Sharif Digital Repository

An improved method for deriving elastic generalized coordinates is considered. Then Kane's equations of motion for multibody systems consisting of an arbitrary number of rigid and elastic bodies is presented. The equations are in general form and are applicable for any desired holonomic system. Flexibility in choosing generalized speeds in terms of generalized coordinate derivatives in Kane's method is used. It is shown that proper choice of a congruency transformation between generalized coordinate derivatives and generalized speeds leads to equations of motion for holonomic multibody systems consisting of an arbitrary number of rigid and elastic bodies. These equations are decoupled in... 

In this paper, a two-link flexible manipulator is considered. For a prescribed motion, Timoshenko and Euler-Bernoulli beam models are considered. Using the Galerkin method, nonlinear equations of motion are solved. The Runge-Kutta method is employed for the time response integration method. A comparative study is made between the Euler-Bernoulli and Timoshenko beam models, with and without foreshortening effects. It is demonstrated that for two-link manipulators, both theories provide good models, and the results for both theories are very similar for all ranges of slenderness ratio. The findings suggest that for two-link manipulators with relatively high slenderness ratios, there is a... 

We present a geometric approach for fault detection and isolation (FDI) in robotic manipulators in presence of model uncertainty. A systematic procedure is introduced for representing robotic system model being affine with respect to faults and disturbances. The proposed residual generator has smooth dynamics with freely selectable functions and it does not require high gains or threshold adjustment for the FDI purpose. No assumption on amplitude of faults and their rate is used. The solvability conditions for the FDI problem lead to a quotient observable subspace unaffected by all unknown inputs except the faults. Simulation example demonstrates localization of faults in presence of... 

In this paper, boundary control (BC) laws are designed to find a BC solution for a single-link nonlinear vertical manipulator to suppress the link’s transverse vibrations and control the rigid body nonlinear large rotating motion. The governing equations of motions and boundary conditions, which all consist of a set of PDEs and ODEs have been derived based on the Hamilton principle. It is desired to regulate large angular orientation, suppress the flexible link’s transverse vibrations and compensate the boundary disturbance simultaneously. The amount of elastic boundary vibration has remained within the constraint range. By considering novel Barrier-Integral Lyapunov functional in order to... 

Problems related to the three-dimensional (3D) dynamics of the deploying flexible arms subjected to base angular motions are studied with simulated tip payloads and actual deployment trajectories. To facilitate the solution, an equivalent dynamical system is developed by introducing the inertial reaction forces on the arm, while the equations of motion are derived in the non-Newtonian reference frame attached to the arm. The dynamic behavior of the arm is investigated both by the finite element and assumed Modes methods for the purpose of verification. This study reveals that base angular motions lead to considerable couplings between the two lateral displacements and axial motions.... 

A robotic manipulator is modelled as a cantilever rotating Euler-Bernoulli beam. Two dynamic transfer functions are derived to describe beam tip motion and angular rotation in terms of the desired angular rotation. Torque disturbance, imprecision in the payload mass, unknown properties of the manipulator link are sources of uncertainty. The objective is to achieve a desired angular rotation while the vibration of manipulator tip is suppressed. The control input of the system is an external driving torque. The -synthesis control approach is used and an H optimal robust controller is developed based on the DK-iteration algorithm. Results show that the designed controller guarantees the robust... 

In this paper, a robotic manipulator modelled as a cantilever rotating Euler-Bernoulli beam is considered. Control objective is achieving a desired angular rotation of the manipulator tip while its lateral vibration is suppressed. An external driving torque is the control input of the system. Two dynamic transfer functions are derived to describe beam tip motion and angular rotation in terms of the desired angular rotation. After state-space representation of the problem, an observer is designed to estimate state variables of the system. Then, a feedback control is designed for both regulation and tracking objectives. Eigenvalues are chosen such that an appropriate response is achieved while... 

In this paper, we introduce a new approach to fault detection and isolation for robot manipulators. Our technique is based on using a new simplified Euler-Lagrange (EL) equation that reduces complexity of the proposed fault detection method. The proposed approach isolates the faults and is capable of handling the uncertainty in manipulator gravity vector. It is shown that the effect of uncalibrated torque sensor measurement is asymptotically rejected in the detection process. A simulation example is presented to illustrate the results. © 2009 IEEE  

This paper introduces a class of time-varying controllers for Euler-Lagrange systems such that the convergence occurs at an arbitrary finite time, independently of initial conditions, and free of chattering. The proposed controller is based on a mapping technique and is designed in two steps: First, a conventional (obstacle avoidance) asymptotically stable controller is specified for the nominal system; then, by a simple substitution, a prescribed-time (obstacle avoidance) controller is achievable for the perturbed system. It is proved that the proposed scheme is uniformly prescribed-time stable for unperturbed systems and prescribed-time attractive for perturbed systems as it rejects... 

In this paper, boundary control (BC) laws are designed to find a BC solution for a single-link nonlinear vertical manipulator to suppress the link’s transverse vibrations and control the rigid body nonlinear large rotating motion. The governing equations of motions and boundary conditions, which all consist of a set of PDEs and ODEs have been derived based on the Hamilton principle. It is desired to regulate large angular orientation, suppress the flexible link’s transverse vibrations and compensate the boundary disturbance simultaneously. The amount of elastic boundary vibration has remained within the constraint range. By considering novel Barrier-Integral Lyapunov functional in order to... 

In this paper, a nonlinear adaptive impedance controller is proposed for UAVs equipped with a robot manipulator that interacts with environment. In this adaptive controller, by considering the nonlinear dynamics model of the UAV plus the robot manipulator in Cartesian coordinates, all of model parameters are considered to be completely uncertain and their estimation is updated using an adaptation law. The objective of the proposed adaptive controller is the control of manipulator's end-effector impedance in Cartesian coordinates to have a stable physical interaction. The adjustable Cartesian impedance is a desired dynamical relationship between the end-effector motion in Cartesian... 

Vibration analysis of a new type of compliant parallel mechanism with flexible intermediate links is investigated. The application of the Timoshenko beam theory to the mathematical modeling of the intermediate flexible link is described, and the equations of motion of the flexible links are obtained by using Lagrange's equation of motion. The equations of motion are obtained in the form of a set of ordinary differential equations by using assumed mode method theory. The governing differential equations of motion are solved using perturbation method. The assumed mode shapes and frequencies are to be obtained based on clamped-clamped boundary conditions. Comparing perturbation method with... 

In this paper, a decentralized controller for trajectory tracking of modular and reconfigurable robot manipulators is developed. The proposed control scheme uses joint-torque sensory feedback; also sliding mode control is employed to make both position and velocity tracking errors of robot manipulators globally converging to zero. Proposed scheme also guarantees that all signals in closed-loop systems will be bounded. In contrast to some of prior works in this scheme, each controller uses a smooth law to achieve its purposes. In this method, each controller uses only local information for producing control law hence separated controller can be used to control each module of manipulator and... 

In this paper, a new nonlinear robust adaptive impedance controller is addressed for Unmanned Aerial Vehicles (UAVs) equipped with a robot manipulator that physically interacts with environment. A UAV equipped with a robot manipulator is a novel system that can perform different tasks instead of human being in dangerous and/or inaccessible environments. The objective of the proposed robust adaptive controller is control of the UAV and its robotic manipulators end-effector impedance in Cartesian space in order to have a stable physical interaction with environment. The proposed controller is robust against parametric uncertainties in the nonlinear dynamics model of the UAV and the robot... 

This study presents a method for global estimation of joint velocities in robotic manipulators. The authors consider a non-minimal model of a robotic manipulator and design an adaptive observer capable of handling uncertainties in robot dynamics. Smoothness of the dynamics of the proposed observer allows its easy implementation in comparison with non-smooth observers. Dimension of the proposed observer is shown to be at least 3n where n stands for the manipulator's degrees of freedom. This number is less than the dimension of most existing globally convergent adaptive observers. Global asymptotic convergence of state estimates to their true values is achieved under no persistency of... 

We present a method for global estimation of joint velocities in robot manipulators. A non-minimal model of a robotic manipulator is used to design an adaptive observer capable of handling uncertainties in robot dynamics. Dimension of the proposed observer is shown to be at least 3n where n stands for the manipulator degrees of freedom. This number is less than the dimension of most of existing globally convergent adaptive observers. Global asymptotic convergence of system state estimates to their true values is achieved under no persistency of excitation condition. Smoothness of the dynamics of the proposed observer allows its easy implementation in comparison with non-smooth observers.... 

The dynamics of the flexible robot arm subjected to tip mass during an actual deployment is studied. The Euler-Bernoulli beam theory and the real deployment are considered in the simulation. A new real axial velocity profile is developed. This new suggested profile simulates the actual deployment such that the arm movement starts from immovability and after attaining the final required length comes back again to the static state. Using Lagrange's equation, the equations of motion of the system are derived to study the system dynamics in this suggested deployment profile. A series approximation is used to represent the lateral elastic displacements. Using variables separation and also some... 

In this paper, a new fuzzy based Model Coordination (F-MC) strategy is proposed for hierarchical control of large-scale systems (LSS). To solve the overall problem with a two-level optimal control strategy, we first decompose the system into several sub-systems at the first level. Then, at the second level, a fuzzy coordinator will be used to predict the interaction between subsystems. The proposed fuzzy based coordination approach is applicable to all types of LSS. Although in this paper, an optimal control of a 2DOF robot manipulator, as a LSS, will be considered. The obtained results are compared with the centralized optimization  

This paper presents a fuzzy-based interaction prediction approach (F-IPA) for two-level optimal control of large-scale systems. The design procedure uses a decomposition/coordination framework of hierarchical structures. At the first level, the system is decomposed into subsystems for which subproblems are formed. At the second level, a fuzzy coordinator is used to predict the coordination parameters needed to coordinate the solutions of the first level subproblems. The fuzzy coordinator uses a critic vector to evaluate its performance and learn its parameters by minimizing an energy function. The proposed control scheme is implemented on a two-degrees-of-freedom (2DOF) model of robot...