Nonlinear Effects in Stiffness Modeling of Robotic Manipulators

The paper focuses on the enhanced stiffness modeling of robotic manipulators by taking into account influence of the external force/torque acting upon the end point. It implements the virtual joint technique that describes the compliance of manipulator elements by a set of localized six-dimensional springs separated by rigid links and perfect joints. In contrast to the conventional formulation, which is valid for the unloaded mode and small displacements, the proposed approach implicitly assumes that the loading leads to the non-negligible changes of the manipulator posture and corresponding amendment of the Jacobian. The developed numerical technique allows computing the static equilibrium and relevant force/torque reaction of the manipulator for any given displacement of the end-effector. This enables designer detecting essentially nonlinear effects in elastic behavior of manipulator, similar to the buckling of beam elements. It is also proposed the linearization procedure that is based on the inversion of the dedicated matrix composed of the stiffness parameters of the virtual springs and the Jacobians/Hessians of the active and passive joints. The developed technique is illustrated by an application example that deals with the stiffness analysis of a parallel manipulator of the Orthoglide family.Comment: ISSN 2070-372

Compensation of compliance errors in parallel manipulators composed of non-perfect kinematic chains

The paper is devoted to the compliance errors compensation for parallel manipulators under external loading. Proposed approach is based on the non-linear stiffness modeling and reduces to a proper adjusting of a target trajectory. In contrast to previous works, in addition to compliance errors caused by machining forces, the problem of assembling errors caused by inaccuracy in the kinematic chains is considered. The advantages and practical significance of the proposed approach are illustrated by examples that deal with groove milling with Orthoglide manipulator.Comment: Advances in Robot Kinematics, France (2012

Compliance error compensation technique for parallel robots composed of non-perfect serial chains

The paper presents the compliance errors compensation technique for over-constrained parallel manipulators under external and internal loadings. This technique is based on the non-linear stiffness modeling which is able to take into account the influence of non-perfect geometry of serial chains caused by manufacturing errors. Within the developed technique, the deviation compensation reduces to an adjustment of a target trajectory that is modified in the off-line mode. The advantages and practical significance of the proposed technique are illustrated by an example that deals with groove milling by the Orthoglide manipulator that considers different locations of the workpiece. It is also demonstrated that the impact of the compliance errors and the errors caused by inaccuracy in serial chains cannot be taken into account using the superposition principle.Comment: arXiv admin note: text overlap with arXiv:1204.175

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

Space robotics: Recent accomplishments and opportunities for future research

The Langley Guidance, Navigation, and Control Technical Committee (GNCTC) was one of six technical committees created in 1991 by the Chief Scientist, Dr. Michael F. Card. During the kickoff meeting Dr. Card charged the chairmen to: (1) establish a cross-Center committee; (2) support at least one workshop in a selected discipline; and (3) prepare a technical paper on recent accomplishments in the discipline and on opportunities for future research. The Guidance, Navigation, and Control Committee was formed and selected for focus on the discipline of Space robotics. This report is a summary of the committee's assessment of recent accomplishments and opportunities for future research. The report is organized as follows. First is an overview of the data sources used by the committee. Next is a description of technical needs identified by the committee followed by recent accomplishments. Opportunities for future research ends the main body of the report. It includes the primary recommendation of the committee that NASA establish a national space facility for the development of space automation and robotics, one element of which is a telerobotic research platform in space. References 1 and 2 are the proceedings of two workshops sponsored by the committee during its June 1991, through May 1992 term. The focus of the committee for the June 1992 - May 1993 term will be to further define to the recommended platform in space and to add an additional discipline which includes aircraft related GN&C issues. To the latter end members performing aircraft related research will be added to the committee. (A preliminary assessment of future opportunities in aircraft-related GN&C research has been included as appendix A.

CAD-based approach for identification of elasto-static parameters of robotic manipulators

The paper presents an approach for the identification of elasto-static parameters of a robotic manipulator using the virtual experiments in a CAD environment. It is based on the numerical processing of the data extracted from the finite element analysis results, which are obtained for isolated manipulator links. This approach allows to obtain the desired stiffness matrices taking into account the complex shape of the links, couplings between rotational/translational deflections and particularities of the joints connecting adjacent links. These matrices are integral parts of the manipulator lumped stiffness model that are widely used in robotics due to its high computational efficiency. To improve the identification accuracy, recommendations for optimal settings of the virtual experiments are given, as well as relevant statistical processing techniques are proposed. Efficiency of the developed approach is confirmed by a simulation study that shows that the accuracy in evaluating the stiffness matrix elements is about 0.1%.Comment: arXiv admin note: substantial text overlap with arXiv:0909.146

Stiffness modeling of non-perfect parallel manipulators

The paper focuses on the stiffness modeling of parallel manipulators composed of non-perfect serial chains, whose geometrical parameters differ from the nominal ones. In these manipulators, there usually exist essential internal forces/torques that considerably affect the stiffness properties and also change the end-effector location. These internal load-ings are caused by elastic deformations of the manipulator ele-ments during assembling, while the geometrical errors in the chains are compensated for by applying appropriate forces. For this type of manipulators, a non-linear stiffness modeling tech-nique is proposed that allows us to take into account inaccuracy in the chains and to aggregate their stiffness models for the case of both small and large deflections. Advantages of the developed technique and its ability to compute and compensate for the compliance errors caused by different factors are illustrated by an example that deals with parallel manipulators of the Or-thoglide famil

A spatial impedance controller for robotic manipulation

Mechanical impedance is the dynamic generalization of stiffness, and determines interactive behavior by definition. Although the argument for explicitly controlling impedance is strong, impedance control has had only a modest impact on robotic manipulator control practice. This is due in part to the fact that it is difficult to select suitable impedances given tasks. A spatial impedance controller is presented that simplifies impedance selection. Impedance is characterized using ¿spatially affine¿ families of compliance and damping, which are characterized by nonspatial and spatial parameters. Nonspatial parameters are selected independently of configuration of the object with which the robot must interact. Spatial parameters depend on object configurations, but transform in an intuitive, well-defined way. Control laws corresponding to these compliance and damping families are derived assuming a commonly used robot model. While the compliance control law was implemented in simulation and on a real robot, this paper emphasizes the underlying theor

Dynamic Modeling and Simulation of a Rotating Single Link Flexible Robotic Manipulator Subject to Quick Stops

Single link robotic manipulators are extensively used in industry and research operations. The main design requirement of such manipulators is to minimize link dynamic deflection and its active end vibrations, and obtain high position accuracy during its high speed motion. To achieve these requirements, accurate mathematical modeling and simulation of the initial design, to increase system stability and precision and to obtain very small amplitudes of vibration, should be considered. In this paper the modeling of such robotic arm with a rigid guide and a flexible extensible link subject to quick stops after each complete revolution is considered and its dynamical behavior analyzed. The extensible link which rotates with constant angular velocity has one end constrained to a predefined trajectory. The constrained trajectory allows trajectory control and obstacle avoidance for the active end of the robotic arm. The dynamic evolution of the system is investigated and the flexural response of the flexible link analyzed under the combined effect of clearance and flexibility.