This paper proposes a discrete-time repetitive optimal control of electrically driven robotic Manipulators using an uncertainty estimator. The proposed control method can be used for performing repetitive motion, which covers many industrial applications of robotic Manipulators. This kind of control law is in the class of torque-based control in which the joint torques are generated by permanent magnet dc motors in the current mode. The motor current is regulated using a proportional-integral controller. The novelty of this paper is a modification in using the discrete-time linear quadratic control for the robot manipulator, which is a nonlinear uncertain system. For this purpose, a novel discrete linear time-variant model is introduced for the robotic system. Then, a time-delay uncertainty estimator is added to the discrete-time linear quadratic control to compensate the nonlinearity and uncertainty associated with the model. The proposed control approach is verified by stability analysis. Simulation results show the superiority of the proposed discrete-time repetitive optimal control over the discrete-time linear quadratic control.

In this paper kinematics model of a nonholonomic mobile manipulator is formulated. The kinematics equations for a mechanical mobile manipulator are developed in such a way that the kinematics interaction between the mobile platform and mechanical manipulator explicitly appears in the equations. In both conditions the motion constraints and kinematics redundancy are considered and analyzed. These concepts are expanded in general cases by using special subjects, on linear algebra and functional analysis. A useful and unique kinematics model for redundancy resolution of mobile Manipulators is introduced by defining specified variables. Finally, the application of the model is verified by simulation results in order to find the maximum allowable load of a mobile manipulator.

This paper develops a computational technique for finding the maximum allowable ‎load of mobile Manipulators for a given trajectory. The maximum allowable loads ‎which can be achieved by a mobile manipulator during a given trajectory are limited ‎by the number of factors; probably the dynamic properties of mobile base and ‎mounted manipulator, their actuator limitations and additional constraints applied to ‎resolving the redundancy are the most important factors. To resolve extra D.O.F ‎introduced by the base mobility, additional constraint functions are proposed directly ‎in the task space of mobile manipulator. Finally, in two numerical examples involving ‎a two-link planar manipulator mounted on a differentially driven mobile base, ‎application of the method to determining maximum allowable load is verified. The ‎simulation results demonstrates the maximum allowable load on a desired trajectory ‎has not a unique value and directly depends on the additional constraint functions ‎which applies to resolve the motion redundancy‏.‏

Mobile platforms with one or more Manipulators are of great interest for their wide area of applications and dexterity. Including a suspension system in such mobile platforms will certainly add to their maneuverability, though causes more complexity. In this paper, a suspended mobile platform with two 6-DOF Manipulators is used to manipulate an object in a mixed circular-straight path. The Multiple Impedance control (MIC) as a Model-Based algorithm, enforces the same impedance law both on the robotic system, and the manipulated object level. To apply model-based control laws, however, it is needed to extract system dynamics equations. For such highly nonlinear dynamical systems, it is necessary to have a concise set of dynamic equations with as few as possible mathematical calculations. Therefore, the concept of Direct Path Method, is extended to derive explicit dynamics modeling for such challenging systems. Then non-holonomic constraint of the wheeled platform is discussed, and obtained dynamics model is reformatted to become more concise using Natural Orthogonal Complement Method. Next, the MIC law is applied to cooperative manipulation of an object by the two Manipulators. The obtained results reveal the success of the suspended mobile robot in its defined mission.

In this study, an adaptive proportional-derivative (PD) control scheme is proposed for trajectory tracking of multidegree-of-freedom robot Manipulators in the presence of model uncertainties and external disturbances whose upper bounds are unknown but bounded. The developed controller takes the advantages of linear control in the sense of simplicity and easy design, but simultaneously possesses high robustness against model uncertainties and disturbances while avoiding the necessity of precise knowledge of the system dynamics. Due to the linear feature of the proposed method, both the transient and steady-state responses are easily controlled to meet desired specifications. Also, an adaptive law for control gains using only position and velocity measurements is introduced so that parameter uncertainties and disturbances are successfully compensated, where the prior knowledge about their upper bounds is not required. Stability analysis is conducted using the Lyapunov’ s direct method and brief guidelines on how to select control parameters are also provided. Simulation results corroborate that the adaptive PD control law proposed in this paper can achieve a fast convergence rate, small tracking errors, low control effort, and small computational cost and its performance is compared with that of an existing nonlinear sliding mode control method.

Background and Objectives: This paper presents a robust passivity-based voltage controller (PBVC) for robot Manipulators with n degree of freedom in the presence of model uncertainties and external disturbance. Methods: The controller design procedure is divided into two steps. First, a model-based controller is designed based on the PBC scheme. An output feedback law is suggested to ensure the asymptotic stability of the closed-loop error dynamics. Second, a regressor-free adaptation law is obtained to estimate the variations of the model uncertainties and external disturbance. The proposed control law is provided in two different orders. Results: The suggested controller inherits both advantages of the passivity-based control (PBC) scheme and voltage control strategy (VCS). Since the proposed control approach only uses the electrical model of the actuators, the obtained control law is simple and also has an independent-joint structure. Moreover, the proposed PBVC overcomes the drawbacks of torque control strategy such as the complexity of manipulator dynamics, practical problems and ignoring the role of actuators. Moreover, computer simulations are carried out for both tracking and regulation purposes. In addition, the proposed controller is compared with a passivity-based torque controller where the simulation results show the appropriate efficiency of the proposed approach. Conclusion: The robust PBVC is proposed for EDRM in presence of external disturbance. To the best of our knowledge, it is the first time that a regressor-free adaptation law is obtained to approximate the lumped uncertainties according to the passivity-based VCS. Moreover, the electrical model of the actuators is utilized in a decentralized form to control each joint separately.

Optimal design of parallel Manipulators is known as a challenging problem especially for cable driven robots. In this paper, optimal design of cable driven redundant parallel Manipulators (CDRPM) is studied in detail. Visual Inspection method is proposed as a systematic design process of the manipulator. A brief review of various design criteria shows that the optimal design of a CDRPM cannot be performed based on single objective. Therefore, a multi objective optimal design problem is formulated in this paper through an overall cost function. Furthermore, a proper weighting selection for the overall cost function is proposed, which can be viewed as a promising method to the open problem of parallel manipulator design. In order to verify the effectiveness of the proposed method, it is applied on the design of KNTU CDRPM, an eight actuated with six degrees of freedom CDRPM, which is under investigation for possible high speed and wide workspace applications in K.N. Toosi University of Technology. Finally, a combined numerical optimization algorithm is used to find the unique global optimum point. The result shows a significant enhancement in the performance characteristics of the KNTU CDRPM compared to that of the other CDRPMs. Since the proposed method is not restricted to any particular assumption on the objectives and design parameters, it can be used for optimal design of other Manipulators.