Linearization of dynamic equations of flexible mechanisms - a finite element approach

A finite element based method is presented for evaluation of linearized dynamic equations of flexible mechanisms about a nominal trajectory. The coefficient matrices of the linearized equations of motion are evaluated as explicit analytical expressions involving mixed sets of generalized co-ordinates of the mechanism with rigid links and deformation mode co-ordinates that characterize deformation of flexible link elements. This task is accomplished by employing the general framework of the geometric transfer function formalism. The proposed method is general in nature and can be applied to spatial mechanisms and manipulators having revolute and prismatic joints. The method also permits investigation of the dynamics of flexible rotors and spinning shafts. Application of the theory is illustrated through a detailed model development of a four-bar mechanism and the analysis of bending vibrations of two single link mechanisms in which the link is considered as a rotating flexible arm or as an unsymmetrical rotating shaft, respectively. The algorithm for the calculation of the matrix coefficients is directly emenable to numerical computation and has been incorporated into the linearization module of the computer program SPACAR

Space robot simulator vehicle

A Space Robot Simulator Vehicle (SRSV) was constructed to model a free-flying robot capable of doing construction, manipulation and repair work in space. The SRSV is intended as a test bed for development of dynamic and static control methods for space robots. The vehicle is built around a two-foot-diameter air-cushion vehicle that carries batteries, power supplies, gas tanks, computer, reaction jets and radio equipment. It is fitted with one or two two-link manipulators, which may be of many possible designs, including flexible-link versions. Both the vehicle body and its first arm are nearly complete. Inverse dynamic control of the robot's manipulator has been successfully simulated using equations generated by the dynamic simulation package SDEXACT. In this mode, the position of the manipulator tip is controlled not by fixing the vehicle base through thruster operation, but by controlling the manipulator joint torques to achieve the desired tip motion, while allowing for the free motion of the vehicle base. One of the primary goals is to minimize use of the thrusters in favor of intelligent control of the manipulator. Ways to reduce the computational burden of control are described

Dynamic modeling, property investigation, and adaptive controller design of serial robotic manipulators modeled with structural compliance

Research results on general serial robotic manipulators modeled with structural compliances are presented. Two compliant manipulator modeling approaches, distributed and lumped parameter models, are used in this study. System dynamic equations for both compliant models are derived by using the first and second order influence coefficients. Also, the properties of compliant manipulator system dynamics are investigated. One of the properties, which is defined as inaccessibility of vibratory modes, is shown to display a distinct character associated with compliant manipulators. This property indicates the impact of robot geometry on the control of structural oscillations. Example studies are provided to illustrate the physical interpretation of inaccessibility of vibratory modes. Two types of controllers are designed for compliant manipulators modeled by either lumped or distributed parameter techniques. In order to maintain the generality of the results, neither linearization is introduced. Example simulations are given to demonstrate the controller performance. The second type controller is also built for general serial robot arms and is adaptive in nature which can estimate uncertain payload parameters on-line and simultaneously maintain trajectory tracking properties. The relation between manipulator motion tracking capability and convergence of parameter estimation properties is discussed through example case studies. The effect of control input update delays on adaptive controller performance is also studied

Modelling and identification of a six axes industrial robot

This paper deals with the modelling and identification of a six axes industrial St ¨aubli RX90 robot. A non-linear finite element method is used to generate the dynamic equations of motion in a form suitable for both simulation and identification. The latter requires that the equations of motion are linear in the inertia parameters. Joint friction is described by a friction model that describes the friction behaviour in the full velocity range necessary for identification. Experimental parameter identification by means of linear least squares techniques showed to be very suited for identification of the unknown parameters, provided that the problem is properly scaled and that the influence of disturbances is sufficiently analysed and managed. An analysis of the least squares problem by means of a singular value decomposition is preferred as it not only solves the problem of rank deficiency, but it also can correctly deal with measurement noise and unmodelled dynamics

Accuracy Improvement for Stiffness Modeling of Parallel Manipulators

The paper focuses on the accuracy improvement of stiffness models for parallel manipulators, which are employed in high-speed precision machining. It is based on the integrated methodology that combines analytical and numerical techniques and deals with multidimensional lumped-parameter models of the links. The latter replace the link flexibility by localized 6-dof virtual springs describing both translational/rotational compliance and the coupling between them. There is presented detailed accuracy analysis of the stiffness identification procedures employed in the commercial CAD systems (including statistical analysis of round-off errors, evaluating the confidence intervals for stiffness matrices). The efficiency of the developed technique is confirmed by application examples, which deal with stiffness analysis of translational parallel manipulators

On the Dynamic Properties of Flexible Parallel Manipulators in the Presence of Type 2 Singularities

International audienceIn the present paper, we expand information about the conditions for passing through Type 2 singular configurations of a parallel manipulator. It is shown that any parallel manipulator can cross the singular configurations via an optimal control permitting the favourable force distribution, i.e. the wrench applied on the end-effector by the legs and external efforts must be reciprocal to the twist along the direction of the uncontrollable motion. The previous studies have proposed the optimal control conditions for the manipulators with rigid links and flexible actuated joints. The different polynomial laws have been obtained and validated for each examined case. The present study considers the conditions for passing through Type 2 singular configurations for the parallel manipulators with flexible links. By computing the inverse dynamic model of a general flexible parallel robot, the necessary conditions for passing through Type 2 singular configurations are deduced. The suggested approach is illustrated by a 5R parallel manipulator with flexible elements and joints. It is shown that a 16 th order polynomial law is necessary for the optimal force generation. The obtained results are validated by numerical simulations carried out using the software ADAMS

Tip position control of single flexible manipulators based on LQR with the Mamdani model

Flexible manipulators have been actively used in various fields, such as aerospace, industry and medical treatment. It remains that the tip of the flexible manipulator should accurately trail the target trajectory without vibration. This paper proposes a novel method of the tip position control of a single flexible manipulator based on LQR with the Mamdani model. Firstly, using the assumed mode method and the Lagrange equations, the dynamic model of the single flexible manipulator is established. Then, the state equations are derived by the dynamic model. Based on the Mamdani model, the fuzzy algorithm is added to the traditional LQR control, and the self-adaptive adjustment of the LQR control variable R is conducted, which improves the adaptability of the control system. Finally, numerical simulations and experiments are presented. The results demonstrate that the novel control method presented in this paper can rapidly achieve the location in the position control and effectively suppress the elastic vibration of the single flexible manipulator, which has more considerable effect compared with the traditional LQR control method

Robotic manipulation with flexible link fingers

A robot manipulator is a spatial mechanism consisting essentially of a series of bodies, called "links", connected to each other at "joints". The joints can be of various types: revolute, rotary, planar, prismatic, telescopic or combinations of these. A serial connection of the links results in an open-chain manipulator. Closed-chain manipulators result from non-serial (or parallel) connections between links. Actuators at the joints of the manipulator provide power for motion. A robot is usually not designed for a very specific or repetitive task which can be done equally well by task-specific machines. Its strength lies in its ability to handle a range of tasks by virtue of being "re-programmable". Therefore, in addition to the mechanical hardware two other elements are integral to the description of a robot: sensors and control. With the advent of micro-electronics and digital computers the availability of sensors is ever increasing and the control is usually done by software executed by computers which also collect the sensory data. It is possible to model quite accurately, the dynamics of robot manipulators for purposes of control. However, for most practical robots the models are complex and numerically intensive to calculate in real-time. Traditional analyses of robot manipulators consider the whole mechanism to be rigid. Relaxation of the assumption of rigidity leads to further complication of the dynamics of the manipulator, leading to more difficulties in control. The overall motion of the manipulator is augmented by additional motion due to the dynamics of flexibility which must be considered. Sensing is also made more difficult. However, the ability to control robots with significant structural flexibilities, referred to as flexible robots in the rest of this thesis, influences robotics in many ways. It allows for consideration of new applications, observance of less conservative structural design and performance enhancements in certain classes of robotic tasks, which will be addressed in greater detail in the sections which follow