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

An investigation of various controller designs for multi-link robotic system (Robogymnast)

An approach to controlling the three-link Robogymnast robotic gymnast and assessing stability is proposed and examined. In the study, a conventionally configured linear quadratic regulator is applied and compared with a fuzzy logic linear quadratic regulator hybrid approach for stabilising the Robogymnast. The Robogymnast is designed to replicate the movement of a human as they hang with both hands holding the high bar and then work to wing up into a handstand, still gripping the bar. The system, therefore has a securely attached link between the hand element and the ‘high bar’, which is mounted on ball bearings and can rotate freely. Moreover, in the study, a mathematical model for the system is linearised, investigating the means of determining the state space in the system by applying Lagrange’s equation. The fuzzy logic linear quadratic regulator controller is used to identify how far the system responses stabilise when it is implemented. This paper investigates factors affecting the control of swing-up in the underactuated three-link Robogymnast. Moreover, a system simulation using MATLAB Simulink is conducted to show the impact of factors including overshoot, rising, and settling time. The principal objective of the study lies in investigating how a linear quadratic regulator or fuzzy logic controller with a linear quadratic regulator (FLQR) can be applied to the Robogymnast, and to assess system behaviour under five scenarios, namely the original value, this value plus or minus ±25%, and plus or minus ±50%. In order to further assess the performance of the controllers used, a comparison is made between the outcomes found here and findings in the recent literature with fuzzy linear quadratic regulator controllers

Combining Passivity-Based Control and Linear Quadratic Regulator to Control a Rotary Inverted Pendulum

In this manuscript, new combination methodology is proposed, which named combining Passivity-Based Control and Linear Quadratic Regulator (for short, CPBC-LQR), to support the stabilization process as the system is far from equilibrium point. More precisely, Linear Quadratic Regulator (for short, LQR) is used together with Passivity-Based Control (for short, PBC) controller. Though passivity-based control and linear quadratic regulator are two control methods, it is possible to integrate them together. The combination of passivity-based control and linear quadratic regulator is analyzed, designed and implemented on so-called rotary inverted pendulum system (for short, RIP). In this work, CPBC-LQR is validated and discussed on both MATLAB/Simulink environment and real-time experimental setup. The numerical simulation and experimental results reveal the ability of CPBC-LQR control scheme in stabilization problem and achieve a good and stable performance. Effectiveness and feasibility of proposed controller are confirmed via comparative simulation and experiments

Control of a Two-wheeled Machine with Two-directions Handling Mechanism Using PID and PD-FLC Algorithms

This paper presents a novel five degrees of freedom (DOF) two-wheeled robotic machine (TWRM) that delivers solutions for both industrial and service robotic applications by enlarging the vehicle′s workspace and increasing its flexibility. Designing a two-wheeled robot with five degrees of freedom creates a high challenge for the control, therefore the modelling and design of such robot should be precise with a uniform distribution of mass over the robot and the actuators. By employing the Lagrangian modelling approach, the TWRM′s mathematical model is derived and simulated in Matlab/Simulink®. For stabilizing the system′s highly nonlinear model, two control approaches were developed and implemented: proportional-integral-derivative (PID) and fuzzy logic control (FLC) strategies. Considering multiple scenarios with different initial conditions, the proposed control strategies′ performance has been assessed

Design of Sliding Mode PID Controller with Improved reaching laws for Nonlinear Systems

In this thesis, advanced design technique in sliding mode control (SMC) is presented with focus on PID (Proportional-Integral-Derivative) type Sliding surfaces based Sliding mode control with improved power rate exponential reaching law for Non-linear systems using Modified Particle Swarm Optimization (MPSO). To handle large non-linearities directly, sliding mode controller based on PID-type sliding surface has been designed in this work, where Integral term ensures fast finite convergence time. The controller parameter for various modified structures can be estimated using Modified PSO, which is used as an offline optimization technique. Various reaching law were implemented leading to the proposed improved exponential power rate reaching law, which also improves the finite convergence time. To implement the proposed algorithm, nonlinear mathematical model has to be decrypted without linearizing, and used for the simulation purposes. Their performance is studied using simulations to prove the proposed behavior. The problem of chattering has been overcome by using boundary method and also second order sliding mode method. PI-type sliding surface based second order sliding mode controller with PD surface based SMC compensation is also proposed and implemented. The proposed algorithms have been analyzed using Lyapunov stability criteria. The robustness of the method is provided using simulation results including disturbance and 10% variation in system parameters. Finally process control based hardware is implemented (conical tank system)

Optimal fuzzy proportional-integral-derivative control for a class of fourth-order nonlinear systems using imperialist competitive algorithms

The proportional integral derivative (PID) controller has gained wide acceptance and use as the most useful control approach in the industry. However, the PID controller lacks robustness to uncertainties and stability under disturbances. To address this problem, this paper proposes an optimal fuzzy-PID technique for a two-degree-of-freedom cart-pole system. Fuzzy rules can be combined with controllers such as PID to tune their coefficients and allow the controller to deliver substantially improved performance. To achieve this, the fuzzy logic method is applied in conjunction with the PID approach to provide essential control inputs and improve the control algorithm efficiency. The achieved control gains are then optimized via the imperialist competitive algorithm. Consequently, the objective function for the cart-pole system is regarded as the summation of the displacement error of the cart, the angular error of the pole, and the control force. This control concept has been tested via simulation and experimental validations. Obtained results are presented to confirm the accuracy and efficiency of the suggested method. © 2022 S. Hadipour Lakmesari et al

Finite-Time State Estimation for an Inverted Pendulum under Input-Multiplicative Uncertainty

A sliding mode observer is presented, which is rigorously proven to achieve finite-time state estimation of a dual-parallel underactuated (i.e., single-input multi-output) cart inverted pendulum system in the presence of parametric uncertainty. A salient feature of the proposed sliding mode observer design is that a rigorous analysis is provided, which proves finite-time estimation of the complete system state in the presence of input-multiplicative parametric uncertainty. The performance of the proposed observer design is demonstrated through numerical case studies using both sliding mode control (SMC)- and linear quadratic regulator (LQR)-based closed-loop control systems. The main contribution presented here is the rigorous analysis of the finite-time state estimator under input-multiplicative parametric uncertainty in addition to a comparative numerical study that quantifies the performance improvement that is achieved by formally incorporating the proposed compensator for input-multiplicative parametric uncertainty in the observer. In summary, our results show performance improvements when applied to both SMC- and LQR-based control systems, with results that include a reduction in the root-mean square error of up to 39% in translational regulation control and a reduction of up to 29% in pendulum angular control

Adaptive Sliding Mode Control of Mobile Manipulators with Markovian Switching Joints

The hybrid joints of manipulators can be switched to either active (actuated) or passive (underactuated) mode as needed. Consider the property of hybrid joints, the system switches stochastically between active and passive systems, and the dynamics of the jump system cannot stay on each trajectory errors region of subsystems forever; therefore, it is difficult to determine whether the closed-loop system is stochastically stable. In this paper, we consider stochastic stability and sliding mode control for mobile manipulators using stochastic jumps switching joints. Adaptive parameter techniques are adopted to cope with the effect of Markovian switching and nonlinear dynamics uncertainty and follow the desired trajectory for wheeled mobile manipulators. The resulting closed-loop system is bounded in probability and the effect due to the external disturbance on the tracking errors can be attenuated to any preassigned level. It has been shown that the adaptive control problem for the Markovian jump nonlinear systems is solvable if a set of coupled linear matrix inequalities (LMIs) have solutions. Finally, a numerical example is given to show the potential of the proposed techniques

Friction compensation in the swing-up control of viscously damped underactuated robotics

A dissertation submitted to the Faculty of Engineering and the Built Environment, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Master of Science in Engineering in the Control Research Group School of Electrical and Information Engineering, Johannesburg, 2017In this research, we observed a torque-related limitation in the swing-up control of underactuated mechanical systems which had been integrated with viscous damping in the unactuated joint. The objective of this research project was thus to develop a practical work-around solution to this limitation. The nth order underactuated robotic system is represented in this research as a collection of compounded pendulums with n-1 actuators placed at each joint with the exception of the first joint. This system is referred to as the PAn-1 robot (Passive first joint, followed by n-1 Active joints), with the Acrobot (PA1 robot) and the PAA robot (or PA2 robot) being among the most well-known examples. A number of friction models exist in literature, which include, and are not exclusive to, the Coulomb and the Stribeck effect models, but the viscous damping model was selected for this research since it is more extensively covered in existing literature. The effectiveness of swing-up control using Lyapunov’s direct method when applied on the undamped PAn-1 robot has been vigorously demonstrated in existing literature, but there is no literature that discusses the swing-up control of viscously damped systems. We show, however, that the application of satisfactory swing-up control using Lyapunov’s direct method is constrained to underactuated systems that are either undamped or actively damped (viscous damping integrated into the actuated joints only). The violation of this constraint results in the derivation of a torque expression that cannot be solved for (invertibility problem, for systems described by n > 2) or a torque expression which contains a conditional singularity (singularity problem, for systems with n = 2). This constraint is formally summarised as the matched damping condition, and highlights a clear limitation in the Lyapunov-related swing-up control of underactuated mechanical systems. This condition has significant implications on the practical realisation of the swing-up control of underactuated mechanical systems, which justifies the investigation into the possibility of a work-around. We thus show that the limitation highlighted by the matched damping condition can be overcome through the implementation of the partial feedback linearisation (PFL) technique. Two key contributions are generated from this research as a result, which iii include the gain selection criterion (for Traditional Collocated PFL), and the convergence algorithm (for noncollocated PFL). The gain selection criterion is an analytical solution that is composed of a set of inequalities that map out a geometric region of appropriate gains in the swing-up gain space. Selecting a gain combination within this region will ensure that the fully-pendent equilibrium point (FPEP) is unstable, which is a necessary condition for swing-up control when the system is initialised near the FPEP. The convergence algorithm is an experimental solution that, once executed, will provide information about the distal pendulum’s angular initial condition that is required to swing-up a robot with a particular angular initial condition for the proximal pendulum, along with the minimum gain that is required to execute the swing-up control in this particular configuration. Significant future contributions on this topic may result from the inclusion of more complex friction models. Additionally, the degree of actuation of the system may be reduced through the implementation of energy storing components, such as torsional springs, at the joint. In summary, we present two contributions in the form of the gain selection criterion and the convergence algorithm which accommodate the circumnavigation of the limitation formalised as the matched damping condition. This condition pertains to the Lyapunov-related swing-up control of underactuated mechanical systems that have been integrated with viscous damping in the unactuated joint.CK201

Finite-Time State Estimation for an Inverted Pendulum under Input-Multiplicative Uncertainty

A sliding mode observer is presented, which is rigorously proven to achieve finite-time state estimation of a dual-parallel underactuated (i.e., single-input multi-output) cart inverted pendulum system in the presence of parametric uncertainty. A salient feature of the proposed sliding mode observer design is that a rigorous analysis is provided, which proves finite-time estimation of the complete system state in the presence of input-multiplicative parametric uncertainty. The performance of the proposed observer design is demonstrated through numerical case studies using both sliding mode control (SMC)- and linear quadratic regulator (LQR)-based closed-loop control systems. The main contribution presented here is the rigorous analysis of the finite-time state estimator under input-multiplicative parametric uncertainty in addition to a comparative numerical study that quantifies the performance improvement that is achieved by formally incorporating the proposed compensator for input-multiplicative parametric uncertainty in the observer. In summary, our results show performance improvements when applied to both SMC- and LQR-based control systems, with results that include a reduction in the root-mean square error of up to 39% in translational regulation control and a reduction of up to 29% in pendulum angular control