Intelligent model-based control of complex three-link mechanisms

The aim of this study is to understand the complexity and control challenges of the locomotion of a three-link mechanism of a robot system. In order to do this a three-link robot gymnast (Robogymnast) has been built in Cardiff University. The Robogymnast is composed of three links (one arm, one torso, one leg) and is powered by two geared DC motors. Currently the robot has three potentiometers to measure the relative angles between adjacent links and only one tachometer to measure the relative angular position of the first link. A mathematical model for the robot is derived using Lagrange equations. Since the model is inherently nonlinear and multivariate, it presents more challenges when modelling the Robogymnast and dealing with control motion problems. The proposed approach for dealing with the design of the control system is based on a discrete-time linear model around the upright position of the Robogymnast. To study the swinging motion of the Robogymnast, a new technique is proposed to manipulate the frequency and the amplitude of the sinusoidal signals as a means of controlling the motors. Due to the many combinations of the frequency and amplitude, an optimisation method is required to find the optimal set. The Bees Algorithm (BA), a novel swarm-based optimisation technique, is used to enhance the performance of the swinging motion through optimisation of the manipulated parameters of the control actions. The time taken to reach the upright position at its best is 128 seconds. Two different control methods are adopted to study the balancing/stablising of the Robogymnast in both the downward and upright configurations. The first is the optimal control algorithm using the Linear Quadratic Regulator (LQR) technique with integrators to help achieve and maintain the set of reference trajectories. The second is a combination of Local Control (LC) and LQR. Each controller is implemented via reduced order state observer to estimate the unmeasured states in terms of their relative angular velocities. From the identified data in the relative angular positions of the upright balancing control, it is reported that the maximum amplitude of the deviation in the relative angles on average are approximately 7.5° for the first link and 18° for the second link. It is noted that the third link deviated approximately by 2.5° using only the LQR controller, and no significant deviation when using the LQR with LC. To explore the combination between swinging and balancing motions, a switching mechanism between swinging and balancing algorithm is proposed. This is achieved by dividing the controller into three stages. The first stage is the swinging control, the next stage is the transition control which is accomplished using the Independent Joint Control (IJC) technique and finally balancing control is achieved by the LQR. The duration time of the transition controller to track the reference trajectory of the Robogymnast at its best is found to be within 0.4 seconds. An external disturbance is applied to each link of the Robogymnast separately in order to study the controller's ability to overcome the disturbance and to study the controller response. The simulation of the Robogymnast and experimental realization of the controllers are implemented using MATLAB® software and the C++ program environment respectively

Intelligent model-based control of complex multi-link mechanisms

Complex under-actuated multilink mechanism involves a system whose number of control inputs is smaller than the dimension of the configuration space. The ability to control such a system through the manipulation of its natural dynamics would allow for the design of more energy-efficient machines with the ability to achieve smooth motions similar to those found in the natural world. This research aims to understand the complex nature of the Robogymnast, a triple link underactuated pendulum built at Cardiff University with the purpose of studying the behaviour of non-linear systems and understanding the challenges in developing its control system. A mathematical model of the robot was derived from the Euler-Lagrange equations. The design of the control system was based on the discrete-time linear model around the downward position and a sampling time of 2.5 milliseconds. Firstly, Invasive Weed Optimization (IWO) was used to optimize the swing-up motion of the robot by determining the optimum values of parameters that control the input signals of the Robogymnast’s two motors. The values obtained from IWO were then applied to both simulation and experiment. The results showed that the swing-up motion of the Robogymnast from the stable downward position to the inverted configuration to be successfully achieved. Secondly, due to the complex nature and nonlinearity of the Robogymnast, a novel approach of modelling the Robogymnast using a multi-layered Elman neural ii network (ENN) was proposed. The ENN model was then tested with various inputs and its output were analysed. The results showed that the ENN model to be capable of providing a better representation of the actual system compared to the mathematical model. Thirdly, IWO is used to investigate the optimum Q values of the Linear Quadratic Regulator (LQR) for inverted balance control of the Robogymnast. IWO was used to obtain the optimal Q values required by the LQR to maintain the Robogymnast in an upright configuration. Two fitness criteria were investigated: cost function J and settling time T. A controller was developed using values obtained from each fitness criteria. The results showed that LQRT performed faster but LQRJ was capable of stabilizing the Robogymnast from larger deflection angles. Finally, fitness criteria J and T were used simultaneously to obtain the optimal Q values for the LQR. For this purpose, two multi-objective optimization methods based on the IWO, namely the Weighted Criteria Method IWO (WCMIWO) and the Fuzzy Logic IWO Hybrid (FLIWOH) were developed. Two LQR controllers were first developed using the parameters obtained from the two optimization methods. The same process was then repeated with disturbance applied to the Robogymnast states to develop another two LQR controllers. The response of the controllers was then tested in different scenarios using simulation and their performance was evaluated. The results showed that all four controllers were able to balance the Robogymnast with the fastest settling time achieved by WMCIWO with disturbance followed by in the ascending order: FLIWOH with disturbance, FLIWOH, and WCMIWO

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

Enhanced Bees Algorithm with fuzzy logic and Kalman filtering

The Bees Algorithm is a new population-based optimisation procedure which employs a combination of global exploratory and local exploitatory search. This thesis introduces an enhanced version of the Bees Algorithm which implements a fuzzy logic system for greedy selection of local search sites. The proposed fuzzy greedy selection system reduces the number of parameters needed to run the Bees Algorithm. The proposed algorithm has been applied to a number of benchmark function optimisation problems to demonstrate its robustness and self-organising ability. The Bees Algorithm in both its basic and enhanced forms has been used to optimise the parameters of a fuzzy logic controller. The purpose of the controller is to stabilise and balance an under-actuated two-link acrobatic robot (ACROBOT) in the upright position. Kalman filtering, as a fast convergence gradient-based optimisation method, is introduced as an alternative to random neighbourhood search to guide worker bees speedily towards the optima of local search sites. The proposed method has been used to tune membership functions for a fuzzy logic system. Finally, the fuzzy greedy selection system is enhanced by using multiple independent criteria to select local search sites. The enhanced fuzzy selection system has again been used with Kalman filtering to speed up the Bees Algorithm. The resulting algorithm has been applied to train a Radial Basis Function (RBF) neural network for wood defect identification. The results obtained show that the changes made to the Bees Algorithm in this research have significantly improved its performance. This is because these enhancements maintain the robust global search attribute of the Bees Algorithm and improve its local search procedure.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Enhanced Bees Algorithm with fuzzy logic and Kalman filtering

The Bees Algorithm is a new population-based optimisation procedure which employs a combination of global exploratory and local exploitatory search. This thesis introduces an enhanced version of the Bees Algorithm which implements a fuzzy logic system for greedy selection of local search sites. The proposed fuzzy greedy selection system reduces the number of parameters needed to run the Bees Algorithm. The proposed algorithm has been applied to a number of benchmark function optimisation problems to demonstrate its robustness and self-organising ability. The Bees Algorithm in both its basic and enhanced forms has been used to optimise the parameters of a fuzzy logic controller. The purpose of the controller is to stabilise and balance an under-actuated two-link acrobatic robot (ACROBOT) in the upright position. Kalman filtering, as a fast convergence gradient-based optimisation method, is introduced as an alternative to random neighbourhood search to guide worker bees speedily towards the optima of local search sites. The proposed method has been used to tune membership functions for a fuzzy logic system. Finally, the fuzzy greedy selection system is enhanced by using multiple independent criteria to select local search sites. The enhanced fuzzy selection system has again been used with Kalman filtering to speed up the Bees Algorithm. The resulting algorithm has been applied to train a Radial Basis Function (RBF) neural network for wood defect identification. The results obtained show that the changes made to the Bees Algorithm in this research have significantly improved its performance. This is because these enhancements maintain the robust global search attribute of the Bees Algorithm and improve its local search procedure

Improved versions of the bees algorithm for global optimisation

This research focuses on swarm-based optimisation algorithms, specifically the Bees Algorithm. The Bees Algorithm was inspired by the foraging behaviour of honey bees in nature. It employs a combination of exploration and exploitation to find the solutions of optimisation problems. This thesis presents three improved versions of the Bees Algorithm aimed at speeding up its operation and facilitating the location of the global optimum. For the first improvement, an algorithm referred to as the Nelder and Mead Bees Algorithm (NMBA) was developed to provide a guiding direction during the neighbourhood search stage. The second improved algorithm, named the recombination-based Bees Algorithm (rBA), is a variant of the Bees Algorithm that utilises a recombination operator between the exploited and abandoned sites to produce new candidates closer to optimal solutions. The third improved Bees Algorithm, called the guided global best Bees Algorithm (gBA), introduces a new neighbourhood shrinking strategy based on the best solution so far for a more effective exploitation search and develops a new bee recruitment mechanism to reduce the number of parameters. The proposed algorithms were tested on a set of unconstrained numerical functions and constrained mechanical engineering design problems. The performance of the algorithms was compared with the standard Bees Algorithm and other swarm based algorithms. The results showed that the improved Bees Algorithms performed better than the standard Bees Algorithm and other algorithms on most of the problems tested. Furthermore, the algorithms also involve no additional parameters and a reduction on the number of parameters as well

Improvements on the bees algorithm for continuous optimisation problems

This work focuses on the improvements of the Bees Algorithm in order to enhance the algorithm’s performance especially in terms of convergence rate. For the first enhancement, a pseudo-gradient Bees Algorithm (PG-BA) compares the fitness as well as the position of previous and current bees so that the best bees in each patch are appropriately guided towards a better search direction after each consecutive cycle. This method eliminates the need to differentiate the objective function which is unlike the typical gradient search method. The improved algorithm is subjected to several numerical benchmark test functions as well as the training of neural network. The results from the experiments are then compared to the standard variant of the Bees Algorithm and other swarm intelligence procedures. The data analysis generally confirmed that the PG-BA is effective at speeding up the convergence time to optimum. Next, an approach to avoid the formation of overlapping patches is proposed. The Patch Overlap Avoidance Bees Algorithm (POA-BA) is designed to avoid redundancy in search area especially if the site is deemed unprofitable. This method is quite similar to Tabu Search (TS) with the POA-BA forbids the exact exploitation of previously visited solutions along with their corresponding neighbourhood. Patches are not allowed to intersect not just in the next generation but also in the current cycle. This reduces the number of patches materialise in the same peak (maximisation) or valley (minimisation) which ensures a thorough search of the problem landscape as bees are distributed around the scaled down area. The same benchmark problems as PG-BA were applied against this modified strategy to a reasonable success. Finally, the Bees Algorithm is revised to have the capability of locating all of the global optimum as well as the substantial local peaks in a single run. These multi-solutions of comparable fitness offers some alternatives for the decision makers to choose from. The patches are formed only if the bees are the fittest from different peaks by using a hill-valley mechanism in this so called Extended Bees Algorithm (EBA). This permits the maintenance of diversified solutions throughout the search process in addition to minimising the chances of getting trap. This version is proven beneficial when tested with numerous multimodal optimisation problems

Enhancing the Bees algorithm for global optimisation using search space manipulation

The aim of this research is to improve the ability of the Bees Algorithm to tackle global optimisation problems. The Bees Algorithm was formulated and inspired by the foraging behaviour of honeybees. The proposed enhancements target the initialisation and global search stages of the algorithm. The reason for this is that the initialisation stage could save efforts by directing the search earlier towards the more promising areas of the search space, leading to a better optimised result. Targeting during the global search is due to the researcher’s belief that the neighbourhood search depends on it and any improvement will positively affect the neighbourhood search. In this research, three enhancements were formulated based on the manipulation of the search space. The first enhancement (BAwSSR) involves continuous and gradual reduction of the search space with different scenarios that vary according to the starting point of reduction. The second enhancement (BADS) deals with the segmentation of search space into independent segments while using two sampling approaches to tackle a wide variety of problems. The third enhancement (BAOSS) also involves the segmentation of search space but divides it into independent segments to increase flexibility in handling a wider range of problems. These proposed algorithms were tested on 24 benchmark functions with a broad range of characteristics. This test involves performance comparisons with the Quick Artificial Bee Colony (qABC) and the Standard Particle Swarm Optimisation 2011 (SPSO2011) algorithms. The obtained test data indicated noticeable improvements with an adequate level of stability over the original Bees Algorithm. The results were supported by the Mann–Whitney significance test, showing the improvements are statically significant for both accuracy and speed. Additionally, the proposed algorithms were tested on two engineering problems that included a comparison with a group of competitor algorithms. However, only the first proposed algorithm (BAwSSR) showed an obvious improvement. The other two algorithms (BADS) and (BAOSS) did not reveal any improvement