S. F. Dehkordi

Bio: S. F. Dehkordi is an academic researcher from Iran University of Science and Technology. The author has contributed to research in topics: Equations of motion & Revolute joint. The author has an hindex of 6, co-authored 22 publications receiving 129 citations.

Systematic modeling of a chain of N-flexible link manipulators connected by revolute–prismatic joints using recursive Gibbs-Appell formulation

Abstract: The main intent of this paper is to represent a systematic algorithm capable of deriving the equations of motion of N-flexible link manipulators with revolute–prismatic joints. The existence of the prismatic joints together with the revolute ones makes the derivation of governing equations difficult. Also, the variations of the flexible parts of the links, with respect to time cause the associated mode shapes of the links to vary instantaneously. So, to derive the kinematic and dynamic equations of motion for such a complex system, the recursive Gibbs-Appell formulation is applied. For a comprehensive and accurate modeling of the system, the coupling effects due to the simultaneous rotating and reciprocating motions of the flexible arms as well as the dynamic interactions between large movements and small deflections are also included. In this study, the links are modeled based on the Euler–Bernoulli beam theory and the assumed mode method. Also, the effects of gravity as well as the longitudinal, transversal and torsional vibrations have been considered in the formulations. Moreover, a recursive algorithm based on 3 × 3 rotational matrices has been applied in order to derive the system’s dynamic equations of motion, symbolically and systematically. Finally, a numerical simulation has been performed by means of a developed computer program in order to demonstrate the ability of this algorithm in deriving and solving the equations of motion related to such systems.

Derivation of motion equation for mobile manipulator with viscoelastic links and revolute–prismatic flexible joints via recursive Gibbs–Appell formulations

Abstract: This paper investigates the dynamic equations of an N-flexible link manipulator with revolute–prismatic joints while considering the effects of manipulator locomotion by the mobile platform bound by non-holonomic kinematic constraints. Such constraints, in addition to creating dynamic interaction between manipulator and platform, cause serious motion limitations and introduction of more computational complexity. The manipulator’s flexible links are modeled by the assumed mode method, where the Timoshenko beam theory is used for the substitution of the assumed mode shapes. The internal and external damping effects are also studied for the model precision. Moreover, revolute–prismatic joints in each arm are exploited to develop the robot mobility. The new joint structure makes it possible to use mobile manipulators with long flexible links. However, in regard to the variations of links length caused by prismatic joints, time-varying dynamic equations are obtained, leading to comparatively complex and lengthy formulations. Therefore, the Gibbs–Appell formulation is utilized as an alternative to the Lagrange equations to facilitate the process of deriving the motion equations. In addition, the non-dimensional form of the Timoshenko beam theory mode shapes is recommended to circumvent the computation of time step mode shapes. It is also necessary to examine the system tip-over stability based on long and variable-length arms, lightweight base, and widespread environmental factors using the zero moment point methods. Finally, a numerical simulation for a mobile manipulator, with two flexible links and revolute–prismatic joints is carried out to demonstrate the performance of the presented model for such complex systems. Different amounts of link elasticity and the effects of internal and external damping coefficients are separately studied. The results are verified by recent fixed base flexible manipulators employing revolute–prismatic joints as well as the IUST Revolute–Prismatic joints experimental setup incorporating rigid links.

Dynamic modeling of flexible cooperative mobile manipulator with revolute-prismatic joints for the purpose of moving common object with closed kinematic chain using the recursive Gibbs–Appell formulation

Abstract: In this paper, the dynamic equations of flexible cooperative manipulators that are kinematically and dynamically constrained to an object and are placed on a non-holonomic mobile platform are explored. The main objective is to develop the dynamics of closed kinematic cooperative manipulators by defining constraints in mobile form while considering the geometric dimensions of the common object instead of assuming a concentrated mass in the gripper as well as the application of manipulator with flexible links and revolute-prismatic joints in the constrained cooperative mobile form. Unlike robots with independent manipulators, the dynamic constraint relates the dynamic equations of object and arms, initiating the motion and introducing interaction forces from the object to arms. In addition, the kinematic constraint keeps the distance between the two arms constant by constraining the relative motion velocity of the arms’ gripper. The dynamic equations of manipulators are derived using the recursive Gibbs–Appell formulation while the object equations are obtained using the Newton-Euler approach. Finally, the motion equations for a cooperative mobile robot with two 2-flexible-link arms are simulated. The results are evaluated at two stages by incorporating dynamic constraints as well as concurrent consideration of kinematic and dynamic constraints. Also, each manipulator's dynamic model weighted by using the experimental test setup with single link and revolute-prismatic joint.

Derivation of dynamic equation of viscoelastic manipulator with revolute–prismatic joint using recursive Gibbs–Appell formulation

Abstract: In this paper, the motion analysis of a viscoelastic manipulator with N-flexible revolute–prismatic joints is being studied with the help of a systematic algorithm The presence of prismatic joints, along with revolute ones, makes the derivation of the equations complicated The link’s axial motions cause variation of its flexible parts with respect to time In order to modify the associated mode shapes concerning an instant link length, dynamic interaction between the rotary reciprocating motion and transverse vibration of the flexible arm is evaluated The links are modeled on the assumed mode method using the Timoshenko beam theory (TBT) Dynamic equations are derived from the recursive Gibbs–Appell formulation The formulation involves fewer mathematical calculations but shows efficient computational performance when compared to other formulations The dynamic model of each joint shows flexibility, damping, backlash and frictions resulting in accuracy of the formulations Applying recursive algorithm based on the $$3\times 3$$ rotational matrix instead of the $$4\times 4$$ one causes the computational performance to fall by separating the rotating matrix Furthermore, motion equations are obtained symbolically and systematically Links linear motion causes TBT mode shapes changes with respect to time This is implemented in a non-dimensional form to avoid computing for each step Finally, the following dynamic equations are solved numerically by MATLAB software for a spatial two-armed manipulator The outcome of the simulations represents the ability of the proposed algorithm to derive and solve the equations of motion Moreover, the data are compared with the rigid and elastic links, modeled by the Euler–Bernoulli beam theory

Dynamic modeling and extended bifurcation analysis of flexible-link manipulator

Abstract: In this article, the nonlinear dynamic analysis of a flexible-link manipulator is presented. Especially, the possibility of chaos occurrence in the system dynamic model is investigated. Upon the oc...

New analytical method based on dynamic response of planar mechanical elastic systems

Abstract: An important stage in an analysis of a multibody system (MBS) with elastic elements by the finite element method is the assembly of the equations of motion for the whole system. This assembly, which seems like an empirical process as it is applied and described, is in fact the result of applying variational formulations to the whole considered system, putting together all the finite elements used in modeling and introducing constraints between the elements, which are, in general, nonholonomic. In the paper, we apply the method of Maggi’s equations to realize the assembly of the equations of motion for a planar mechanical systems using finite two-dimensional elements. This presents some advantages in the case of mechanical systems with nonholonomic liaisons.

An approach for jerk-continuous trajectory generation of robotic manipulators with kinematical constraints

Abstract: This paper proposes a methodology to generate online smooth joint trajectories of robots based on an improved sinusoidal jerk model. The multi-segment trajectory model is designed to allow a more sufficient exploitation of the actuation capability, thereby shortening the execution time while ensuring continuity up to the jerk level. Afterwards, the general mathematical expressions of the motion profiles are derived from integration of the jerk function. By analyzing the critical constraint conditions corresponding to each possible profile type, a complete closed-form solution to the minimum time planning problem with consideration of kinematic constraints has then been worked out, where a parameter named the ramp coefficient that manages the ratio of the sine jerk period is introduced to simplify the determination of the motion formulas. Thus the method results in a computationally light optimization procedure for facile implementation and enables a higher level of regularity for achieving desirable motion behaviours in light of the operation requirements and joint characteristics. Experimental results conducted on a robot manipulator reveal that the proposed approach is capable of yielding better performance than existing techniques in terms of efficiency and jerk suppression.

Derivation of motion equation for mobile manipulator with viscoelastic links and revolute–prismatic flexible joints via recursive Gibbs–Appell formulations

Abstract: This paper investigates the dynamic equations of an N-flexible link manipulator with revolute–prismatic joints while considering the effects of manipulator locomotion by the mobile platform bound by non-holonomic kinematic constraints. Such constraints, in addition to creating dynamic interaction between manipulator and platform, cause serious motion limitations and introduction of more computational complexity. The manipulator’s flexible links are modeled by the assumed mode method, where the Timoshenko beam theory is used for the substitution of the assumed mode shapes. The internal and external damping effects are also studied for the model precision. Moreover, revolute–prismatic joints in each arm are exploited to develop the robot mobility. The new joint structure makes it possible to use mobile manipulators with long flexible links. However, in regard to the variations of links length caused by prismatic joints, time-varying dynamic equations are obtained, leading to comparatively complex and lengthy formulations. Therefore, the Gibbs–Appell formulation is utilized as an alternative to the Lagrange equations to facilitate the process of deriving the motion equations. In addition, the non-dimensional form of the Timoshenko beam theory mode shapes is recommended to circumvent the computation of time step mode shapes. It is also necessary to examine the system tip-over stability based on long and variable-length arms, lightweight base, and widespread environmental factors using the zero moment point methods. Finally, a numerical simulation for a mobile manipulator, with two flexible links and revolute–prismatic joints is carried out to demonstrate the performance of the presented model for such complex systems. Different amounts of link elasticity and the effects of internal and external damping coefficients are separately studied. The results are verified by recent fixed base flexible manipulators employing revolute–prismatic joints as well as the IUST Revolute–Prismatic joints experimental setup incorporating rigid links.

Adaptive Control and Optimization of Mobile Manipulation Subject to Input Saturation and Switching Constraints

Abstract: In this paper, a hierarchical hybrid motion/force control architecture for the manipulation and grasping of mobile manipulators is presented, where the systems are subject to varieties of physical constraints such as Coulomb friction cones, nonholonomic/holonomic constraints, and actuator saturation limits. The incorporation of a projection-based operation space control and an adaptive controller based on the neural networks used in this paper formulates a novel control scheme, so the system stability is further guaranteed and the uncertain dynamics is handled without redesigning the minimal-order dynamics model. Considering the effects of these constraints, the actuator saturation limits are handled by an auxiliary designed system, and the neural dynamics optimization is applied for the quadratically constrained programing problem of the optimal robotic grasping. The dynamic uncertainties can be estimated online by using the developed motion/force control strategy, and the application of a novel disturbance observer is explored to ensure the good tracking performance. The experimental results are presented to verify the performance and the efficiency of the proposed method. Note to Practitioners —This paper is motivated by the problems of robotic grasping, the trajectory tracking of mobile manipulation, which are with time-varying topology (e.g., actuator saturation limits, switching constraints). Traditional approaches tackling such problems mainly use multiple-models switching control architecture; however, these methods are not suitable for the switching conditions. Therefore, it is necessary to develop a novel control approach dealing with these issues together. In this paper, a unified hierarchical hybrid motion/force control architecture is proposed using the notion of projection operator, and the control inputs are decomposed into the null space, which produces the motion complement of the system and the orthogonal complement space constructing physical constraints, respectively. In addition, an auxiliary system is also designed to solve the limits from the actuator saturation. The feasibility of the system is demonstrated by the extensive experiment results including trajectory tracking and the switching constraints in the developed mobile manipulator.