A robot is a mechanical or virtual artificial agent, usually an electro-mechanical machine that is guided by a computer program or electronic circuitry. Robots can be autonomous or semi-autonomous. In this thesis, design optimization strategies and synthesis for robotic arm are studied. In the design process, novel optimization methods have been developed to reduce the mass of the whole robotic arm. The optimization of the robotic arm is conducted at three different levels, with the main objective to minimize the robot mass. At the first level, only the drive-train of the robotic arm is optimized. The design process of a robotic arm is decomposed into selection of components for the drive-train to reduce the weight At the second level, kinematic data is combined with the drive-train in the optimization. For this purpose, a dynamic model of the robot is required. Constraints are formulated on the motors, gearboxes and kinematic performance At the third level, a systematic optimization approach is developed, which contains design variables of structural dimensions, geometric dimensions and drive-train composes. Constraints are formulated on the stiffness and deformation. The stiffness and deformation of the arm are calculated through FEA simulation. The main objective of the thesis is to design optimization and synthesis analysis of robotic arm. The corresponding deflections, stresses and strains for that load will be find out by suing the method of finite element analysis.
Kineto-Elasto Dynamic Analysis of Robot Manipulator Puma-560IOSR Journals
Current industrial robots are made very heavy to achieve high Stiffness
which increases the accuracy of their motion. However this heaviness limits the robot speed and in masses the
required energy to move the system. The requirement for higher speed and better system performance makes it
necessary to consider a new generation of light weight manipulators as an alternative to today's massive
inefficient ones. Light weight manipulators require Less energy to move and they have larger payload abilities
and more maneuverability. However due to the dynamic effects of structural flexibility, their control is much
more difficult. Therefore, there is a need to develop accurate dynamic models for design and control of such
systems.This project presents the flexibility and Kineto - Elasto dynamic analysis of robot manipulator
considering deflection. Based on the distributed parameter method, the generalized motion equations of robot
manipulator with flexible links are derived. The final formulation of the motion equations is used to model
general complex elastic manipulators with nonlinear rigid-body and elastic motion in dynamics and it can be
used in the flexibility analysis of robot manipulators and spatial mechanisms. Manipulator end-effector path
trajectory, velocity and accelerations are plotted. Joint torques is to be determined for each joint trajectory
(Dynamics) .Using joint torques, static loading due to link’s masses, masses at joints, and payload, the robot
arms elastic deformations are to be found by using ANSYS-12.0 software package. Elastic compensation is
inserted in coordinates of robotic programming to get exact end-effectors path. A comparison of paths
trajectory of the end-effector is to be plotted. Also variation of torques is plotted after considering elastic
compensation. These torque variations are included in the robotic programming for getting the accurate endeffect
or’s path trajectory
This document describes a computational model called the Vehicle Dynamic Model (VDM) that was developed to analyze the dynamic behavior of vehicles. The VDM allows users to define vehicle parameters and evaluate the vehicle's vertical response when traversing different track profiles. It provides four types of results: 1) steady state response, 2) frequency response curves, 3) animation of the vehicle running on a track profile, and 4) natural frequencies and vibration modes. The model accounts for components like tires, springs, dampers and vehicle geometry. It was tested using literature data and allows analyzing ride performance by changing parameters and checking the vehicle's response over different tracks.
Measuring Axle Weight of Moving Vehicle Based on Particle Swarm OptimizationIJRES Journal
The dynamic tire forces are the important factor influencing weigh-in-motion of vehicle. This paper presents a method to separate the dynamic tire forces contained in axle-weight signal. On the basis of analyzing the characteristic of axle-weight signal, the model of axle-weight signal and the objective function are constructed. After introducing the principle of particle swarm optimization (PSO), an improved PSO is employed to estimate the unknown parameters of the objective function. According to the obtained estimates of parameters, the dynamic tire forces contained in axle-weight signal are reconstructed. Subtract the reconstructed dynamic tire forces from the axle-weight signal, and get the estimate of axle weight of moving vehicle. Simulation and field experiments are conducted to demonstrate the performance of the proposed method.
This document proposes an adaptive synchronized control method for coordinating multirobot assembly tasks. The key points are:
- It uses a synchronization scheme based on motion synchronization to maintain certain kinematic relationships between robots, without requiring complex hybrid position/force control.
- The controller incorporates cross-coupling technology into an adaptive control architecture. It guarantees asymptotic convergence to zero of both position tracking errors and synchronization errors simultaneously for coordinated robots.
- The method is applied first to coordinate two robots holding a common payload. It is then extended to coordinate multiple robots, where each robot synchronizes its motion with the other two robots to achieve overall synchronization. Experiments demonstrate the effectiveness of the approach.
SIMULTANEOUS OPTIMIZATION OF SEMIACTIVE QUARTER CAR SUSPENSION PARAMETERS USI...ijmech
In present paper, a methodology is presented related to the optimization of semi-active quarter car model
suspension parameters having three degrees of freedom, subjected to bump type of road excitation.
Influence of primary suspension stiffness, primary suspension damping, secondary suspension stiffness and
secondary suspension damping are studied on the passenger ride comfort, taking root mean square (RMS)
values of passenger seat displacement and settling time into account. Semi-active quarter car model
assembled with magneto-rheological (MR) shock absorber is selected for optimization of suspension
parameters using Taguchi method in combination with Grey relational analysis. Confirmatory results with
simulation run indicates that the optimized results of suspension parameters are helpful in achieving the
best ride comfort to travelling passengers in terms of minimization of passenger seat displacement and
settling time values.
Identifying the Slider-Crank Mechanism System by the MPSO Methodijtsrd
This document summarizes a research paper that proposes a modified particle swarm optimization (MPSO) method to identify the parameters of a slider-crank mechanism driven by a field-oriented PM synchronous motor. The MPSO method considers a "distance" term in the fitness function to avoid local optima. Dynamic formulations of the slider-crank mechanism are presented with one independent variable. Experimental results validate that the MPSO identification method can accurately determine the slider-crank mechanism parameters.
Aplanning algorithm offive-axis feedrate interpolation based on drive and jer...IJRES Journal
CNC technology marks the core of modern manufacturing, and CNC interpolation module is one of the most important numerical control technology modules. Avery important feature of the CNC is to implement the feed rate that consists in producing the set points based on a NC program. In the high speed machining, the feed rate is restricted by the velocity, acceleration, and jerk. And the NURBS curve is a free curve, due to the many advantages of NURBS curves, it can be well applied to the CNC feed rate interpolation. The algorithm can get more smooth feed rate curves, which makes better use of kinematical characteristics of the machine. Finally, according to each machine axis capability, one can use the feed rate control method which is verified by simulation analysis and processing to test this method. The results show that the algorithm can effectively control the speed, acceleration and jerk.
This document discusses different control methods for vehicle lateral control, including classical control theory, modern control theory, fuzzy logic, sliding mode control, and neural networks. It develops a 2DOF bicycle model of a vehicle and uses pole placement control to design a lateral controller. Simulation results show the vehicle can track a reference input but with large overshoots in yaw rate and velocity. An improved controller is designed with slower response but smaller state variable fluctuations. Future work involves implementing the controller with an observer and designing longitudinal control.
Kineto-Elasto Dynamic Analysis of Robot Manipulator Puma-560IOSR Journals
Current industrial robots are made very heavy to achieve high Stiffness
which increases the accuracy of their motion. However this heaviness limits the robot speed and in masses the
required energy to move the system. The requirement for higher speed and better system performance makes it
necessary to consider a new generation of light weight manipulators as an alternative to today's massive
inefficient ones. Light weight manipulators require Less energy to move and they have larger payload abilities
and more maneuverability. However due to the dynamic effects of structural flexibility, their control is much
more difficult. Therefore, there is a need to develop accurate dynamic models for design and control of such
systems.This project presents the flexibility and Kineto - Elasto dynamic analysis of robot manipulator
considering deflection. Based on the distributed parameter method, the generalized motion equations of robot
manipulator with flexible links are derived. The final formulation of the motion equations is used to model
general complex elastic manipulators with nonlinear rigid-body and elastic motion in dynamics and it can be
used in the flexibility analysis of robot manipulators and spatial mechanisms. Manipulator end-effector path
trajectory, velocity and accelerations are plotted. Joint torques is to be determined for each joint trajectory
(Dynamics) .Using joint torques, static loading due to link’s masses, masses at joints, and payload, the robot
arms elastic deformations are to be found by using ANSYS-12.0 software package. Elastic compensation is
inserted in coordinates of robotic programming to get exact end-effectors path. A comparison of paths
trajectory of the end-effector is to be plotted. Also variation of torques is plotted after considering elastic
compensation. These torque variations are included in the robotic programming for getting the accurate endeffect
or’s path trajectory
This document describes a computational model called the Vehicle Dynamic Model (VDM) that was developed to analyze the dynamic behavior of vehicles. The VDM allows users to define vehicle parameters and evaluate the vehicle's vertical response when traversing different track profiles. It provides four types of results: 1) steady state response, 2) frequency response curves, 3) animation of the vehicle running on a track profile, and 4) natural frequencies and vibration modes. The model accounts for components like tires, springs, dampers and vehicle geometry. It was tested using literature data and allows analyzing ride performance by changing parameters and checking the vehicle's response over different tracks.
Measuring Axle Weight of Moving Vehicle Based on Particle Swarm OptimizationIJRES Journal
The dynamic tire forces are the important factor influencing weigh-in-motion of vehicle. This paper presents a method to separate the dynamic tire forces contained in axle-weight signal. On the basis of analyzing the characteristic of axle-weight signal, the model of axle-weight signal and the objective function are constructed. After introducing the principle of particle swarm optimization (PSO), an improved PSO is employed to estimate the unknown parameters of the objective function. According to the obtained estimates of parameters, the dynamic tire forces contained in axle-weight signal are reconstructed. Subtract the reconstructed dynamic tire forces from the axle-weight signal, and get the estimate of axle weight of moving vehicle. Simulation and field experiments are conducted to demonstrate the performance of the proposed method.
This document proposes an adaptive synchronized control method for coordinating multirobot assembly tasks. The key points are:
- It uses a synchronization scheme based on motion synchronization to maintain certain kinematic relationships between robots, without requiring complex hybrid position/force control.
- The controller incorporates cross-coupling technology into an adaptive control architecture. It guarantees asymptotic convergence to zero of both position tracking errors and synchronization errors simultaneously for coordinated robots.
- The method is applied first to coordinate two robots holding a common payload. It is then extended to coordinate multiple robots, where each robot synchronizes its motion with the other two robots to achieve overall synchronization. Experiments demonstrate the effectiveness of the approach.
SIMULTANEOUS OPTIMIZATION OF SEMIACTIVE QUARTER CAR SUSPENSION PARAMETERS USI...ijmech
In present paper, a methodology is presented related to the optimization of semi-active quarter car model
suspension parameters having three degrees of freedom, subjected to bump type of road excitation.
Influence of primary suspension stiffness, primary suspension damping, secondary suspension stiffness and
secondary suspension damping are studied on the passenger ride comfort, taking root mean square (RMS)
values of passenger seat displacement and settling time into account. Semi-active quarter car model
assembled with magneto-rheological (MR) shock absorber is selected for optimization of suspension
parameters using Taguchi method in combination with Grey relational analysis. Confirmatory results with
simulation run indicates that the optimized results of suspension parameters are helpful in achieving the
best ride comfort to travelling passengers in terms of minimization of passenger seat displacement and
settling time values.
Identifying the Slider-Crank Mechanism System by the MPSO Methodijtsrd
This document summarizes a research paper that proposes a modified particle swarm optimization (MPSO) method to identify the parameters of a slider-crank mechanism driven by a field-oriented PM synchronous motor. The MPSO method considers a "distance" term in the fitness function to avoid local optima. Dynamic formulations of the slider-crank mechanism are presented with one independent variable. Experimental results validate that the MPSO identification method can accurately determine the slider-crank mechanism parameters.
Aplanning algorithm offive-axis feedrate interpolation based on drive and jer...IJRES Journal
CNC technology marks the core of modern manufacturing, and CNC interpolation module is one of the most important numerical control technology modules. Avery important feature of the CNC is to implement the feed rate that consists in producing the set points based on a NC program. In the high speed machining, the feed rate is restricted by the velocity, acceleration, and jerk. And the NURBS curve is a free curve, due to the many advantages of NURBS curves, it can be well applied to the CNC feed rate interpolation. The algorithm can get more smooth feed rate curves, which makes better use of kinematical characteristics of the machine. Finally, according to each machine axis capability, one can use the feed rate control method which is verified by simulation analysis and processing to test this method. The results show that the algorithm can effectively control the speed, acceleration and jerk.
This document discusses different control methods for vehicle lateral control, including classical control theory, modern control theory, fuzzy logic, sliding mode control, and neural networks. It develops a 2DOF bicycle model of a vehicle and uses pole placement control to design a lateral controller. Simulation results show the vehicle can track a reference input but with large overshoots in yaw rate and velocity. An improved controller is designed with slower response but smaller state variable fluctuations. Future work involves implementing the controller with an observer and designing longitudinal control.
CPREDICTION OF INVERSE KINEMATICS SOLUTION OF A REDUNDANT MANIPULATOR USING A...Ijripublishers Ijri
In this thesis, a method for forward and inverse kinematics analysis of a 5-DOF and a 7- DOF Redundant manipulator
is proposed. Obtaining the trajectory and computing the required joint angles for a higher DOF robot manipulator is one
of the important concerns in robot kinematics and control. The difficulties in solving the inverse kinematics equations
of these redundant robot manipulator arises due to the presence of uncertain, time varying and non-linear nature of
equations having transcendental functions. In this thesis, the ability of ANFIS is used to the generated data for solving
inverse kinematics problem. A single- output Sugeno-type FIS using grid partitioning has been modeled in this work.
The forward kinematics and inverse kinematics for a 5-DOF and 7-DOF manipulator are analyzed systemically. The Efficiency
of ANFIS can be concluded by observing the surface plot, residual plot and normal probability plot. This current
study in using different nonlinear models for the prediction of the IKs of a 5-DOF and 7-DOF Redundant manipulator
will give a valuable source of information for other modellers.
Keywords: 5-DOF and 7-DOF Redundant Robot Manipulator; Inverse kinematics; ANFIS; Denavit-Harbenterg (D-H)
notation.
Development of a quadruped mobile robot and its movement system using geometr...journalBEEI
As the main testbed platform of Artificial Intelligence, the robot plays an essential role in creating an environment for industrial revolution 4.0. According to their bases, the robot can be categorized into a fixed based robot and a mobile robot. Current robotics research direction is interesting since people strive to create a mobile robot able to move in the land, water, and air. This paper presents development of a quadruped mobile robot and its movement system using geometric-based inverse kinematics. The study is related to the movement of a four-legged (quadruped) mobile robot with three Degrees of Freedom (3 DOF) for each leg. Because it has four legs, the movement of the robot can only be done through coordinating the movements of each leg. In this study, the trot gait pattern method is proposed to coordinate the movement of the robot's legs. The end-effector position of each leg is generated by a simple trajectory generator with half rectified sine wave pattern. Furthermore, to move each robot's leg, it is proposed to use geometric-based inverse kinematic. The experimental results showed that the proposed method succeeded in moving the mobile robot with precision. Movement errors in the translation direction are 1.83% with the average pose error of 1.33 degrees, means the mobile robot has good walking stability.
Comparative Analysis for NN-Based Adaptive Back-stepping Controller and Back-...IJERA Editor
This work primarily addresses the design and implementation of a neural network based controller for the trajectory tracking of a differential drive mobile robot. The proposed control algorithm is an NN-based adaptive controller which tunes the gains of the back-stepping controller online according to the robot reference trajectory and its initial posture. In this method, a neural network is needed to learn the characteristics of the plant dynamics and make use of it to determine the future inputs that will minimize error performance index so as to compensate the back-stepping controller gains. The advantages and disadvantages of theproposed control algorithms will be discussed in each section with illustrations.Comprehensive system modeling including robot kinematics and dynamics modeling has been done. The dynamic modeling is done using Newtonian and Lagrangian methodologies for nonholonomic systems and the results are compared to verify the accuracy of each method. Simulation of the robot model and different controllers has been done using Matlab and Matlab Simulink.
The performance evaluation is one of most important issues in the analysis and design of parallel manipulators.
Characteristics such as manipulability and minimum singular value are used to determine the performance of the manipulators. The performance indices are used to eliminate the singularity and it’s near configurations. In this paper 6-UPS spatial parallel manipulator is considered and its performance indices such as condition number, manipulability and minimum singular value are determined for different structures.
Simulation of Robot Manipulator Trajectory Optimization DesignIJRESJOURNAL
ABSTRACT: Most of the trajectory planning based on robot dynamics and kinematics start from the joint space, can not guarantee the robot end track corresponding relationship. To solve the above problem, the method of trajectory planning is proposed and the optimization algorithm is used to solve the optimization trajectory. Taking the SCARA robot as an example, the trajectory of the end trajectory is preset, the first trajectory is planned by combining the first order acceleration planning and the arc transition. Then, the target model is optimized for the average power and the movement time. Finally, a non-dominated sorting algorithm is introduced to optimize the trajectory to obtain the best performance trajectory. The simulation results show that the optimized trajectory has a certain amount of time-consuming increase compared with the traditional trajectory of SCARA robot, but its energy consumption is obviously reduced, and the overall optimization result is obvious.
This document discusses algorithms for avoiding kinematic singularities in 6-DOF robotic manipulators controlled in real time using a teaching pendant. It proposes two algorithms: (1) non-redundancy avoidance using damped least squares to modify the inverse kinematic solution near singularities, and (2) redundancy avoidance using a potential function based on manipulability to incorporate singularity avoidance for redundant manipulators. The algorithms are experimentally tested on a DENSO VP-6242G robot to evaluate performance near shoulder and wrist singularities during teaching pendant controlled motion.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
Improvement of vehicle ride comfort using geneticalgorithm optimization and p...ahmedgeweda
This document presents a study that aims to improve vehicle ride comfort using genetic algorithm optimization and a PI controller. The following key points are discussed:
1. A 7 degree-of-freedom full vehicle model is developed in MATLAB SIMULINK to study ride comfort.
2. A genetic algorithm is used to optimize the values of spring stiffness and damping coefficients for the front and rear passive suspension at different velocities.
3. A proportional-integral controller is also implemented to study its effect on ride comfort.
4. Comparisons of body acceleration and sprung mass displacement are made between the optimized suspension parameters, model with PI controller, and passive suspension system to evaluate ride performance improvements.
This document describes the development of a pick and place robot using a programmable logic controller (PLC) as the controller. The robot has four degrees of freedom and is designed to accurately locate and grip objects in a customized workspace. The author details the mechanical and electrical design of the robot, including the 3D printed links and joints, PLC and motor control circuitry, and sensors. Simulation results are presented showing the robot can successfully operate within its load capacity to grip and move objects as intended.
Simulation design of trajectory planning robot manipulatorjournalBEEI
Robots can be mathematically modeled with computer programs where the results can be displayed visually, so it can be used to determine the input, gain, attenuate and error parameters of the control system. In addition to the robot motion control system, to achieve the target points should need a research to get the best trajectory, so the movement of robots can be more efficient. One method that can be used to get the best path is the SOM (Self Organizing Maps) neural network. This research proposes the usage of SOM in combination with PID and Fuzzy-PD control for finding an optimal path between source and destination. SOM Neural network process is able to guide the robot manipulator through the target points. The results presented emphasize that a satisfactory trajectory tracking precision and stability could be achieved using SOM Neural networking combination with PID and Fuzzy-PD controller.The obtained average error to reach the target point when using Fuzzy-PD=2.225% and when using PID=1.965%.
Manipulability index of a parallel robot manipulatorIAEME Publication
This document discusses manipulability index, which is a measure of a robot's ability to manipulate objects in different positions and orientations. It defines manipulability index as the determinant of the product of a robot's Jacobian matrix and its transpose. A higher manipulability index indicates better velocity transmission capabilities and dexterity. The document analyzes manipulability index values for different robot structures using MATLAB. It also describes how velocity and force ellipsoids can represent a robot's velocity and force transmission characteristics based on its Jacobian matrix.
This document summarizes the kinematics analysis of a 3-UPU (universal-prismatic-universal) parallel robot. Each of the robot's three legs consists of two universal joints connected by a prismatic joint. The document establishes recursive matrix relations for solving the inverse kinematics problem given the position of the mobile platform. Simulation graphs are generated for the input displacements, velocities, and accelerations. The kinematics analysis determines the nine independent variables that define the robot's configuration based on vector-loop equations relating the joint parameters and platform position.
Kinematic control with singularity avoidance for teaching-playback robot mani...Baron Y.S. Yong
This article proposes and investigates three methods for avoiding kinematic singularities in a teaching-playback robot manipulator system:
1. Nonredundancy singularity avoidance (NRSA) and redundancy singularity avoidance (RSA) modify the Jacobian matrix to reduce both position and orientation errors or prioritize position error reduction.
2. Point-to-point singularity avoidance (PTPSA) moves the end-effector through singular regions via joint-interpolated control without maintaining position and orientation.
Experimental case studies evaluate the three methods when the end-effector approaches wrist and shoulder singularities. Results show the methods effectively avoid singularities and enhance robot capability for industrial automation.
Real-time Estimation of Human’s Intended Walking Speed for Treadmill-style Lo...toukaigi
This document discusses estimating a human's intended walking speed using force plates under a treadmill. It first introduces the problem and experimental setup using two force plates under a treadmill. It then describes Experiment 1 which found that a proposed force index, defined as the minimum value of the ratio of forward ground reaction force to total ground reaction force during one gait cycle, has a strong linear correlation with intended walking speed. Experiment 2 showed the coefficients of this linear relationship vary little, ensuring tolerance of individual variations. Finally, a treadmill-style locomotion interface is presented that allows a user to actively control the treadmill speed with their feet based on intended walking speed estimation, providing a promising human-machine interface.
The document describes a new adaptive treadmill control strategy that allows the treadmill speed to be controlled by the user's intended walking speed. It analyzes the center of pressure formula and simulation results to identify the ratio of reaction forces yF and zF (denoted as ,y zR ) as a key index related to intended walking speed. An experiment is conducted where subjects walk on a treadmill while viewing a virtual reality shopping scene. Force plate data is used to model the relationship between ,y zR and treadmill velocity V, and least squares regression is used to calibrate the model. The results show the treadmill speed can be smoothly controlled to match the user's intended speed.
Recognition and classification of human motionHutami Endang
This document describes research on recognizing and classifying human motions using hidden Markov models for building a motion database. Key points:
1) Human motions are extracted using bilateral control to obtain both position and force information.
2) Extracted motions are modeled as states defined by constant velocity segments and applied force vectors.
3) A real-time motion search method is proposed using hidden Markov models and the Viterbi algorithm to recognize motions as they occur based on velocity and force features.
4) The method is intended to allow a robot to accurately assist humans by recognizing their intended motions from a database in real-time using both kinematic and force information.
Design and analysis of x y- positioning stage based on redundant parallel li...eSAT Journals
Abstract This paper presents the concept of a planar positioning stage based on a kinematically redundant parallel linkage. Basic kinematics and workspace analysis of base redundant manipulator is initially explained and the procedure of static analysis to predict the actuated joint torques is described. As there are six actuators in the linkage, the redundancy can be overcome by proper selection of the base joint variables. Also it is assumed that the motion is at a constant speed. A numerical example is shown with a straight line trajectory to illustrate the workspace and joint force calculation aspects of this linkage. The possible arrangement of the stage with electrostatic actuation and sensing are finally highlighted. Keywords: Kinematic redundancy, Parallel mechanism, Static analysis, and Workspace characteristics
Indigenously Design Development and Motion Control of Multi-DoF Robotic Manip...IRJET Journal
This document describes the design and development of a 6 degree of freedom (DOF) robotic manipulator. The key points are:
1) The mechanical design of the robotic arm is discussed, including the use of aluminum 7075 material, timing belt-pulley mechanisms to increase torque, and a functional gripper.
2) The forward and inverse kinematics models are derived based on the Denavit-Hartenberg convention. Expressions for the joint variables in terms of the end-effector pose are provided for inverse kinematics.
3) The robot dynamics are modeled using the Euler-Lagrange formulation to describe the relationship between joint torques and accelerations. Transfer functions for the DC motors are
PSO APPLIED TO DESIGN OPTIMAL PD CONTROL FOR A UNICYCLE MOBILE ROBOTJaresJournal
In this work, we propose a Particle Swarm Optimization (PSO) to design Proportional Derivative
controllers (PD) for the control of Unicycle Mobile Robot. To stabilize and drive the robot precisely with
the predefined trajectory, a decentralized control structure is adopted where four PD controllers are used.
Their parameters are given simultaneously by the proposed algorithm (PSO). The performance of the
system from its desired behavior is quantified by an objective function (SE). Simulation results are
presented to show the efficiency of the method. ).
The results are very conclusive and satisfactory in terms of stability and trajectory tracking of unicycle
mobile robot
This document summarizes a study that analyzed and optimized the lower control arm of an automobile suspension system using finite element analysis. The existing lower control arm model was modeled, meshed, and analyzed under static loads to determine stresses and deformation. Topology optimization was then performed to reduce the weight of the lower control arm. The optimized model weight was reduced by 15% compared to the original. Static analysis was repeated on the optimized model to ensure stresses remained below yield strength. Cost analysis found the optimized design provided cost savings due to the reduced material usage.
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CPREDICTION OF INVERSE KINEMATICS SOLUTION OF A REDUNDANT MANIPULATOR USING A...Ijripublishers Ijri
In this thesis, a method for forward and inverse kinematics analysis of a 5-DOF and a 7- DOF Redundant manipulator
is proposed. Obtaining the trajectory and computing the required joint angles for a higher DOF robot manipulator is one
of the important concerns in robot kinematics and control. The difficulties in solving the inverse kinematics equations
of these redundant robot manipulator arises due to the presence of uncertain, time varying and non-linear nature of
equations having transcendental functions. In this thesis, the ability of ANFIS is used to the generated data for solving
inverse kinematics problem. A single- output Sugeno-type FIS using grid partitioning has been modeled in this work.
The forward kinematics and inverse kinematics for a 5-DOF and 7-DOF manipulator are analyzed systemically. The Efficiency
of ANFIS can be concluded by observing the surface plot, residual plot and normal probability plot. This current
study in using different nonlinear models for the prediction of the IKs of a 5-DOF and 7-DOF Redundant manipulator
will give a valuable source of information for other modellers.
Keywords: 5-DOF and 7-DOF Redundant Robot Manipulator; Inverse kinematics; ANFIS; Denavit-Harbenterg (D-H)
notation.
Development of a quadruped mobile robot and its movement system using geometr...journalBEEI
As the main testbed platform of Artificial Intelligence, the robot plays an essential role in creating an environment for industrial revolution 4.0. According to their bases, the robot can be categorized into a fixed based robot and a mobile robot. Current robotics research direction is interesting since people strive to create a mobile robot able to move in the land, water, and air. This paper presents development of a quadruped mobile robot and its movement system using geometric-based inverse kinematics. The study is related to the movement of a four-legged (quadruped) mobile robot with three Degrees of Freedom (3 DOF) for each leg. Because it has four legs, the movement of the robot can only be done through coordinating the movements of each leg. In this study, the trot gait pattern method is proposed to coordinate the movement of the robot's legs. The end-effector position of each leg is generated by a simple trajectory generator with half rectified sine wave pattern. Furthermore, to move each robot's leg, it is proposed to use geometric-based inverse kinematic. The experimental results showed that the proposed method succeeded in moving the mobile robot with precision. Movement errors in the translation direction are 1.83% with the average pose error of 1.33 degrees, means the mobile robot has good walking stability.
Comparative Analysis for NN-Based Adaptive Back-stepping Controller and Back-...IJERA Editor
This work primarily addresses the design and implementation of a neural network based controller for the trajectory tracking of a differential drive mobile robot. The proposed control algorithm is an NN-based adaptive controller which tunes the gains of the back-stepping controller online according to the robot reference trajectory and its initial posture. In this method, a neural network is needed to learn the characteristics of the plant dynamics and make use of it to determine the future inputs that will minimize error performance index so as to compensate the back-stepping controller gains. The advantages and disadvantages of theproposed control algorithms will be discussed in each section with illustrations.Comprehensive system modeling including robot kinematics and dynamics modeling has been done. The dynamic modeling is done using Newtonian and Lagrangian methodologies for nonholonomic systems and the results are compared to verify the accuracy of each method. Simulation of the robot model and different controllers has been done using Matlab and Matlab Simulink.
The performance evaluation is one of most important issues in the analysis and design of parallel manipulators.
Characteristics such as manipulability and minimum singular value are used to determine the performance of the manipulators. The performance indices are used to eliminate the singularity and it’s near configurations. In this paper 6-UPS spatial parallel manipulator is considered and its performance indices such as condition number, manipulability and minimum singular value are determined for different structures.
Simulation of Robot Manipulator Trajectory Optimization DesignIJRESJOURNAL
ABSTRACT: Most of the trajectory planning based on robot dynamics and kinematics start from the joint space, can not guarantee the robot end track corresponding relationship. To solve the above problem, the method of trajectory planning is proposed and the optimization algorithm is used to solve the optimization trajectory. Taking the SCARA robot as an example, the trajectory of the end trajectory is preset, the first trajectory is planned by combining the first order acceleration planning and the arc transition. Then, the target model is optimized for the average power and the movement time. Finally, a non-dominated sorting algorithm is introduced to optimize the trajectory to obtain the best performance trajectory. The simulation results show that the optimized trajectory has a certain amount of time-consuming increase compared with the traditional trajectory of SCARA robot, but its energy consumption is obviously reduced, and the overall optimization result is obvious.
This document discusses algorithms for avoiding kinematic singularities in 6-DOF robotic manipulators controlled in real time using a teaching pendant. It proposes two algorithms: (1) non-redundancy avoidance using damped least squares to modify the inverse kinematic solution near singularities, and (2) redundancy avoidance using a potential function based on manipulability to incorporate singularity avoidance for redundant manipulators. The algorithms are experimentally tested on a DENSO VP-6242G robot to evaluate performance near shoulder and wrist singularities during teaching pendant controlled motion.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
Improvement of vehicle ride comfort using geneticalgorithm optimization and p...ahmedgeweda
This document presents a study that aims to improve vehicle ride comfort using genetic algorithm optimization and a PI controller. The following key points are discussed:
1. A 7 degree-of-freedom full vehicle model is developed in MATLAB SIMULINK to study ride comfort.
2. A genetic algorithm is used to optimize the values of spring stiffness and damping coefficients for the front and rear passive suspension at different velocities.
3. A proportional-integral controller is also implemented to study its effect on ride comfort.
4. Comparisons of body acceleration and sprung mass displacement are made between the optimized suspension parameters, model with PI controller, and passive suspension system to evaluate ride performance improvements.
This document describes the development of a pick and place robot using a programmable logic controller (PLC) as the controller. The robot has four degrees of freedom and is designed to accurately locate and grip objects in a customized workspace. The author details the mechanical and electrical design of the robot, including the 3D printed links and joints, PLC and motor control circuitry, and sensors. Simulation results are presented showing the robot can successfully operate within its load capacity to grip and move objects as intended.
Simulation design of trajectory planning robot manipulatorjournalBEEI
Robots can be mathematically modeled with computer programs where the results can be displayed visually, so it can be used to determine the input, gain, attenuate and error parameters of the control system. In addition to the robot motion control system, to achieve the target points should need a research to get the best trajectory, so the movement of robots can be more efficient. One method that can be used to get the best path is the SOM (Self Organizing Maps) neural network. This research proposes the usage of SOM in combination with PID and Fuzzy-PD control for finding an optimal path between source and destination. SOM Neural network process is able to guide the robot manipulator through the target points. The results presented emphasize that a satisfactory trajectory tracking precision and stability could be achieved using SOM Neural networking combination with PID and Fuzzy-PD controller.The obtained average error to reach the target point when using Fuzzy-PD=2.225% and when using PID=1.965%.
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This document discusses manipulability index, which is a measure of a robot's ability to manipulate objects in different positions and orientations. It defines manipulability index as the determinant of the product of a robot's Jacobian matrix and its transpose. A higher manipulability index indicates better velocity transmission capabilities and dexterity. The document analyzes manipulability index values for different robot structures using MATLAB. It also describes how velocity and force ellipsoids can represent a robot's velocity and force transmission characteristics based on its Jacobian matrix.
This document summarizes the kinematics analysis of a 3-UPU (universal-prismatic-universal) parallel robot. Each of the robot's three legs consists of two universal joints connected by a prismatic joint. The document establishes recursive matrix relations for solving the inverse kinematics problem given the position of the mobile platform. Simulation graphs are generated for the input displacements, velocities, and accelerations. The kinematics analysis determines the nine independent variables that define the robot's configuration based on vector-loop equations relating the joint parameters and platform position.
Kinematic control with singularity avoidance for teaching-playback robot mani...Baron Y.S. Yong
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2. Point-to-point singularity avoidance (PTPSA) moves the end-effector through singular regions via joint-interpolated control without maintaining position and orientation.
Experimental case studies evaluate the three methods when the end-effector approaches wrist and shoulder singularities. Results show the methods effectively avoid singularities and enhance robot capability for industrial automation.
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Indigenously Design Development and Motion Control of Multi-DoF Robotic Manip...IRJET Journal
This document describes the design and development of a 6 degree of freedom (DOF) robotic manipulator. The key points are:
1) The mechanical design of the robotic arm is discussed, including the use of aluminum 7075 material, timing belt-pulley mechanisms to increase torque, and a functional gripper.
2) The forward and inverse kinematics models are derived based on the Denavit-Hartenberg convention. Expressions for the joint variables in terms of the end-effector pose are provided for inverse kinematics.
3) The robot dynamics are modeled using the Euler-Lagrange formulation to describe the relationship between joint torques and accelerations. Transfer functions for the DC motors are
PSO APPLIED TO DESIGN OPTIMAL PD CONTROL FOR A UNICYCLE MOBILE ROBOTJaresJournal
In this work, we propose a Particle Swarm Optimization (PSO) to design Proportional Derivative
controllers (PD) for the control of Unicycle Mobile Robot. To stabilize and drive the robot precisely with
the predefined trajectory, a decentralized control structure is adopted where four PD controllers are used.
Their parameters are given simultaneously by the proposed algorithm (PSO). The performance of the
system from its desired behavior is quantified by an objective function (SE). Simulation results are
presented to show the efficiency of the method. ).
The results are very conclusive and satisfactory in terms of stability and trajectory tracking of unicycle
mobile robot
This document summarizes a study that analyzed and optimized the lower control arm of an automobile suspension system using finite element analysis. The existing lower control arm model was modeled, meshed, and analyzed under static loads to determine stresses and deformation. Topology optimization was then performed to reduce the weight of the lower control arm. The optimized model weight was reduced by 15% compared to the original. Static analysis was repeated on the optimized model to ensure stresses remained below yield strength. Cost analysis found the optimized design provided cost savings due to the reduced material usage.
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This document discusses using MATLAB's Robotics Toolbox to simulate a robotic arm with up to 6 degrees of freedom. The toolbox allows users to model different robotic arm configurations using revolute or prismatic joints. It covers the technical background of forward and inverse kinematics analysis. Some advantages of the toolbox are that the code is mature and provides a basis for comparison. The future scope is that data from the toolbox can be used with other MATLAB tools like neural networks. Results show the end effector positions can be found for different joint angles.
This document compares kinematic and dynamic models for robotics. The kinematic model studies robot motion without considering forces/torques, and can be used to determine end effector position from joint positions. The dynamic model relates joint torques to motion, and is important for analyzing a robot's dynamic behavior. Key differences include the kinematic model using Denavit-Hartenberg notation while dynamic models employ Lagrange-Euler and Newton-Euler formulations. Both models are essential for robot control and simulation.
IRJET- Design and Analysis of Lower Wishbone arm using Finite Element Analysi...IRJET Journal
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The document discusses forward and inverse kinematics for humanoid robots. It presents an analytical solution to the forward and inverse kinematics problems for the Aldebaran NAO humanoid robot. The solution decomposes the robot into five independent kinematic chains (head, two arms, two legs). It uses the Denavit-Hartenberg method and solves a non-linear system of equations to find exact closed-form solutions. The implemented kinematics library allows real-time transformations between joint configurations and physical positions, enabling motions like balancing and tracking a moving ball.
The Effect of Arm Stiffness on the Elasto-Kinematic Properties of Single-Axle...theijes
The paper is focused on the stiffness analysis of the longitudinal arm of single-axle suspension on elastokinematic behaviour of the vehicle axle which is highly important when considering the handling characteristics related tovehicle safety.The elasto-kinematic behaviour of the axle determines the course of the geometrical parameters of wheel suspension, the toe angle and camber as the function of wheel movement during force loading. This paper presents the complex MBS (Multi-Body Simulation)model of the wheel suspension with nonlinear characteristics of rubber-metal bushings. The model also comprises force elements such as springs, shock absorbers, stops and the transverse stabilizer. The model of flexible arm is implemented in the MBS model using the Craig-Bampton method, which represents a flexible body based on the synthesis of its own modal shapes. Subsequently,elasto-kinematic simulations are performed with the help ofthe computational system Hyperwork. The computational part of the paper presents the results of the elasto-kinematic behaviour of wheel axle for the flexible arm with different sheet metal thicknesses (2, 3 and 4 mm) and different materials (steel and aluminium alloy AlSi7Mg). Individual calculation models are compared to each other and also to the model of suspension with therigidarm. Elasto-kinematic analyses are also validated by the measurement inthe testing stage.
Intelligent swarm algorithms for optimizing nonlinear sliding mode controller...IJECEIAES
This document describes research into using intelligent swarm algorithms to optimize the parameters of a nonlinear sliding mode controller for a robot manipulator. Specifically, particle swarm optimization and social spider optimization were used to determine optimal values for the parameters of an integral sliding mode controller designed to control a 6 degree-of-freedom PUMA robot manipulator. Simulation results showed that social spider optimization achieved the best fitness value and performance in minimizing error for the robot controller parameters.
Impact analysis of actuator torque degradation on the IRB 120 robot performan...IJECEIAES
Actuators in a robot system may become faulty during their life cycle. Locked joints, free-moving joints, and the loss of actuator torque are common faulty types of robot joints where the actuators fail. Locked and free-moving joint issues are addressed by many published articles, whereas the actuator torque loss still opens attractive investigation challenges. The objectives of this study are to classify the loss of robot actuator torque, named actuator torque degradation, into three different cases: Boundary degradation of torque, boundary degradation of torque rate, and proportional degradation of torque, and to analyze their impact on the performance of a typical 6-DOF robot (i.e., the IRB 120 robot). Typically, controllers of robots are not pre-designed specifically for anticipating these faults. To isolate and focus on the impact of only actuator torque degradation faults, all robot parameters are assumed to be known precisely, and a popular closed-loop controller is used to investigate the robot’s responses under these faults. By exploiting MATLAB-the reliable simulation environment, a simscape-based quasi-physical model of the robot is built and utilized instead of an actual expensive prototype. The simulation results indicate that the robot responses cannot follow the desired path properly in most fault cases.
IRJET- Design and Fabrication of PLC and SCADA based Robotic Arm for Material...IRJET Journal
This document describes the design and fabrication of a PLC and SCADA-controlled robotic arm for material handling. The robotic arm uses pneumatic cylinders connected by joints to move along three axes (X, Y, and Z). A mechanical gripper is attached to the end of the arm to grip objects on a conveyor belt. The movements of the pneumatic cylinders and gripper are controlled by a PLC based on sensor inputs from the conveyor belt. The PLC and robotic arm are integrated with a SCADA system for centralized control and monitoring. The robotic arm is intended to automate repetitive picking and placing tasks to reduce labor costs compared to manual operations.
Effect of Rack Friction, Column Friction and Vehicle Speed on Electric Power ...IRJET Journal
This document describes a study on the effect of rack friction, column friction, and vehicle speed on the electric power steering (EPS) system of a vehicle. A complete wheel-to-wheel steering model is developed in Amesim simulation software, including all associated components. With the validated model, the variation of total torque required at the pinion gear is plotted at different vehicle speeds from 0 to 160 kmph. The friction torque at the column, steering rack, and motor is also plotted to understand how it changes over time for a given steering angle input and vehicle speed. The results are analyzed to develop an understanding of how the components in the steering system interact so that the necessary power can be requested from the system without compromising
Dynamics and control of a robotic arm having four linksAmin A. Mohammed
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Path tracking control of differential drive mobile robot based on chaotic-bi...IJECEIAES
This summary provides the key details about the document in 3 sentences:
The document presents a new chaotic-billiards optimizer (C-BO) algorithm to optimize the parameters of a controller for a differential-drive mobile robot. The C-BO algorithm is used to tune the controller parameters to improve path tracking performance. Simulation results show that the C-BO algorithm achieves better path tracking accuracy compared to an ant colony optimization algorithm, with a steady state error of 0.6% versus 0.8%.
IRJET- Review on Hyper Maneuverable Multi-Functional RobotIRJET Journal
This document reviews research on a proposed hyper maneuverable multi-functional robot. It would use mecanum wheels for omni-directional movement and a jointed robotic arm for multiple functions. The arm would be controlled in real-time using sensors on the human arm to detect gestures and movements. The document provides background on mecanum wheels, reviews previous research on related topics, and proposes using accelerometers, gyroscopes and hall-effect sensors on the human arm to control the robot arm.
Assessment of Robotic Arm and it’s ParametersIRJET Journal
This document provides an overview of robotic arm parameters and applications. It examines features such as the number of axes, degrees of freedom, kinematics, payload, speed and acceleration. Robotic arms are used widely in industrial, commercial and residential settings. While research has enhanced parameters like degrees of freedom and kinematics, gaps still remain around expanding working envelopes and increasing payloads. The document surveys literature on robotic arm studies and identifies opportunities to optimize arms through additional research.
DESIGN AND ANALYSIS OF DOUBLE WISHBONE SUSPENSION SYSTEM USING FINITE ELEMENT...ijsrd.com
Double wishbone designs allow the engineer to carefully control the motion of the wheel throughout suspension travel. 3-D model of the Lower Wishbone Arm is prepared by using CAD software for modal and stress analysis. The forces and moments are used as the boundary conditions for finite element model of the wishbone arm. By using these boundary conditions static analysis is carried out. Then making the load as a function of time; quasi-static analysis of the wishbone arm is carried out. A finite element based optimization is used to optimize the design of lower wishbone arm. Topology optimization and material optimization techniques are used to optimize lower wishbone arm design.
Analysis of Cabin Mounting Bracket of Truck Using ANSYSinventionjournals
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Study and Analysis of Design Optimization and Synthesis of Robotic ARM
1. International Journal of Advanced Engineering, Management and Science (IJAEMS) [Vol-2, Issue-5, May- 2016]
Infogain Publication (Infogainpublication.com) ISSN: 2454-1311
www.ijaems.com Page | 453
Study and Analysis of Design Optimization and
Synthesis of Robotic ARM
Bhupender1
, Rahul2
1
Department of ME, CBS Group of Institution, Jhajjar, Haryana, India
2
Assistant Professor, Department of ME, CBS Group of Institution, Jhajjar, Haryana, India
Abstract— A robot is a mechanical or virtual artificial
agent, usually an electro-mechanical machine that is
guided by a computer program or electronic circuitry.
Robots can be autonomous or semi-autonomous. In this
thesis, design optimization strategies and synthesis for
robotic arm are studied. In the design process, novel
optimization methods have been developed to reduce the
mass of the whole robotic arm. The optimization of the
robotic arm is conducted at three different levels, with the
main objective to minimize the robot mass.
At the first level, only the drive-train of the robotic arm is
optimized. The design process of a robotic arm is
decomposed into selection of components for the drive-
train to reduce the weight
At the second level, kinematic data is combined with the
drive-train in the optimization. For this purpose, a
dynamic model of the robot is required. Constraints are
formulated on the motors, gearboxes and kinematic
performance
At the third level, a systematic optimization approach is
developed, which contains design variables of structural
dimensions, geometric dimensions and drive-train
composes.
Constraints are formulated on the stiffness and
deformation. The stiffness and deformation of the arm
are calculated through FEA simulation.
The main objective of the thesis is to design optimization
and synthesis analysis of robotic arm. The corresponding
deflections, stresses and strains for that load will be find
out by suing the method of finite element analysis.
Keywords— robotic arm, inverse kinematics, dynamics,
Jacobian method, motor selection and drive train
optimization.
I. INTRODUCTION
A robotic arm is a type of mechanical arm, usually
programmable, with similar functions to the human arm;
the arm may be the sum total of the mechanism or may be
part of a more complex robot. The links of such a
manipulator are connected by joints allowing either
rotational motion (such as in an articulated robot) or
translated (linear) displacement. The links of the
manipulator can be considered to form a kinematic chain
of the manipulator is called the end effectors and it is
analogous to the human hand.
In this section, I look at some basic arm geometries. As I
said before, a robot arm or manipulator is composed of a
set of joints, links, grippers and base part. The joints are
where the motion in the arms occurs, while the links are
of fixed construction. Thus the links maintain a fixed
relationship between the joints. The joints may be
actuated by motors or hydraulic actuators.
II. ROBOT OPTIMIZATION AND SYNTHESIS
• DRIVE TRAIN OPTIMIZATION
A general method of motor and gearbox selection and
optimization of servo drive system was introduced. The
method automated the solution procedure for the servo
drive design problem by virtue of the normalization of
torques, velocities, and transmission ratios. Moreover,
and selection criteria separated the motor characteristics
from the load characteristics and its graphical
representation facilitated the feasibility check of a certain
drive and the comparison between different systems.
These methods above are applicable to the design of a
single joint combining a motor and a gearbox, and they
do not address the discrete nature of the selection process.
For design of robotic drive train consisting of multiple
joints, the challenge is that not only the characteristics of
motor and gearbox at a single joint, but also the dynamics
of the robot should be taken into account. An early
attempt on drive-train design optimization can be found in
which Chasmal and Gautier proposed a method for the
optimum selection of robot actuators of minimize the total
mass of all actuators. The modeling of the system took
into account the inertia of the links and actuators, viscous
and Coulomb friction effects, and the thermal model of
the actuators as well.
• Dimensional Optimization
Dimensional optimization can contribute to the
improvement of robotic performance, either kinematic
performance or dynamic one. An integrated structure-
control design optimization method of a two-link flexible
robot arm was presented, where the structural and control
2. International Journal of Advanced Engineering, Management and Science (IJAEMS) [Vol-2, Issue-5, May- 2016]
Infogain Publication (Infogainpublication.com) ISSN: 2454-1311
www.ijaems.com Page | 454
parameters were optimized simultaneously. The method
used a genetic algorithm and the performance was
compared with that of an arm with uniform links and an
optimized control system. The simultaneous optimization
yielded a design with higher bandwidth and less weight of
the arm system. An optimal design of manipulator
parameter using an evolutionary optimization method was
proposed in which a modification in differential evolution
optimization technique was proposed to incorporate the
effect of noises in the optimization process and obtain the
optimal design of a manipulator. An optimum robot
design method based on a specified task was proposed in
which dimensions were optimized based on dynamic
analysis. Three evolutionary techniques were applied to
minimize the torque required to perform the defined
motion subject to constraints on link parameters and the
end-effectors deflection.
• Structural optimization
Single arm robot design of structural parts may lead to a
significant reduction in the weight of the robot. Regarding
structural optimization, finite element analysis (FEA) is
widely used. FEA was utilized to conduct structural
topology optimization in the design of humanoid robots.
Multimode system simulation (MBS) was employed to
investigate the dynamics of the robot. By integrating
MBS simulation into structural optimization processes,
components in mechatronic systems could be optimized
regarding the interaction between parts of mechanical
properties and the overall system dynamics. FEA based
design optimization was conducted on a 2-dof robot to
minimize the vibration frequency. The optimized design
was compared with an experimental investigation of the
structure vibration frequencies design obtained on the
actual manipulator. The utilization of FEA in robotic arm
design and structural optimization can be found.
The above robotic optimization technologies are
summarized in Table 1.1.
N
o.
Objectiv
e
Design
Variabl
es
Constrai
nts
Optimizat
ion
algorithm
1 Total
mass
Motor
mass
Minimize
motor
torques
KTNC
2 Mass,
cost
Motor
torques
Motor,
joint
dynamics
Complex
3 Control
performa
nce
Controll
er, drive
train
Dynamic
s
Pattern
search,
GA
4 Dynamic
s
Motor
selectio
Motor
torques
---
-
performa
nce
n
5 Control
performa
nce
Structur
al
dimensi
ons
Control
GA
6 Kinemati
cs and
dynamic
performa
nce
Geometr
ic
dimensi
on, link
mass
Boundar
y limits GA
7 Joint
torques
Structur
al
dimensi
ons
Stiffness,
deflectio
n
GA
1 Kuhn-Tucker Necessary Conditions
2 Genetic Algorithm
• Design considerations
The robotic arm is an anthropomorphic arm as it follows the
nature design of a human arm. A human arm consists of
seven dof, three at the shoulder, two at the elbow, and two
at the wrist. The concept design of the robotic arm
includes 5 dof, which reduces one dof in the shoulder and
one in the elbow. When the concept design has been
determined the physical properties from the design can be
used to recalculate motions and torques. These can then
again be used to redesign the first concept to a new and
better one. This iteration process would be efficient to put
inside an optimization procedure, where motors,
gearboxes and structural design would be optimization
factors.
The robotic arm will be used to handle daily tasks of
people assistance applications. The total reach distance is
1 m (without the gripper), which is a bit longer than a
human arm. The workspace of each joint is based on the
corresponding joint workspace of the human arm.
Table: Joint workspace of the robotic arm
Joint i Max Workspace Constrained Workspace
1 0 ∼ 2π 0 ∼ π
2 0 ∼ 3π/2 0 ∼ 3π/2
3 0 ∼ 3π/2 0 ∼ 3π/4
4 0 ∼ 2π 0 ∼ 2π
5 0 ∼ 3π/2 0 ∼ 3π/4
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Kinematics
Robot kinematics is the study of the motions (kinematics) of
robots. In a kinematic analysis the position, velocity and
acceleration of all the links are calculated without considering
the forces that cause this motion.
Robot kinematics deals with aspect of redundancy,
collision avoidance and singularity avoidance. While
dealing with the kinematics used in the robot we deal
each parts of the robot by assigning a frame of reference
to it and hence a robot with many parts may have any
individual frames assigned to each movable parts. For
simplicity we deal with single manipulator arm or the
robot. Each frames are named systematically with
numbers, for example the immovable base part of the
manipulator is numbered 0, and the first link joined to the
base is numbered 1, and the next ink 2 and similarly till n
for the last nth link.
In the kinematic analysis of manipulator position, there
are two separate problems solve: direct kinematics, and
the inverse
kinematics. Direct kinematics involves solving the
forward transformation equation to find the location of
the hand in terms of the angles and displacements
between the links. Inverse kinematics involves solving
the inverse transformation equation to the find the
relationships between the links of the manipulator from
the location of the hand in space.
III. BASIC MANIPULATOR GEOMETRIES
In this types of the arm, mechanics of a manipulator can
be represented as a kinematic chain of rigid bodies (links)
connected by revolute or prismatic joints. One end of the
chain is constrained to a base, while an end effector is
mounted to the other end of the chain.
Fig.1:Shows an open chain serial robot arm
Open chain manipulator kinematics
In the open chain robot arm, The resulting motion is
obtained by composition of the elementary motions of
each link with respect to the previous one. The joints
must be controlled individually
Closed Chain Manipulator Kinematics
Closed Chain Manipulator is much more difficult than
open chain manipulator. Even analysis has to take into
account statics, constraints from other links, etc. Parallel
robot is a closed chain. For this type of robots, the best
example is the Stewart platform. Figure-3.2 shows
Stewart platform.
Fig.2:Stewart platform
Homogenous Transformation
Homogeneous transformation is used to calculate the new
coordinate values for a robot part. Transformation matrix
must be in square form. Figure-5.4 shows the
transformation matrix.
Fig.3:Homogeneous Transformation matrix.
3x3 rotation matrix may change with respect to rotation
value. 3x1 translation matrix shows the changing value
between the coordinate systems. Global scale value is fix
and Also 1x3 perspective matrix is fix.
Inverse Kinematics (IK)
Inverse kinematics is the opposite of forward kinematics.
This is when you have a
desired end effector position, but need to know the joint
angles required to achieve it. The inverse position
kinematics (IPK) solves the following problem:"Given
the actual end effector pose, what are the corresponding
joint positions?" In contrast to the forward problem, the
solution of the inverse problem is not always unique: the
same end effector pose can be reached in several
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configurations, corresponding to distinct joint position
vectors. Although way more useful than forward
kinematics, this calculation is much more complicated
too.
Fig.4:Inverse kinematics
The problems in IK :
There may be multiple solutions,
For some situations, no solutions,
Redundancy problem.
Solving The Inverse Kinematics
Although way more useful than forward kinematics, this
calculation is much more complicated. There are several
methods to solve the inverse kinematics.
Cos(a)= (Cosine Law.)
using the cosine law angles are found
Cos( ) =
=
cos ( )
Cos( ) =
cos ( ) +
Cos(180 ) =
% &
= 180-cos ( )
Inverse Jacobian Method
It is used when linkage is complicated. Iteratively the
joint angles change to approach the goal position and
orientation.
Jacobian is the n by m matrix relating differential changes
of q to differential changes of P(dP).
Jacobian maps velocities in joint space to velocities in
cartesian space
J( ) (=V
f( () = )
J( )* = *)
+,-=
./0
.10
An example of Jacobian Matrix,
2
3
45 = 6
7 (1)
7 (1)
8 = 9
: ;<= + : ;<= + :> ;<= >
: ?@A − : ?@A + :>?@A >
C
9
3(
4(
C = JD
(
(
>
(
E
J =
D
./ (1)
.1
./ (1)
.1
./ (1)
.1F
./ (1)
.1
./ (1)
.1
./ (1)
.1F
E=
9
−: ?@A −: ?@A −:>?@A >
−: ;<= −: ;<= −:>;<= >
C
f
1
(P), V J( ) ( , J
1
( )V
In the Jacobian method, the solving can be linearizable
about G locally using small increments
Dynamics
Dynamics deals with the forces and torques that cause the
motion of a system of bodies. Analogously to direct and
inverse kinematics analysis, there is direct and inverse
dynamic analysis.
Jacobian matrix
The joint angular velocity can be calculated with the
Jacobian matrix.
( = + HI/
Where (= [ ( , ( , … … . . (M] denotes an n-dimensional (n
denotes the number of dof) vector of the joint angular
velocities, J is the Jacobian of the robotic arm, and HI/the
velocity of the end-effectors.
+( = O+( , +( , … … +(MP +, = QR, ), ]
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R, = S, Q0 0 1] , ), = S, T, + U,
Inverse dynamics
The computation of the inverse dynamics is a prerequisite
for evaluating any given design with given load and
prescribed trajectory. Here we briefly recall the Lagrange-
Euler formulation. The Lagrange equation is
V
VW
X
.
.10
Y −
.
.10
= Z,; @ = 1, … . . A (5.25)
Where the Langraingian L= K-U= ∑ (],
M
, ^,). For
the ith link the K.E and P.E is given by
], _,H`,,, H`,, + a, b,a, ^, = _,c U`,, (5.26)
M( ) d + V( , )( + e( ) = Z
M = ∑ (+f,,
M
, _,+f,, + +g,,b,+g,,) (5.28)
Where +f,, and +g,, are 3*n matrices. For revolute joints
the Jth coloumn vectors of +f,, and +g,, can be easily
calculated.
+f,,
-
= R- ∗ )`.,
-
, +g,,
-
= R- 7<i j ≤ @
+f,,
-
= +g,,
-
= Q0 0 0] 7<i @ < j ≤ A
_, _m,, + _n,, + _o,,
IV. FORMULATION OF DESIGN PROBLEM
For formulating the design problem let we consider a
drive train model for the single joint and for the harmonic
drive gearbox, the gear efficiency varies depending on the
output torque. With the inertia of motor and gear, the
required motor torque for the ith joint is derived as
Fig.5: Schematic view of drive train model for a single
joint.
Zn,, = Qp+n + +oq (r)d s +
t(W)
uvo
], ; i=1,….5
where i is the gear ratio
Jg is the gear inertia with respect to the input motor axis
Jm is the motor inertia
g is the gear efficiency
4.1 Motor Selecting Criteria
The criteria for selecting motor and gearbox are
applicable to each single joint, Motor selection criteria
Motors for robotic arms are usually selected from two
motor groups, brushed and brushless DC motors. In
selecting motors, the following three constraints must not
be violated:
• Nominal torque limit. The nominal torque is
the so-called maximum continuous torque. The
root mean square (RMS) value Zwnmof the
required motor torque xnhas to be smaller than
or equal to the nominal torque of the motor Tm
Zwnm ≤ xn
Where Zwnm = y
VW
z Zn
∆W
|
*r with ∆r being the
duration of characterstics of working cycle.
• Stall torque limit. The stall torque is the peak
torque of the motor. The required peak torque
Z} has to be smaller than or equal to the stall
torque Zn
n~•
of the motor
€• ≤ €‚
‚ƒ„
Where Z} = _…3|xn|
• Maximum permissible speed limit. The
maximum permissible speed for DC motors is
primarily limited by the commutation system. A
further reason for limiting the speed is the
rotor’s residual mechanical imbalance which
shortens the service life of the bearings. The
required peak speed A} corresponding to the
motor has to be smaller than or equal to the
maximum permissible speed ‡n
n~•
of the motor
A} ≤ ‡n
n~•
Where A} = max {Œ2Ž (r). s( Œ}
The inequalities (6.1) to (6.3) represent the constraints
that must be fulfilled by any motor in the drive train.
4.2 Gearbox selection criteria
In the selection of gearboxes, the following three
constraints are considered:
• Rated output torque limit. It is recommended
by the Harmonic Drive gearbox manufacturer
to use the RMC value for calculating rated
torque. The RMC value is a measure of the
accumulated fatigue on a structural component
and reflects typical endurance curves of steel
and aluminium. It is therefore relevant to
gearbox lifetime, and this criterion has also
been used in robotic applications. With this
criterion, a constraint is derived
ım
J
Link
q
Motor ı(t)
8 8
. ..
mg Jg 4g
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as
Zwnm ≤ xo (6.4)
Where Zwnm = y
VW
z Z>∆W
|
*r
F
with Z(t) being the
required torque from the gearbox output. xo is the limit
for rated torque of the gearbox.
• Maximum output torque limit. The required
peak torque Zo with respect to the output side
has to be smaller than or equal to the allowable
peak torque xo
n~•
of the harmonic drive
Zo ≤ xo
n~•
(6.5)
Where Zo = _…3{|Z(r)|}
• Maximum permissible input speed limit. The
required maximum input peak speed A,M has to
be smaller than or equal to the maximum
permissible input speed ‡o
n~•
of a gearbox
A,M ≤ ‡o
n~•
(6.6)
Where A,M = max {| (r). s|}
4.3 Objective function formulation
The objective of the optimization is to minimize the mass
of the robotic arm. In this formulation, we minimize only
the mass of the power transmission, while the mass of the
arm structures remains constant. Therefore, the
optimization task is to find the lightest combination of
motor and gearbox for all five dof that fulfill all
constraints associated with the motors and gearboxes. The
objective function, f(x), is defined as the sum of the mass
of the motors and gears, as shown in the above Equation
_@A
•
f(X)= z {_M(‘n
’
,
) + _o(‘o)}, (6.7)
• = Q‘n, ‘o}
subject to
xn,, ≥ ”
∆W
{X+n (•) + +o (•)Y (r)s +
t(W,•)
uM•
d
} . *r
xn,,
n~•
≥ {–(+n(•) + +o + (•)) (r)s +
t(W,•)
uM•
d
–}, (6.9)
‡n,,
n~•
≥ max {Œ2Ž ((r). sŒ}, (6.10)
xo,, ≥ y
∆W
z Z,F
∆W
|
(r, 3)*r
F
xo,,
n~•
≥ max {| Z(r, 3)*r |},
‡o,,
n~•
≥ max {Œ ((r). s Œ},
where design variables in x includes the index numbers of
motors ‘n = Q‘n , … … . . ‘n ] and gearboxes ‘o =
Q‘o , … … ‘o ]relative to databases containing
commercially available components. So far, we have
formulated the design problem as a discrete optimization
problem, which can be solved by commercial available
codes. We select a non-gradient method called Complex
for this purpose. The implementation is outlined in the
next section.
4.Procedure of optimization
The optimization method is developed as a Matlab and
MSC.ADAMS co-simulation
platform. The optimization algorithm is based on the
Complex method, which is briefly discussed.
• Optimization by Complex
The Complex method is a non-gradient based
optimization method, first presented by Box. In the
Complex method, several possible designs (design
population) are manipulated. The method is based on a
feasible domain, containing a design population as a set
of design points. The number of design points has to be
greater than the number of independent design variables.
The starting design points (initial population) are
randomly generated, and evaluated through the objective
function to check performance and constraint violation.
Among all populations, the set of design variables having
the minimal objective function is denoted as the best
point xb, while the one having the maximal objective
function is denoted as the worst point xw. Their
corresponding values of objective function are noted as
the best and worst values. The centroid point is calculated
as
•` =
n
∑ •,
n
, , •, ≠ •˜
•, = Q3 , 3 , … … . 3M]
The main idea of the Complex method is to replace the
worst point by a new and better point. The new point is
found by the reflection of the worst point through the
centroid with a reflection coefficient, yielding the
following expression for the new design point
•`~MV = •` + (•` − •™)
The coefficient _ = 1:3 is used in this study, as
recommended . The candidate point •` and is checked
through explicit and implicit constraints. When it
conforms to the constraints, •` and replaces •™. This
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method cannot handle the situation when the centroid is
trapped in a local minimum. Therefore, the method has
been modified such that the point moves toward the best
point if it continues to be the worst one. To avoid the
collapse of the algorithm, a random value is also added to
the new point. The modified method to calculate the
reflection point is given as
•`~MV
MI™
= (•`~MV
š›V
+∈ •` + (1−∈)•˜+(•` − •˜) (1−∈
)(2• −1)
where k is a random number varying in the interval [0; 1],
with
∈= (
Mž
Mž Gž
)
Ÿž ž¡
Ÿž
Here kr is the number of times the same point has
repeatedly been identified as the worst point, and nr is a
tuning parameter which is set to 4. The convergence
criterion of the Complex method in this work is the
difference between the best and worst objective function
values is less than a user defined tolerance.
• Dynamics model with MSC.ADAMS
The drive requirements of the whole robotic arm system
are determined from inverse kinematic and dynamic
analysis within MSC.ADAMS. The inverse kinematic and
dynamic analysis is developed as a simulation package,
which will be called by the optimization program. To this
end, the mass of motors and gearboxes are parameterized,
while the trajectory of the robotic arm is prescribed.
For each variation of motors and gearboxes, the required
motor torques are accurately calculated. The mass of
distribution is updated during the optimization procedure.
The inverse kinematic and dynamic analysis of the
robotic arm in ADAMS follows a so-called master-slave
approach. The basic concept of this approach is that we
make two models of the robotic arm in ADAMS, a master
model and a slave one. In the master model, the inverse
kinematic analysis is executed to record the joint motions
corresponding to the prescribed end-effector trajectory. In
the slave model, the joint motion data is imported and
imposed on the joints, and payload is also attached to the
end-effector. Then the inverse dynamic calculation is
performed to solve the required joint torques for actuating
the robotic arm.
Fig.6: The procedure of inverse kinematic and dynamic
analysis
In the master-slave approach, we can define different
trajectories and payloads for the robotic arm model,
which makes the model more flexible for different
simulation conditions. This approach can be applicable to
other serial and parallel robot systems.
• Matlab-ADAMSco-simulation platform
The design optimization is mainly concerned of two
tasks: the optimization routine and creation of a
parametric dynamic simulation model. Both tasks can be
performed on a Matlab-ADAMS co-simulation platform
developed in this work. As shown in Fig. 3.6, the
platform works with two modules. The ADAMS module
is used to simulate the inverse kinematics and dynamics
of the robotic arm. The Matlab module implements the
Complex method to call the ADAMS simulation in batch
mode.
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Fig.7:Diagram of the optimization routine in the co-
simulation platform
V. CONCLUSION
The main scope of this work is the development of a
novel optimization approach for the design of robotic
arms. A new optimization approach was developed for
robot optimization to handle selection of motors and
gearboxes, geometric and structural dimensions. This was
achieved through stepwise optimization in three levels,
starting from the constraints of motors and gearboxes,
then the constraints of kinematic performance, and finally
structural strength constraints.
Fig.7: Different fields of technology involved in the
architecture of robotic arms.
Scope of work
The aim of this project is to design robotic arm. The
works involved in the thesis are summarized in above
Figure.
To reduce the weight of the robotic arm, optimization
method will be developed in the design process. The
approachoftheprojectissummarized inthefollowingsteps:
Study basic kinematics and dynamics of robotic arms.
Model and design a 5-dof robotic arm.
1. Optimize the robotic arm to reduce the weight.
2. Optimize the drive-train components (motors
and gearboxes).
3. Optimize the link lengths together with the
drive-train.
4. Optimize the structural dimensions, link lengths
and the drive-train.
VI. CONTRIBUTIONS
Within this project, the following contributions to the
design and optimization
of robotic arms were made
New robotic optimization methods were
developed. It is the first time to integrate the
drive-train, kinematics and structural dimensions
together in the optimization design of robots for
minimal mass.
Three extensible simulation platforms for robot
simulation were developed. The platforms
integrate numeric programming software with
commercial dynamic simulation and FEA
simulation software. The platforms could be
easily expanded to contain more design variables
on different robotic parameters and the
corresponding constraints.
A prototype of the 5-dof robotic arm was built to
validate the optimization approaches. The
prototype can be used to validate the different
simulation models developed within the project.
VII. FUTURE WORK
The optimization approach in this thesis focused on the
mechatronic part of the robotic arm. Robot control is a
key competence for robot manufacturers and is very
important in order to getas much performance as possible
out of a robot. Tuning of control parameters is also crucial
for a robotic arm.
One possible direction of the future work is to combine
the mechanical system design together with the control
system design in the whole system optimization. Control
parameters could be taken as design variables in the
optimization.
Involved in
Kinematics
Robotic theory
Dynamics
Structural
design
Motor
Drive train
Gear transmission
Trajectory
planning
Control system
Robotic
Arm
Sensor
Control theory
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