (K). Since the sliding surface gain (λ) and linear inner loop gain (K) are adjusted by linear error-based tuning method. In this research new λ and new K are obtained by the previous λ and K multiple gains updating factor(α). The results demonstrate that the error-based linear SMC and CTC are model-based controllers which works well in certain and uncertain system. These controllers have acceptable performance in presence of uncertainty.

Refer to this paper, an intelligent-fuzzy feed-forward computed torque estimator for Proportional-Integral-Derivative (PID) controller is proposed for highly nonlinear continuum robot manipulator. In the absence of robot knowledge, PID may be the best controller, because it is model-free, and its parameters can be adjusted easily and separately and it is the most used in robot manipulators. In order to remove steady-state error caused by uncertainties and noise, the integrator gain has to be increased. This leads to worse transient performance, even destroys the stability. The integrator in a PID controller also reduces the bandwidth of the closed-loop system. Model-based compensation for PD control is an alternative method to substitute PID control. Computed torque compensation is one of the nonlinear compensator. The main problem of the pure computed torque compensator (CTC) was highly nonlinear dynamic parameters which related to system’s dynamic parameters in certain and uncertain systems. The nonlinear equivalent dynamic problem in uncertain system is solved by using feed-forward fuzzy inference system. To eliminate the continuum robot manipulator system’s dynamic; Mamdani fuzzy inference system is design and applied to CTC. This methodology is based on design feed-forward fuzzy inference system and applied to CTC. The results demonstrate that the model base feed-forward fuzzy CTC estimator works well to compensate linear PID controller in presence of partly uncertainty system (e.g., continuum robot).

The control problem for manipulators is to determine the joint inputs required to case the end-effector execute the commanded motion. The nonminimum phase characteristic of a rigid manipulator makes the design of stable controller that ensure stringent tracking requirements a highly nontrivial and challenging problem. A useful controller in the computed torque family is the PD-plus-gravity controller. Methodology. To compensate the dynamic parameters, fuzzy logic methodology is used and applied parallel to this method. when the arm is at rest, the only nonzero terms in the dynamic is the gravity. Proposed method can cancels the effects of the terms of gravity. In this case inorder to decrease the error and satteling time, higher gain controller is design and applied to nonlinear system.

The main purpose of this paper is to design a suitable control scheme that confronts the uncertainties in a robot. Sliding mode controller (SMC) is one of the most important and powerful nonlinear robust controllers which has been applied to many non-linear systems. However, this controller has some intrinsic drawbacks, namely, the chattering phenomenon, equivalent dynamic formulation, and sensitivity to the noise. This paper focuses on applying artificial intelligence integrated with the sliding mode control theory. Proposed adaptive fuzzy sliding mode controller optimized by Particle swarm algorithm (AFSMC-PSO) is a Mamdani’s error based fuzzy logic controller (FLS) with 7 rules integrated with sliding mode framework to provide the adaptation in order to eliminate the high frequency oscillation (chattering) and adjust the linear sliding surface slope in presence of many different disturbances and the best coefficients for the sliding surface were found by offline tuning Particle Swarm Optimization (PSO). Utilizing another fuzzy logic controller as an impressive manner to replace it with the equivalent dynamic part is the main goal to make the model free controller which compensate the unknown system dynamics parameters and obtain the desired control performance without exact information about the mathematical formulation of model.

First three degree of six degree of freedom robotic manipulator is controlled by a new fuzzy sliding feedback linearization controller. The robot arm has six revolute joints allowing the corresponding links to move horizontally. When developing a controller using conventional control methodology (e.g., feedback linearization methodology), a design scheme has to be produced, usually based on a system’s dynamic model. The work outline in this research utilizes soft computing applied to new conventional controller to address these methodology issues. Feedback linearization controller (FLC) is influential nonlinear controllers to certain systems which this method is based on compute the required arm torque using nonlinear feedback control law. When all dynamic and physical parameters are known FLC works superbly; practically a large amount of systems have uncertainties and fuzzy feedback linearization controller (FFLC) reduce this kind of limitation. Fuzzy logic provides functional capability without the use of a system dynamic model and has the characteristics suitable for capturing the approximate, varying values found in a MATLAB based area. To increase the stability and robustness new mathematical switching sliding mode methodology is applied to FFLC. Based on this research model free mathematical tunable gain new sliding switching feedback linearization controller applied to robot manipulator is presented to have a stable and robust nonlinear controller and have a good result compared with conventional and pure fuzzy logic controllers.

Internal combustion (IC) engines are optimized to meet exhaust emission requirements with the best fuel economy. Closed loop combustion control is a key technology that is used to optimize the engine combustion process to achieve this goal. In order to conduct research in the area of closed loop combustion control, a control oriented cycle-to-cycle engine model, containing engine combustion information for each individual engine cycle as a function of engine crank angle, is a necessity. In this research, the IC engine is modeled according to fuel ratio, which is represented by the mass of air. In this research, a multi-input-multi-output baseline computed fuel control scheme is used to simultaneously control the mass flow rate of both port fuel injection (PFI) and direct injection (DI) systems to regulate the fuel ratio of PFI to DI to desired levels. The control target is to maintain the fuel ratio at stoichiometry and the fuel ratio to a desired value between zero and one. The performance of the baseline computed fuel controller is compared with that of a baseline proportional, integral, and derivative (PID) controller.

This paper expands a Multi Input Multi Output (MIMO) fuzzy baseline variable structure control (VSC) which controller coefficient is off-line tuned by gradient descent algorithm. The main goal is to adjust the optimal value for fuel ratio (FR) in motor engine. The fuzzy inference system in proposed methodology is works based on Mamdani-Lyapunov fuzzy inference system (FIS). To reduce dependence on the gain updating factor coefficients of the fuzzy methodology, PID baseline method is introduced. This new method provides an optimal setting for other factors which crated by PID baseline method. The gradient descent methodology is off-line tune all coefficients of baseline fuzzy and variable structure function based on mathematical optimization methodology. The performance of proposed methodology is validated through comparison with fuzzy variable structure methodology (FVSC). Simulation results signify good performance of fuel ratio in presence of different torque load and external disturbance.

Internal combustion (IC) engines are optimized to meet exhaust emission requirements with the best fuel economy. Closed loop combustion control is a key technology that is used to optimize the engine combustion process to achieve this goal. In order to conduct research in the area of closed loop combustion control, a control oriented cycle-to-cycle engine model, containing engine combustion information for each individual engine cycle as a function of engine crank angle, is a necessity. This research aims to design a new methodology to fix the fuel ratio in internal combustion (IC) engine. Baseline method is a linear methodology which can be used for highly nonlinear system’s (e.g., IC engine). To optimize this method, new linear part sliding mode method (NLPSM) is used. This online optimizer can adjust the optimal coefficient to have the best performance.

Design a nonlinear controller for second order nonlinear uncertain dynamical systems is the main challenge in this paper. This paper focuses on the design and analysis of a chattering free Mamdani’s fuzzy-based tuning gradient descent optimal error-based fuzzy sliding mode controller for highly nonlinear dynamic six degrees of freedom robot manipulator, in presence of uncertainties. Conversely, pure sliding mode controller is used in many applications; it has two important drawbacks namely; chattering phenomenon and nonlinear equivalent dynamic formulation in uncertain dynamic parameter. In order to solve the uncertain nonlinear dynamic parameters, implement easily and avoid mathematical model base controller, Mamdani’s performance/error-based fuzzy logic methodology with two inputs and one output and 49 rules is applied to pure sliding mode controller. Pure sliding mode controller and error-based fuzzy sliding mode controller have difficulty in handling unstructured model uncertainties. To solve this problem applied fuzzy-based tuning method to error-based fuzzy sliding mode controller for adjusting the sliding surface gain. Since the sliding surface gain is adjusted by gradient descent optimization method. Fuzzy-based tuning gradient descent optimal error-based fuzzy sliding mode controller is stable model-free controller which eliminates the chattering phenomenon without to use the boundary layer saturation function. Lyapunov stability is proved in fuzzy-based tuning gradient descent optimal fuzzy sliding mode controller based on 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).

Congetive method is used in this research to create portfilo of movement robot manipulator. Gradient descent (GD) artificial intelligence based switching feedback linearization controller was used and robot's postures and trajectory were expected in MATLAB/SIMULINK environment. Feedback linearization controller (CTC) is an influential nonlinear controller to certain systems which it is based on feedback linearization and computes the required torques using the nonlinear feedback control law in certain systems. Practically a large amount of systems have uncertainties accordingly this method has a challenge. Switching feedback linearization controller is a significant combination nonlinear stable-robust controller under condition of partly uncertain dynamic parameters of system. This technique is used to control of highly nonlinear systems especially in nonlinear time varient nonlinear dynamic system. To increase the stability and robustness with regards to improve the robustness switching methodology is applied to feedback linearization controller. Lyapunov stability is proved in proposed controller based on switching function. To compensate for the dependence on switching parameters baseline methodology is used.The nonlinear model dynamic formulation problem in uncertain system can be solved by using artificial intelligence theorem. Fuzzy logic theory is used to estimate the system dynamic. Forward kinematics implemented the manipulator's movements. Results validated the robot's range of possible postures and trajectories