Integral Resonant Control for vibration damping and precise tip-positioning of a single-link flexible manipulator

Peer reviewedPostprin

A family of asymptotically stable control laws for flexible robots based on a passivity approach

A general family of asymptotically stabilizing control laws is introduced for a class of nonlinear Hamiltonian systems. The inherent passivity property of this class of systems and the Passivity Theorem are used to show the closed-loop input/output stability which is then related to the internal state space stability through the stabilizability and detectability condition. Applications of these results include fully actuated robots, flexible joint robots, and robots with link flexibility

Application of Stable Inversion to Flexible Manipulators Modeled by the ANCF

Compared to conventional robots, flexible manipulators offer many advantages, such as faster end-effector velocities and less energy consumption. However, their flexible structure can lead to undesired oscillations. Therefore, the applied control strategy should account for these elasticities. A feedforward controller based on an inverse model of the system is an efficient way to improve the performance. However, unstable internal dynamics arise for many common flexible robots and stable inversion must be applied. In this contribution, an approximation of the original stable inversion approach is proposed. The approximation simplifies the problem setup, since the internal dynamics do not need to be derived explicitly for the definition of the boundary conditions. From a practical point of view, this makes the method applicable to more complex systems with many unactuated degrees of freedom. Flexible manipulators modeled by the absolute nodal coordinate formulation (ANCF) are considered as an application example

Dynamics and control of flexible manipulators

Flexible link manipulators (FLM) are well-known for their light mass and small energy consumption compared to rigid link manipulators (RLM). These advantages of FLM are even of greater importance in applications where energy efficiency is crucial, such as in space applications. However, RLM are still preferred over FLM for industrial applications. This is due to the fact that the reliability and predictability of the performance of FLM are not yet as good as those of RLM. The major cause for these drawbacks is link flexibility, which not only makes the dynamic modeling of FLM very challenging, but also turns its end-effector trajectory tracking (EETT) into a complicated control problem. The major objectives of the research undertaken in this project were to develop a dynamic model for a FLM and model-based controllers for the EETT. Therefore, the dynamic model of FLM was first derived. This dynamic model was then used to develop the EETT controllers. A dynamic model of a FLM was derived by means of a novel method using the dynamic model of a single flexible link manipulator on a moving base (SFLMB). The computational efficiency of this method is among its novelties. To obtain the dynamic model, the Lagrange method was adopted. Derivation of the kinetic energy and the calculation of the corresponding derivatives, which are required in the Lagrange method, are complex for the FLM. The new method introduced in this thesis alleviated these complexities by calculating the kinetic energy and the required derivatives only for a SFLMB, which were much simpler than those of the FLM. To verify the derived dynamic model the simulation results for a two-link manipulator, with both links being flexible, were compared with those of full nonlinear finite element analysis. These comparisons showed sound agreement. A new controller for EETT of FLM, which used the singularly perturbed form of the dynamic model and the integral manifold concept, was developed. By using the integral manifold concept the links’ lateral deflections were approximately represented in terms of the rotations of the links and input torques. Therefore the end-effector displacement, which was composed of the rotations of the links and links’ lateral deflections, was expressed in terms of the rotations of the links and input torques. The input torques were then selected to reduce the EETT error. The originalities of this controller, which was based on the singularly perturbed form of the dynamic model of FLM, are: (1) it is easy and computationally efficient to implement, and (2) it does not require the time derivative of links’ lateral deflections, which are impractical to measure. The ease and computational efficiency of the new controller were due to the use of the several properties of the dynamic model of the FLM. This controller was first employed for the EETT of a single flexible link manipulator (SFLM) with a linear model. The novel controller was then extended for the EETT of a class of flexible link manipulators, which were composed of a chain of rigid links with only a flexible end-link (CRFE). Finally it was used for the EETT of a FLM with all links being flexible. The simulation results showed the effectiveness of the new controller. These simulations were conducted on a SFLM, a CRFE (with the first link being rigid and second link being flexible) and finally a two-link manipulator, with both links being flexible. Moreover, the feasibility of the new controller proposed in this thesis was verified by experimental studies carried out using the equipment available in the newly established Robotic Laboratory at the University of Saskatchewan. The experimental verifications were performed on a SFLM and a two-link manipulator, with first link being rigid and second link being flexible.Another new controller was also introduced in this thesis for the EETT of single flexible link manipulators with the linear dynamic model. This controller combined the feedforward torque, which was required to move the end-effector along the desired path, with a feedback controller. The novelty of this EETT controller was in developing a new method for the derivation of the feedforward torque. The feedforward torque was obtained by redefining the desired end-effector trajectory. For the end-effector trajectory redefinition, the summation of the stable exponential functions was used. Simulation studies showed the effectiveness of this new controller. Its feasibility was also proven by experimental verification carried out in the Robotic Laboratory at the University of Saskatchewan

Stable inversion based output tracking control of robotic systems

This thesis addresses stable inversion based output tracking control and its applications to robotic systems. It considers the non-causal invertibility (stable inversion) problem of control systems in its various aspects including properties of stable inverses and algorithms for constructing stable inverses. Then, the stable inversion approach is applied to solve a control problem of long-standing interest: output tracking control for non-minimum phase nonlinear systems;A minimum energy property of stable inverses is firstly established. The property claims that given any desired output trajectory, out of infinitely many possible inverse solutions, the one provided by the stable inversion process is the only one that has finite energy. Based on this property, a numerical procedure is developed to provide an efficient approach to construct stable inverses;Secondly, a new output tracking control design is developed. The design incorporates stable inverses and assumes a controller structure of feed-forward plus feedback. It achieves high precision tracking together with closed-loop stability. Furthermore, when system uncertainties are considered and assumed to satisfy the so-called matching conditions , a modified controller structure is presented and the corresponding robust tracking performance is discussed;Finally, the stable inversion based tracking control design is applied to three flexible robotic systems. The first study is output tracking control of a flexible-joint robot. The application demonstrates how the new design deals with the undesirable non-minimum phase property and achieves desired output tracking. The second application is tip trajectory tracking for a two-flexible-link manipulator. This thesis, for the first time, addresses the problem of stable tip trajectory tracking without any transient or steady-state errors for such non-minimum phase systems. In the third application, a new optimal motion control strategy for a flexible space robot is presented. The space robot system is assumed to consist of a two-link flexible manipulator attached to rigid space-craft. Optimality is in the sense that a performance index measured by maneuvering time, control effort, and structural vibrations is minimized while the interference from the manipulator to spacecraft is kept satisfactorily small;Studies on three applications demonstrate that the stable inversion based control design is very effective on output tracking for various robotic systems. This approach is expected to perform equivalently well for many other realistic non-minimum phase nonlinear systems

Flexible-Link Robot Control Using a Linear Parameter Varying Systems Methodology

This paper addresses the issues of the Linear Parameter Varying (LPV) modelling and control of flexible-link robot manipulators. The LPV formalism allows the synthesis of nonlinear control laws and the assessment of their closed-loop stability and performances in a simple and effective manner, based on the use of Linear Matrix Inequalities (LMI). Following the quasi-LPV modelling approach, an LPV model of a flexible manipulator is obtained, starting from the nonlinear dynamic model stemming from Euler-Lagrange equations. Based on this LPV model, which has a rational dependence in terms of the varying parameters, two different methods for the synthesis of LPV controllers are explored. They guarantee the asymptotic stability and some level of closed-loop ℒ 2 -gain performance on a bounded parametric set. The first method exploits a descriptor representation that simplifies the rational dependence of the LPV model, whereas the second one manages the troublesome rational dependence by using dilated LMI conditions and taking the particular structure of the model into account. The resulting controllers involve the measured state variables only, namely the joint positions and velocities. Simulation results are presented that illustrate the validity of the proposed control methodology. Comparisons with an inversion-based nonlinear control method are performed in the presence of velocity measurement noise, model uncertainties and high-frequency inputs

Decoupling and adaptive control and stabilization of two-link elastic robotic arm

In this thesis the control and stabilization of a two link flexible robotic arm is considered. The first scheme is based on nonlinear inversion, a nonlinear controller is designed for the trajectory control of the joint angles using joint torquers. The inverse controller includes a servocompensator for robustness. A simplified controller has also been designed neglecting the Coriolis and Centrifugal forces; In the second scheme the control system design is based on nonlinear adaptive control and linear stabilization. First a nonlinear adaptive control law is derived such that in the closed-loop system the joint-angles are precisely controlled to track reference trajectories. A linear stabilizer designed based on a linear model of the arm is switched to accomplish the final capture of the desired state; Simulation results are presented for all cases to show that in the closed-loop system accurate joint angle trajectory tracking and elastic mode stabilization can be accomplished inspite of the uncertainity in the payload. (Abstract shortened with permission of author.) ftn*This research was supported by the U.S. Army Research Office under ARO Grant No. DAAL03-87-G-004

Enhanced stiffness modeling of manipulators with passive joints

The paper presents a methodology to enhance the stiffness analysis of serial and parallel manipulators with passive joints. It directly takes into account the loading influence on the manipulator configuration and, consequently, on its Jacobians and Hessians. The main contributions of this paper are the introduction of a non-linear stiffness model for the manipulators with passive joints, a relevant numerical technique for its linearization and computing of the Cartesian stiffness matrix which allows rank-deficiency. Within the developed technique, the manipulator elements are presented as pseudo-rigid bodies separated by multidimensional virtual springs and perfect passive joints. Simulation examples are presented that deal with parallel manipulators of the Ortholide family and demonstrate the ability of the developed methodology to describe non-linear behavior of the manipulator structure such as a sudden change of the elastic instability properties (buckling)

Passivity/Lyapunov based controller design for trajectory tracking of flexible joint manipulators

A passivity and Lyapunov based approach for the control design for the trajectory tracking problem of flexible joint robots is presented. The basic structure of the proposed controller is the sum of a model-based feedforward and a model-independent feedback. Feedforward selection and solution is analyzed for a general model for flexible joints, and for more specific and practical model structures. Passivity theory is used to design a motor state-based controller in order to input-output stabilize the error system formed by the feedforward. Observability conditions for asymptotic stability are stated and verified. In order to accommodate for modeling uncertainties and to allow for the implementation of a simplified feedforward compensation, the stability of the system is analyzed in presence of approximations in the feedforward by using a Lyapunov based robustness analysis. It is shown that under certain conditions, e.g., the desired trajectory is varying slowly enough, stability is maintained for various approximations of a canonical feedforward