Elastic Arm Research Articles

Track reconstruction in the ATLAS detector using elastic arms

The elastic arms algorithm for track reconstruction is implemented on the proposed ATLAS detector at LHC. New features are two parameterizations of tracks in fields, an improved Hough transform and the use of Hessian matrices for updating. The handling of hit ambiguities is incorporated in the algorithm. The results are well in accordance with the theoretical expectations.

A unified treatment of track reconstruction and particle identification

In this note, the deformable template or elastic arm approach to track reconstruction described previously will be extended to include particle identification. The discussion will first develop the mathematical and algorithmic structure of the pattern recognition problem using the methodology and language of statistical mechanics and then sketch its implementation in an object-oriented programming language. This unified treatment will allow the user the freedom to organize the analysis in a variety of ways, with intermediate results available and documented.

Deformable templates — revisited and extended — with an OOP implementation

In this note, a general approach to track reconstruction will be described, the deformable template or elastic arms algorithm. The review part of the paper is meant to be pedagogical with the physical interpretation of the algorithm kept paramount. The extension of this approach to handle hit ambiguities (mirror charges), delta rays, vee-tracks, etc., will be given. Finally, the implementation of the algorithm in an object oriented computer language will be sketched and the resulting advantages discussed.

Study of a Fan Using the Weis-Fogh Mechanism. (An Experimental Fan and Its Characteristics).

A fan using the Weis-Fogh mechanism was built and its characteristics were studied. Two wings were set to move out-of-phase by an arm which rotates changing its directions in a square channel. Characteristics for two types of arms and wings were investigated. The best performance was achieved with a combination of an elastic arm and elastic wings which elastically deform. The Weis-Fogh mechanism is shown to be applicable to fans as well as pumps or propulsion equipment for ships. However, further investigations are required for diminishing the noise and vibration.

Extensions and explorations of the elastic arms algorithm

The deformable templates method for track finding in high energy physics is reviewed and extended to handle multiple and secondary vertex positions. An automatized minimization method that handles different types of parametrizations is derived. It is based on the gradient descent method but modified with an explicit calculation of the natural metric. Also a simplified and more intuitive derivation of the algorithm using Potts mean field theory equations is given.

Control of an Active Mass Damper Using a Neural Network.

We present a new control method for an active mass damper. Conventionally, a pole assignment method and Linear Quadratic control theory are used for designing the controller of the active mass damper. However, these design methods are not convenient when output of the actuator and movement range of the damper mass is limited, because they cannot restrict any variable directly. Hence, we propose to determine the reference orbit of damper mass first, and control damper mass by a learning controller using the neural network. Our method can keep a mass damper with in a designated range. The performance of our method is better than that of LQ controller in settling time. To show the effectiveness of our method, we apply it to control of an active mass damper for an elastic arm which is a one-degree-of freedom structure. Moreover, we control the experimental system using a neuralnetwork which is learned in a simulation environment.

Track finding with deformable templates — the elastic arms approach

A novel algorithm for particle tracking is presented and evaluated. It is based on deformable templates that converge using a deterministic annealing algorithm. These deformable templates are initialized by Hough transforms. The algorithm, which effectively represents a merger between neuronic decision making and parameter fitting, naturally lends itself to parallel execution. Very good performance is obtained for both non-magnetic and magnetic tracks. For the latter simulated TPC tracks from the CERN DELPHI detector are used.

Nonlinear ultimate boundedness control and stabilization of a flexible robotic arm

We treat the question of control of an elastic robotic arm of two links. Of course, this approach can be extended to other elastic arms. A nonlinear ultimate boundedness controller (UBC) is synthesized such that in the closed-loop system the joint angle tracking error is uniformly bounded and tends to a certain small neighborhood of the origin. The controller includes a reference joint angle trajectory generator and integral error feedback. Although the joint angles are controlled using the UBC, elastic modes are excited. A feedback stabilizer is designed for the linearized model including the UBC about the terminal state that is switched only in the vicinity of the equilibrium state for stabilization. Simulation results are presented to show that in the closed-loop system including the UBC and the stabilizer accurate joint angle trajectory following and elastic mode stabilization are accomplished in the presence of uncertainty.

Sliding Mode Control and Elastic Mode Stabilization of a Robotic Arm With Flexible Links

This paper treats the question of control of an elastic robotic arm of two links based on variable structure system (VSS) theory and pole assignment technique for stabilization. A discontinuous joint angle control law, based on VSS theory, is designed which accomplishes asymptotic decoupled joint angle trajectory tracking. In the closed-loop system, the trajectories are attracted toward a chosen hypersurface in the state space and then slide along it. Although, joint angles are controlled using variable structure control (VSC) law, the flexible modes of the links are excited. Using center manifold theory, it is shown that the closed-loop system, including the sliding mode controller, is stable. Based on a linearized model about the terminal state, a stabilizer is designed using pole assignment technique to control the elastic oscillations of the links. A control logic is included which switches the stabilizer at the instant when the joint angle trajectory enters a specified neighborhood of the terminal state. Simulation results are presented to show that in the closed-loop system, accurate joint angle trajectory tracking, and elastic mode stabilization are accomplished in the presence of payload uncertainty.

On the mechanics of the modern working-recurve bow

Characteristic for the bow are the slender elastic arms or limbs. The bow is braced by putting a string shorter than the bow between the tips of the limbs. Additional deformation energy is stored in the elastic limbs by drawing the bow into the fully drawn position. Part of this amount of energy is transformed into kinetic energy of a light arrow.

Modelling and Control of an Elastic Robot Arm with Rotary and Prismatic Joints

The application of industrial robots to advanced manufacturing tasks requires highly accurate position and/or force control. Actual limitations to these requirements are mainly caused by elasticity, Coulomb friction and backlash in the system. Conventional control algorithms do not consider these effects and can hardly provide sufficient control accuracy or yield limit cycles. In this paper the common multibody approach of models of industrial robots is extended to derive more realistic models including elasticity of both joints and links, Coulomb friction and backlash. For the rotatory motion of an elastic robot arm with a revolute joint an algorithm for a highly accurate position control is developed based on (i) multi-layer control to damp quickly the elastic motions "separately" from the rigid-body motion of the robot, and (ii) compensation of Coulomb friction and backlash by the method of disturbance rejection control. In contrast to the very successful results in case of rotatory motion, the modelling and a suitable design of a control system for the translational motion of an elastic arm with a prismatic joint is a much more difficult Problem. A complex control system is obtained represented approximately by a set of ordinary linear time-variant differential equations of vanable order depending on the actual arm length driven out. Certam approaches of designing a feedback control are discussed.

Dual mode control of an elastic robotic arm: non-linear inversion and stabilization by pole assignment

This paper considers control of an elastic robotic arm of two links based on non–linear inversion and pole assignment for stabilization. The design is performed in two steps. First, based on non-linear inversion, a non–linear controller is designed for the trajectory control of the joint angles using joint torquers. The inverse controller accomplishes trajectory control of the joint angles, this excites the elastic modes of the arm. In order to damp the elastic oscillations, a stabilizer is designed for a linearized system about the terminal state using the pole assignment technique. In the closed–loop system, first the inverse controller acts when a command is given, and the stabilizer automatically switches when the joint angle trajectory enters a specified neighbourhood of the final commanded position. Simulation results are presented to show that in the closed–loop system accurate joint angle trajectory tracking and elastic mode stabilization can be accomplished in spite of payload uncertainty in the ...

Issues in the dynamics and control of flexible robot manipulators

Issues associated with modeling and control of robots with elastic arms are considered. An approach similar to substructure synthesis is used to model the system, where each link is first modeled independently of the others. The joint displacements are then used as constraints to synthesize the equations of motion. It is shown that the centrifugal stiffening effect is the dominating factor for the overall system behavior. Different approaches are discussed for the control design. The effects of flexibility on the response and on the closed-loop control are examined within the context of an example. N important issue of concern in the control of robots is the difference between the total mass of the manipulator and the mass of the payload. If a robot is compared with the human body, it is easily concluded that the manipulator is very inefficient. An inefficient robot implies low productivity and higher costs. A robot can be made more efficient by reducing the thickness of its arms. The resulting increased flexibility, unless considered properly, reduces pointing accuracies and affects the stability of the payload. Another source of inaccuracy is flexibility of the joints. There is considerable debate in the literature as to which source causes more inaccuracies. This paper is concerned with the modeling and control of manipulators with substantial flexibility in the arms. An approach similar to substructure synthesis is used to model the manipulator, and different control strategies are discussed. The mathematical formulation is applicable to robots with revolute or spherical joints. Several methods of modeling manipulators with elastic joints or with flexible arms exist in the literature.111 Each of the approaches uses a variety of assumptions. For example, Refs. 1-4 consider only the static deflections of the links; Ref. 1 treats the connecting links as massless, and Ref. 4 considers only one flexible bending mode for each link. Refer

Control and stabilization of nonlinear uncertain elastic robotic arm

An approach is presented to the control of an uncertain nonlinear flexible robot arm (PUMA-type) with three rotational joints. The third link is assumed to be elastic. A torquer control law, which is a function of the trajectory error, is derived for controlling the joint angles. The knowledge of the system dynamics is not required for the derivation of the controller. This controller includes a reference model to generate command joint angle trajectories, and a dynamic system in the feedback path which requires only joint angle and rate for feedback. The torquer controller asymptotically decouples the elastic dynamics into two subsystems, representing the transverse vibration of the elastic link in two orthogonal planes. For the damping of the elastic vibration, a force control law using modal velocity feedback is synthesized. Simulation results are presented to show that the combination of the torque and force control law accomplishes reference joint angle trajectory tracking and elastic mode stabilization despite the uncertainty in the system. >

Optimal control of elastic structure systems taking account of spillover. (Application to a position control of elastic rotating arm).

A digital controller for an elastic structure system suffers from spillover of residual modes. In this study, this problem is formulated as a control structure constraint for the elastic system. A sub-optimization technique is applied to the optimal control problem with a control structure constraint and a suboptimal control law is derived taking account of the spillover. This method is very simple, since it needs only a solution of the Riccati equation and matrix operations. This method is applied to the optimal positioning control of a rotating elastic arm. In the numerical calculation, it is indicated that the controlled system synthesized by this method remains stable and has good control performance, while the one synthesized by the optimal control theory within the reduced order system becomes unstable. Furthermore, the usefulness of this method is demonstrated in the simulation and control experiment.

Modeling and control of a flexible structure system. Suppression of spillover instability.

In this paper, the modeling and control of flexible structure systems are studied by taking an elastic arm system as an example. Especially, high-speed positioning control suppressing spillover instability is examined. First of all, an equation of motion is derived using the finite element method for a controlled object, and a modal analysis is applied to the equation in order to obtain a reduced order model of the object. Subsequently, the transfer function method based on design freedom is adopted to design the controller. The effectiveness of the controller derived by this method is demonstrated in computer simulation results on time responses. Also, the results are compared with those obtained by the theory of optimal control.

On the Automatic Generation of The Equations of Motion for Robots with Elastically Deformable ARMS

A method for the numeric computation of the equations of motion for robots with elastic arms is presented. The robots considered may consist of an arbitrary number of rigid and elastic bodies interconected by joints. The equations of motion are derived using d'Alembert's principle. For the elastic deformations a Ritz approximation is performed. The equations of motion are first developed in a general nonlinear form and then linearized. It will be shown that the nonlinear terms of second order in the deformation geometry have to be considered in order to get the correct linear equations. According to the described method a computer program has been installed and two examples will be presented.

Synchronization in impact winning machines

1) Synchronization of the natural vibration frequency with the frequency of impact perturbation in an impact winning machine leads to a reduction in vibration amplitude and it provides a constant backing force for the bit on the face. 2) Synchronization is achieved by selecting the appropriate impact amplitude or frequency. 3) Synchronization conditions obtained for an impact winning machine may be used to calculate parameters for individual strikers with an elastic suspension arm on the machine.

PLANAR LIBRATIONS OF AN EXTENSIBLE DUMBBELL SATELLITE

If a gravitationally stabilized satellite has a tip mass connected to it through a long elastic arm, the librational motion about the local vertical will excite longitudinal or pumping vibrations of the elastic arm. If the pumping motions are damped out by some type of internal (passive) friction, the librational motion will be damped also. In this paper, the equations of planar motion for such a system are derived and then linearized for the case of viscous in a circular orbit. The complete solution is given in terms of two nondimensional parameters, which are a measure of spring stiffness and viscous damping, respectively. It is shown that, if the internal friction arises from material damping within the spring, there will be relatively little of a viscous nature ; however, there is a nonlinear timeindependent type of hysteretic which could be significant. It is shown how the latter type of may be analyzed by a technique of equivalent viscous damping. A configuration of practical interest is examined in a numerical example.