This note presents a modification of the integrated friction model structure proposed by Swevers et al. (2000), called the Leuven model. The Leuven model structure allows accurate modeling both in the presliding and the sliding regimes without the use of a switching function. The model incorporates a hysteresis function with nonlocal memory and arbitrary transition curves. This note presents two modifications of the Leuven model. A first modification overcomes a recently detected shortcoming of the original Leuven model: a discontinuity in the friction force which occurs during certain transitions in presliding. A second modification, using the general Maxwell slip model to implement the hysteresis force, eliminates the problem of stack overflow, which can occur with the implementation of the hysteresis force.

Technical Note: modification of the Leuven integrated friction model structure

A survey on underactuated robotic systems: Bio-inspiration, trajectory planning and control

Observer design for a flexible-link manipulator with PDE model

With the development of space technology, lighter and larger space manipulators will be born, of which flexible characteristics are more obvious. The manipulator vibration caused by the flexibility not only reduces the efficiency of the manipulator but also affects the accuracy of the operation. The flexibility of space manipulator mainly comes from structural flexibility of links and transmission flexibility of harmonic gear reducer in joints. The vibrations generated by these two kinds of flexibility are coupled and transformed mutually, making the dynamics characteristics of space manipulator system complicated. Therefore it is difficult to assess respective effects of these flexibilities on vibrations of the manipulator tip. And the characteristics of integrated vibration of manipulator tip with different link and joint stiffnesses are not very clear. In this paper, the dynamic equations of multi-link multi-DOF flexible manipulator are established. Then, vibration responses of the tip under different elastic modulus, damping and joint stiffness were studied, and vibration characteristics of the tip with both link and joint were also analyzed. Moreover, the effects of motion planning on the vibration of the tip were analyzed. Finally, the vibration characteristics of the manipulator with flexible joints and links are verified by a two-degree-of-freedom manipulator experimental system. Dynamics analysis results presented some useful rules for the path planning and control to suppress the vibration of the flexible space manipulator.

Dynamic modeling and vibration characteristics analysis of flexible-link and flexible-joint space manipulator

Global mode method for dynamic modeling of a flexible-link flexible-joint manipulator with tip mass

A New Method for Dynamic Modeling of Flexible-Link Flexible-Joint Manipulators

In this article, the closed-form dynamic equations of planar flexible link manipulators (FLMs), with revolute joints and constant cross sections, are derived combining Lagrange’s equations and the assumed mode shape method. To overcome the lengthy and complicated derivative calculation of the Lagrangian function of a FLM, these computations are done only once for a single flexible link manipulator with a moving base (SFLMB). Employing the Lagrange multipliers and the dynamic equations of the SFLMB, the equations of motion of the FLM are derived in terms of the dependent generalized coordinates. To obtain the closed-form dynamic equations of the FLM in terms of the independent generalized coordinates, the natural orthogonal complement of the Jacobian constraint matrix, which is associated with the velocity constraints in the linear homogeneous form, is used. To verify the proposed closed-form dynamic model, the simulation results obtained from the model were compared with the results of the full nonlinear finite element analysis. These comparisons showed sound agreement. One of the main advantages of this approach is that the derived dynamic model can be used for the model based end-effector control and the vibration suppression of planar FLMs.

A Constrained Lagrange Formulation of Multilink Planar Flexible Manipulator

A new controller for the end-effector trajectory tracking of a single flexible link manipulator is introduced. The linear dynamic model of the single flexible link manipulator is expressed in the singularly perturbed form. To reduce the end-effector trajectory tracking error, a corrective torque is added to the computed torque command of the rigid link counterpart of the single flexible link manipulator. The corrective torque is derived based on the concept of the integral manifold of the singularly perturbed differential equations. This corrective torque is of order e2 where  [image omitted], and f is the fundamental natural frequency of the single flexible link manipulator. The implementation of the introduced technique does not require the full-state measurements since by designing an observer, the time derivative of the link's lateral deflection is estimated. The stability proof of the new controller, which is based on the Lyapunov criterion, is presented. The results of the simulation and experimental studies are also included to, respectively, show the effectiveness and feasibility of the new controller.

End-effector trajectory tracking of a flexible link manipulator using integral manifold concept

In this paper a new controller for the end-effector trajectory tracking (EETT) of multilink flexible manipulators (MLFM) is introduced The new controller is derived utilizing the concept of the integral manifold of the singularly perturbed differential equations Based on the new controller, to reduce the end-effector trajectory tracking error, a corrective term of order e 2 has to be added to the computed torque command (CTC) of the rigid link counterpart of the MLFM, where the parameter e = 1 / 2 π f and f is the smallest non-zero natural frequency (first natural frequency) of the MLFM in the specified range of operation of the manipulator The implementation of the new controller does not require measurement of the time derivative of the links’ lateral deflections, which may be practically impossible This is achieved since the time derivative of the links’ lateral deflections is estimated by using an observer, which is designed based on the gain-scheduling technique The stability of the proposed controller is proven using the Lyapunov criterion Simulation results showed the effectiveness of the new controller One of the main contributions of this work is in the derivation of a new EETT controller for the MLFM, based on the integral manifold concept, which: (1) requires the fewest corrective terms in addition to the CTC and (2) its calculation effort is minimized

Maneuver control of the multilink flexible manipulators

https://www.tpbin.com/Uploads/Subjects/05ab2f88-743d-4005-a0dc-b5be35110437.pdf

Energy-based approach for friction identification of robotic joints

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