Study of Motion Control of A Flexible Link

20th century has witnessed massive upsurge in the use of manipulators in several industries especially in space, defense, and medical industries. Among the types of manipulators used, single link manipulators are the most widely used. A single link robotic manipulator is nothing but a link controlled by an actuator to carry out a particular function such as placing a payload from point A to point B. For low power requirements single link manipulators are made up of light weight materials which require flexibility considerations.Flexibility makes the dynamics of the link heavily non-linear which induces vibrations and overshoot. In this project initially the dynamic model of rigid flexible manipulator is explained, then the state space model of the manipulator system is incorporated into MATLAB. The link flexibility is studied by a single beam FEmodel, where expressions for kinetic and potential energyare employed to derive the torqueequation.The 3 flexible link equations are coupled in terms of 3 variables, θ, Ø and v. The tip angle is finally given aslvfor flexible case whereas for the rigid manipulator the tip angle is same as the hub angle θ. Thereforeaccurate computation of v is very important. The joint flexibility is excluded from analysis.Several comparisons were made between the rigid and flexible link for torque requirement. The relation between the trajectory and hub angle is also plotted in a graph.Finally a PD controller taking the errors and its derivative is designed based on the rigid link dynamics

Analysis and design of a complex-valued sliding mode controller of a 2-link planar manipulator

Robotics and robot manipulators are some common concepts which nowadays are seen as something usual in a lot of industries. However, they are quite young fields in engineering and they include lots of different specialities such as mathematics and mechanical or elec- trical engineering. These lasts decades, the development of new robots and their control techniques have grown a lot, having now a wide variety of knowledge about their behavior and control algorithms that allow them to do their specific tasks with low errors and high performance. This project presents a new strategy in control engineering for the robotics field, which consists of an extension of a sliding mode controller to a complex-valued domain. This controller allows to track the tool center position (TCP) of a 2-link planar manipulator without the direct use of inverse kinematics and working always in the complex space. Hence, the forward kinematics of the end-effector of the robot are modeled with complex variables to design the nonlinear controller and be able to analyze its performance and study the potential of this new approach in this application field. Moreover, three more different controllers (a real-valued sliding mode controller, a state-feedback and a PID con- trol) are also designed so the main controller (Complex-valued sliding mode controller) can be analyzed and compared with other solutions to study the possible benefits and disad- vantages it may have. All the controllers are analyzed and compared with Matlab and simulated with Simulink and the results obtained are studied according to a qualitative and quantitative analysis based on some Key Performance Indicators (KPIs). Finally, all the results obtained during all the development of this project are summarized, discussed and presented with the conclusions extractedLa robòtica i els robots manipuladors són conceptes que actualment es contemplen com a temes habituals en moltes indústries. De totes maneres, es tracta de camps relativa- ment nous en l’enginyeria i inclouen diverses especialitats com la matemàtica i l’enginyeria mecànica o elèctrica. Durant aquestes últimes dècades, el desenvolupament d’aquests robots i les seves tècniques de control han crescut considerablement, arribant a tenir un am- pli coneixement sobre el seu comportament i els algorismes de control que els hi permeten realitzar les seves tasques amb errors baixos i gran rendiment. Aquest projecte presenta una estratègia nova en l’enginyeria de control pel camp de la robòtica, la qual consisteix en una extensió del control per mode de lliscament (sliding mode control, en anglès) en un domini complex. Aquest controlador permet fer un seguiment de la posició final d’un robot manipulador pla de dos braços sense l’ús directe de la cinemàtica inversa i treballant sempre a l’espai complex. D’aquesta manera, la cinemàtica directa del robot s’ha modelat amb variables complexes per tal de dissenyar el controlador no lineal i poder analitzar el seu rendiment i estudiar el potencial d’aquest nou enfocament en aquest camp d’aplicació. A més, s’han dissenyat també tres controladors (un control per mode de lliscament estàndard, un PID i un control per realimentació d’estat) per a poder analitzar i comparar el controlador principal (control per mode de lliscament complex) amb altres solucions i, d’aquesta manera, estudiar les seves possibles avantatges i inconvenients. Tots els controladors s’analitzen i comparen fent servir Matlab i se simulen amb Simulink, estudiant els resultats obtinguts fent una anàlisi qualitativa i quantitativa basada en uns Indicadors Clau de Rendiment (KPIs). Finalment, tots els resultats obtinguts durant el desenvolupament del projecte es re- sumeixen, discuteixen i presenten amb les conclusions extretesLa robótica y los robots manipuladores son conceptos que actualment se contemplan como temas habituales en muchas industrias. De todas maneras, se trata de campos relativa- mente nuevos en la ingeniería e incluyen diversas especialidades como la matemática i la ingeniería mecánica o eléctrica. Durante estas últimas décadas, el desarrollo de estos robots y sus técnicas de control han crecido considerablemente, llegando a tener un amplio conocimiento sobre su comportamiento y los algoritmos de control que les permiten realizar sus tareas con bajo error y gran rendimiento. Este proyecto presenta una estrategia nueva en ingeniería de control para el campo de la robótica, consistente en una extensión de un controlador en modo deslizante (sliding mode control, en inglés) a un dominio de valores complejos. Este controlador permite seguir la posición final de la herramienta de un manipulador plano de 2 eslabones sin el uso directo de la cinemática inversa y trabajando siempre en el espacio complejo. De esta manera, la cinemática directa del efector final del robot se modela con variables complejas para diseñar el controlador no lineal y poder analizar su rendimiento y estudiar el potencial de este nuevo enfoque en este campo de aplicación. Además, también se han disseñado tres controladors (un control en modo deslizante, un PID y un control por realimentación de estado) para poder analizar y comparar el controlador principal (un control en modo deslizante complejo) con otras soluciones y, de esta manera, estudiar sus posibles ventajas e inconvenientes. Todos los controladores se analizan y comparan usando Matlab y se simulan con Simulink, estudiando los resultados obtenidos con un análisis cualitativo y cuantitativo basado en unos Indicadores Clave de Rendimiento (KPIs). Finalmente, todos los resultados obtenidos durante el desarrollo del proyecto se resumen, discuten y presentan junto a las conclusiones extraída

Advanced Strategies for Robot Manipulators

Amongst the robotic systems, robot manipulators have proven themselves to be of increasing importance and are widely adopted to substitute for human in repetitive and/or hazardous tasks. Modern manipulators are designed complicatedly and need to do more precise, crucial and critical tasks. So, the simple traditional control methods cannot be efficient, and advanced control strategies with considering special constraints are needed to establish. In spite of the fact that groundbreaking researches have been carried out in this realm until now, there are still many novel aspects which have to be explored

Output-feedback adaptive SP-SD-Type control with an extended continuous adaptation algorithm for the global regulation of robot manipulators with bounded inputs

"In this work, an output-feedback adaptive SP-SD-type control scheme for the global position stabilization of robot manipulators with bounded inputs is proposed. Compared with the output-feedback adaptive approaches previously developed in a bounded-input context, the proposed velocity-free feedback controller guarantees the adaptive regulation objective globally (i.e. for any initial condition), avoiding discontinuities throughout the scheme, preventing the inputs from reaching their natural saturation bounds and imposing no saturation-avoidance restrictions on the choice of the P and D control gains. Moreover, through its extended structure, the adaptation algorithm may be configured to evolve either in parallel (independently) or interconnected to the velocity estimation (motion dissipation) auxiliary dynamics, giving an additional degree of design flexibility. Furthermore, the proposed scheme is not restricted to the use of a specific saturation function to achieve the required boundedness, but may involve any one within a set of smooth and non-smooth (Lipschitz-continuous) bounded passive functions that include the hyperbolic tangent and the conventional saturation as particular cases. Experimental results on a 3-degree-of-freedom manipulator corroborate the efficiency of the proposed scheme

A Comparative Study of LQR and Integral Sliding Mode Control Strategies for Position Tracking Control of Robotic Manipulators

This paper provides a systematic comparative study of position tracking control of nonlinear robotic manipulators. The main contribution of this study is a comprehensive numerical simulation assessing position tracking performances and energy consumption of integral sliding mode control (ISMC), a linear-quadratic regulator with integral action (LQRT), and optimal integral sliding mode control (OISMC) under three conditions; namely, Case I) without the coupling effect, Case II) with the coupling effect on Link 1 only, and Case III) with the coupling effect on Link 2 only. The viability of the concept is evaluated based on three performance criteria, i.e., the step-response characteristics, position tracking error, and energy consumption of the aforementioned controllers. Based upon the simulation study, it has been found that OISMC offers performances almost similar to ISMC with more than 90% improvement of tracking performance under several cases compared to LQRT; however, energy consumption is successfully reduced by 3.6% in comparison to ISMC. Energy consumption of OISMC can be further reduced by applying optimization algorithms in tuning the weighting matrices. This paper can be considered significant as a robotic system with high tracking accuracy and low energy consumption is highly demanded to be implemented in smart factories, especially for autonomous systems

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

Performance comparison of structured H∞ based looptune and LQR for a 4-DOF robotic manipulator

We explore looptune, a MATLAB-based structured H1 synthesis technique in the context of robotics. Position control of a 4 Degree of Freedom (DOF) serial robotic manipulator developed using Simulink is the problem under consideration. Three full state feedback control systems were developed, analyzed and compared for both steady-state and transient performance using the Linear Quadratic Regulator (LQR) and looptune. Initially, a single gain feedback controller was synthesized using LQR. This system was then modified by augmenting the state feedback controller with Proportional Integral (PI) and Integral regulators, thereby creating a second and third control system respectively. In both the second and third control systems, the LQR synthesized gain and additional gains were further tuned using looptune to achieve improvement in performance. The second and third systems were also compared in terms of tracking a time-dependent trajectory. Finally, the LQR and looptune synthesized controllers were tested for robustness by simultaneously increasing the mass of each manipulator link. In comparison to LQR, the second system consisting of Single Input Single Output (SISO) PI controllers and the state feedback matrix succeeded in meeting the control objectives in terms of performance, optimality, trajectory tracking, and robustness. The third system did not improve performance in contrast to LQR, but still showed robustness under mass variation. In conclusion, our results have shown looptune to have a comparatively better performance over LQR thereby highlighting its promising potential for future emerging control system applications

Robust prescribed trajectory tracking control of a robot manipulator using adaptive finite-time sliding mode and extreme learning machine method

This study aims to provide a robust trajectory tracking controller which guarantees the prescribed performance of a robot manipulator, both in transient and steady-state modes, experiencing parametric uncertainties. The main core of the controller is designed based on the adaptive finite-time sliding mode control (SMC) and extreme learning machine (ELM) methods to collectively estimate the parametric model uncertainties and enhance the quality of tracking performance. Accordingly, the global estimation with a fast convergence rate is achieved while the tracking error and the impact of chattering on the control input are mitigated significantly. Following the control design, the stability of the overall control system along with the finite-time convergence rate is proved, and the effectiveness of the proposed method is investigated via extensive simulation studies. The results of simulations confirm that the prescribed transient and steady-state performances are obtained with enough accuracy, fast convergence rate, robustness, and smooth control input which are all required for practical implementation and applications