Optimization Approach for Inverse Kinematic Solution

Inverse kinematics of serial or parallel manipulators can be computed from given Cartesian position and orientation of end effector and reverse of this would yield forward kinematics. Which is nothing but finding out end effector coordinates and angles from given joint angles. Forward kinematics of serial manipulators gives exact solution while inverse kinematics yields number of solutions. The complexity of inverse kinematic solution arises with the increment of degrees of freedom. Therefore it would be desired to adopt optimization techniques. Although the optimization techniques gives number of solution for inverse kinematics problem but it converses the best solution for the minimum function value. The selection of suitable optimization method will provides the global optimization solution, therefore, in this paper proposes quaternion derivation for 5R manipulator inverse kinematic solution which is later compared with teachers learner based optimization (TLBO) and genetic algorithm (GA) for the optimum convergence rate of inverse kinematic solution. An investigation has been made on the accuracies of adopted techniques and total computational time for inverse kinematic evaluations. It is found that TLBO is performing better as compared GA on the basis of fitness function and quaternion algebra gives better computational cost

Development of Novel Task-Based Configuration Optimization Methodologies for Modular and Reconfigurable Robots Using Multi-Solution Inverse Kinematic Algorithms

Modular and Reconfigurable Robots (MRRs) are those designed to address the increasing demand for flexible and versatile manipulators in manufacturing facilities. The term, modularity, indicates that they are constructed by using a limited number of interchangeable standardized modules which can be assembled in different kinematic configurations. Thereby, a wide variety of specialized robots can be built from a set of standard components. The term, reconfigurability, implies that the robots can be disassembled and rearranged to accommodate different products or tasks rather than being replaced. A set of MRR modules may consist of joints, links, and end-effectors. Different kinematic configurations are achieved by using different joint, link, and end-effector modules and by changing their relative orientation. The number of distinct kinematic configurations, attainable by a set of modules, varies with respect to the size of the module set from several tens to several thousands. Although determining the most suitable configuration for a specific task from a predefined set of modules is a highly nonlinear optimization problem in a hybrid continuous and discrete search space, a solution to this problem is crucial to effectively utilize MRRs in manufacturing facilities. The objective of this thesis is to develop novel optimization methods that can effectively search the Kinematic Configuration (KC) space to identify the most suitable manipulator for any given task. In specific terms, the goal is to develop and synthesize fast and efficient algorithms for a Task-Based Configuration Optimization (TBCO) from a given set of constraints and optimization criteria. To achieve such efficiency, a TBCO solver, based on Memetic Algorithms (MA), is proposed. MAs are hybrids of Genetic Algorithms (GAs) and local search algorithms. MAs benefit from the exploration abilities of GAs and the exploitation abilities of local search methods simultaneously. Consequently, MAs can significantly enhance the search efficiency of a wide range of optimization problems, including the TBCO. To achieve more optimal solutions, the proposed TBCO utilizes all the solutions of the Inverse Kinematics(IK) problem. Another objective is to develop a method for incorporating the multiple solutions of the IK problem in a trajectory optimization framework. The output of the proposed trajectory optimization method consists of a sequence of desired tasks and a single IK solution to reach each task point. Moreover, the total cost of the optimized trajectory is utilized in the TBCO as a performance measure, providing a means to identify kinematic configurations with more efficient optimized trajectories. The final objective is to develop novel IK solvers which are both general and complete. Generality means that the solvers are applicable to all the kinematic configurations which can be assembled from the available module inventory. Completeness entails the algorithm can obtain all the possible IK solutions

Comparison Between Genetic Algorithm and Electromagnetism-Like Algorithm for Solving Inverse Kinematics

A comparison study between Electromagnetism-Like Algorithm (EM) and Genetic Algorithm (GA)has been presented in this work to solve the Inverse Kinematics (IK) of a four-link planar robot manipulator. The comparison is focused on some points for both algorithms like the accuracy of the results and the speed of convergence. Different target points have been taken to check the performance of each algorithm to solve the IK problem. The results showed that EM algorithm needs less population size and number of generations to get the true solution. There are multiple robot configurations at the goal points and both algorithms are able to find these solutions at each point. Self developed software simulator is used to display some of these solutions at each goal position

Discovering the Elite Hypervolume by Leveraging Interspecies Correlation

Evolution has produced an astonishing diversity of species, each filling a different niche. Algorithms like MAP-Elites mimic this divergent evolutionary process to find a set of behaviorally diverse but high-performing solutions, called the elites. Our key insight is that species in nature often share a surprisingly large part of their genome, in spite of occupying very different niches; similarly, the elites are likely to be concentrated in a specific "elite hypervolume" whose shape is defined by their common features. In this paper, we first introduce the elite hypervolume concept and propose two metrics to characterize it: the genotypic spread and the genotypic similarity. We then introduce a new variation operator, called "directional variation", that exploits interspecies (or inter-elites) correlations to accelerate the MAP-Elites algorithm. We demonstrate the effectiveness of this operator in three problems (a toy function, a redundant robotic arm, and a hexapod robot).Comment: In GECCO 201

Applications of parallel computing in robotics problems

"December 2013.""A Thesis presented to the Faculty of the Graduate School University of Missouri In Partial Fulfillment Of the Requirements for the Degree Master of Science."Thesis advisor: Dr. Guilherme N. DeSouza.Many typical robotics problems involve search in high-dimensional spaces, where real-time execution is hard to be achieved. This thesis presents two case studies of parallel computation in such robotics problems. More specifically, two problems of motion planning-the Inverse Kinematics of robotic manipulators and Path Planning for mobile robots-are investigated and the contributions of parallel algorithms are highlighted. For the Inverse Kinematics problem, a novel and fast solution is proposed for general serial manipulators. This new approach relies on the computation of multiple (parallel) numerical estimations of the inverse Jacobian while it selects the current best path to the desire con- figuration of the end-effector. Unlike other iterative methods, our method converges very quickly, achieving sub-millimeter accuracy in 20.48ms in average. We demonstrate such high accuracy and the real-time performance of our method by testing it with six different robots, at both non-singular and singular configurations, including a 7-DoF redundant robot. The algorithm is implemented in C/C++ using a configurable number of POSIX threads, and it can be easily expanded to use many-core GPUs. For the Path Planning problem, a solution to the problem of smooth path planning for mobile robots in dynamic and unknown environments is presented. A novel concept of Time-Warped Grids is introduced to predict the pose of obstacles on a grid-based map and avoid collisions. The algorithm is implemented using C/C++ and the CUDA programming environment, and combines stochastic estimation (Kalman filter), Harmonic Potential Fields and a Rubber Band model, and it translates naturally into the parallel paradigm of GPU programing. The proposed method was tested using several simulation scenarios for the Pioneer P3- DX robot, which demonstrated the robustness of the algorithm by finding the optimum path in terms of smoothness, distance, and collision-free either in static or dynamic environments, even with a very large number of obstacles.Includes bibliographical references (pages 70-78)

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

Inverse Kinematic Analysis of Robot Manipulators

An important part of industrial robot manipulators is to achieve desired position and orientation of end effector or tool so as to complete the pre-specified task. To achieve the above stated goal one should have the sound knowledge of inverse kinematic problem. The problem of getting inverse kinematic solution has been on the outline of various researchers and is deliberated as thorough researched and mature problem. There are many fields of applications of robot manipulators to execute the given tasks such as material handling, pick-n-place, planetary and undersea explorations, space manipulation, and hazardous field etc. Moreover, medical field robotics catches applications in rehabilitation and surgery that involve kinematic, dynamic and control operations. Therefore, industrial robot manipulators are required to have proper knowledge of its joint variables as well as understanding of kinematic parameters. The motion of the end effector or manipulator is controlled by their joint actuator and this produces the required motion in each joints. Therefore, the controller should always supply an accurate value of joint variables analogous to the end effector position. Even though industrial robots are in the advanced stage, some of the basic problems in kinematics are still unsolved and constitute an active focus for research. Among these unsolved problems, the direct kinematics problem for parallel mechanism and inverse kinematics for serial chains constitute a decent share of research domain. The forward kinematics of robot manipulator is simpler problem and it has unique or closed form solution. The forward kinematics can be given by the conversion of joint space to Cartesian space of the manipulator. On the other hand inverse kinematics can be determined by the conversion of Cartesian space to joint space. The inverse kinematic of the robot manipulator does not provide the closed form solution. Hence, industrial manipulator can achieve a desired task or end effector position in more than one configuration. Therefore, to achieve exact solution of the joint variables has been the main concern to the researchers. A brief introduction of industrial robot manipulators, evolution and classification is presented. The basic configurations of robot manipulator are demonstrated and their benefits and drawbacks are deliberated along with the applications. The difficulties to solve forward and inverse kinematics of robot manipulator are discussed and solution of inverse kinematic is introduced through conventional methods. In order to accomplish the desired objective of the work and attain the solution of inverse kinematic problem an efficient study of the existing tools and techniques has been done. A review of literature survey and various tools used to solve inverse kinematic problem on different aspects is discussed. The various approaches of inverse kinematic solution is categorized in four sections namely structural analysis of mechanism, conventional approaches, intelligence or soft computing approaches and optimization based approaches. A portion of important and more significant literatures are thoroughly discussed and brief investigation is made on conclusions and gaps with respect to the inverse kinematic solution of industrial robot manipulators. Based on the survey of tools and techniques used for the kinematic analysis the broad objective of the present research work is presented as; to carry out the kinematic analyses of different configurations of industrial robot manipulators. The mathematical modelling of selected robot manipulator using existing tools and techniques has to be made for the comparative study of proposed method. On the other hand, development of new algorithm and their mathematical modelling for the solution of inverse kinematic problem has to be made for the analysis of quality and efficiency of the obtained solutions. Therefore, the study of appropriate tools and techniques used for the solution of inverse kinematic problems and comparison with proposed method is considered. Moreover, recommendation of the appropriate method for the solution of inverse kinematic problem is presented in the work. Apart from the forward kinematic analysis, the inverse kinematic analysis is quite complex, due to its non-linear formulations and having multiple solutions. There is no unique solution for the inverse kinematics thus necessitating application of appropriate predictive models from the soft computing domain. Artificial neural network (ANN) can be gainfully used to yield the desired results. Therefore, in the present work several models of artificial neural network (ANN) are used for the solution of the inverse kinematic problem. This model of ANN does not rely on higher mathematical formulations and are adept to solve NP-hard, non-linear and higher degree of polynomial equations. Although intelligent approaches are not new in this field but some selected models of ANN and their hybridization has been presented for the comparative evaluation of inverse kinematic. The hybridization scheme of ANN and an investigation has been made on accuracies of adopted algorithms. On the other hand, any Optimization algorithms which are capable of solving various multimodal functions can be implemented to solve the inverse kinematic problem. To overcome the problem of conventional tool and intelligent based method the optimization based approach can be implemented. In general, the optimization based approaches are more stable and often converge to the global solution. The major problem of ANN based approaches are its slow convergence and often stuck in local optimum point. Therefore, in present work different optimization based approaches are considered. The formulation of the objective function and associated constrained are discussed thoroughly. The comparison of all adopted algorithms on the basis of number of solutions, mathematical operations and computational time has been presented. The thesis concludes the summary with contributions and scope of the future research work

Non-weighted aggregate evaluation function of multi-objective optimization for knock engine modeling

In decision theory, the weighted sum model (WSM) is the best known Multi-Criteria Decision Analysis (MCDA) approach for evaluating a number of alternatives in terms of a number of decision criteria. Assigning weights is a difficult task, especially if the number of criteria is large and the criteria are very different in character. There are some problems in the real world which utilize conflicting criteria and mutual effect. In the field of automotive, the knocking phenomenon in internal combustion or spark ignition engines limits the efficiency of the engine. Power and fuel economy can be maximized by optimizing some factors that affect the knocking phenomenon, such as temperature, throttle position sensor, spark ignition timing, and revolution per minute. Detecting knocks and controlling the above factors or criteria may allow the engine to run at the best power and fuel economy. The best decision must arise from selecting the optimum trade-off within the above criteria. The main objective of this study was to proposed a new Non-Weighted Aggregate Evaluation Function (NWAEF) model for non-linear multi-objectives function which will simulate the engine knock behavior (non-linear dependent variable) in order to optimize non-linear decision factors (non-linear independent variables). This study has focused on the construction of a NWAEF model by using a curve fitting technique and partial derivatives. It also aims to optimize the nonlinear nature of the factors by using Genetic Algorithm (GA) as well as investigate the behavior of such function. This study assumes that a partial and mutual influence between factors is required before such factors can be optimized. The Akaike Information Criterion (AIC) is used to balance the complexity of the model and the data loss, which can help assess the range of the tested models and choose the best ones. Some statistical tools are also used in this thesis to assess and identify the most powerful explanation in the model. The first derivative is used to simplify the form of evaluation function. The NWAEF model was compared to Random Weights Genetic Algorithm (RWGA) model by using five data sets taken from different internal combustion engines. There was a relatively large variation in elapsed time to get to the best solution between the two model. Experimental results in application aspect (Internal combustion engines) show that the new model participates in decreasing the elapsed time. This research provides a form of knock control within the subspace that can enhance the efficiency and performance of the engine, improve fuel economy, and reduce regulated emissions and pollution. Combined with new concepts in the engine design, this model can be used for improving the control strategies and providing accurate information to the Engine Control Unit (ECU), which will control the knock faster and ensure the perfect condition of the engine

Mining a Small Medical Data Set by Integrating the Decision Tree and t-test

[[abstract]]Although several researchers have used statistical methods to prove that aspiration followed by the injection of 95% ethanol left in situ (retention) is an effective treatment for ovarian endometriomas, very few discuss the different conditions that could generate different recovery rates for the patients. Therefore, this study adopts the statistical method and decision tree techniques together to analyze the postoperative status of ovarian endometriosis patients under different conditions. Since our collected data set is small, containing only 212 records, we use all of these data as the training data. Therefore, instead of using a resultant tree to generate rules directly, we use the value of each node as a cut point to generate all possible rules from the tree first. Then, using t-test, we verify the rules to discover some useful description rules after all possible rules from the tree have been generated. Experimental results show that our approach can find some new interesting knowledge about recurrent ovarian endometriomas under different conditions.[[journaltype]]國外[[incitationindex]]EI[[booktype]]紙本[[countrycodes]]FI