This document analyzes the motion of a two-link robotic arm manipulator using MATLAB. It develops linearized equations of motion and proportional controllers for each joint to simulate the robot's movement from an initial to final position. Graphs are generated to compare the desired and actual motion paths, velocities, accelerations, and positions over time. The results show larger errors in the actual path as the end effector moves farther from the linearized region around the initial position. Replacing the proportional controller with a PID controller is suggested to improve precision.
The document discusses optimization of tool path for robots in an assembly environment. It aims to develop new algorithms and techniques to optimize the tool path for increased productivity and efficiency with lower energy costs. This includes formulating the tool path optimization problem as a traveling salesman problem (TSP) and developing insertion and reordering algorithms to find optimal non-intersecting paths between target points visited by the robot tool. The document also covers inverse kinematics techniques to determine robot joint parameters required to reach specified target points.
Research Inventy : International Journal of Engineering and Scienceinventy
The document presents an adaptive tracking control method for a welding mobile manipulator. The mobile manipulator consists of a three-linked planar manipulator mounted on a two-wheeled mobile platform. Controllers are designed using Lyapunov stability analysis to guarantee the end-effector tracks a desired welding trajectory despite unknown dimensional parameters of the manipulator. Simulation and experimental results demonstrate the effectiveness of the proposed adaptive controllers.
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.
The document discusses forward kinematics, which is finding the position and orientation of the end effector given the joint angles of a robot. It covers different types of robot joints and configurations. It introduces the Denavit-Hartenberg coordinate system for defining the relationship between successive links of a robot. The document also discusses forward kinematic calculations, inverse kinematics, robot workspaces, and trajectory planning.
Force isotropy of three limb spatial parallel manipulatorIAEME Publication
This document summarizes a research paper that analyzes the force isotropy of a three-limb spatial parallel manipulator with two identical limbs. The researchers identify nearly isotropic configurations using the condition number concept, which quantifies how well-conditioned the manipulator is to minimize errors in force from input torques. A MATLAB code is developed to analyze the manipulator's Jacobian matrix at different configurations and identify where the condition number is closest to one, indicating maximum force isotropy and error minimization. The manipulator's inverse kinematics are also analyzed to relate its joint variables to the end effector pose.
This document provides an overview of the key topics that will be covered in a Control Systems course, including:
1) Definitions of open-loop and closed-loop systems and how they differ.
2) Modeling of mechanical systems using Newton's laws and differential equations.
3) Analysis of systems using transfer functions, block diagrams, and signal flow graphs.
4) Time response analysis including steady state errors and classification of systems.
5) Stability analysis using the s-domain and tools like Routh's criterion and frequency response.
6) State space representation including state variables, state space, controllability, and observability.
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 describes genetic algorithm experiments with the Traveling Salesman Problem. It implemented different representations, selection methods, crossover operators, and mutation operators in MATLAB. Key results include:
1. Path and adjacency representations had similar solution quality and speed, with adjacency slightly faster.
2. K-tournament selection with continuous K values performed well, allowing adjustment of selection pressure. It was used in subsequent experiments.
3. Order crossover and sequential constructive crossover had strong performance. Heuristic edge recombination crossover also did well. Simple inversion mutation worked best.
4. Automating experiments in MATLAB and processing results with Perl scripts enabled efficient evaluation of many parameter combinations. This revealed best performing operators.
The document discusses optimization of tool path for robots in an assembly environment. It aims to develop new algorithms and techniques to optimize the tool path for increased productivity and efficiency with lower energy costs. This includes formulating the tool path optimization problem as a traveling salesman problem (TSP) and developing insertion and reordering algorithms to find optimal non-intersecting paths between target points visited by the robot tool. The document also covers inverse kinematics techniques to determine robot joint parameters required to reach specified target points.
Research Inventy : International Journal of Engineering and Scienceinventy
The document presents an adaptive tracking control method for a welding mobile manipulator. The mobile manipulator consists of a three-linked planar manipulator mounted on a two-wheeled mobile platform. Controllers are designed using Lyapunov stability analysis to guarantee the end-effector tracks a desired welding trajectory despite unknown dimensional parameters of the manipulator. Simulation and experimental results demonstrate the effectiveness of the proposed adaptive controllers.
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.
The document discusses forward kinematics, which is finding the position and orientation of the end effector given the joint angles of a robot. It covers different types of robot joints and configurations. It introduces the Denavit-Hartenberg coordinate system for defining the relationship between successive links of a robot. The document also discusses forward kinematic calculations, inverse kinematics, robot workspaces, and trajectory planning.
Force isotropy of three limb spatial parallel manipulatorIAEME Publication
This document summarizes a research paper that analyzes the force isotropy of a three-limb spatial parallel manipulator with two identical limbs. The researchers identify nearly isotropic configurations using the condition number concept, which quantifies how well-conditioned the manipulator is to minimize errors in force from input torques. A MATLAB code is developed to analyze the manipulator's Jacobian matrix at different configurations and identify where the condition number is closest to one, indicating maximum force isotropy and error minimization. The manipulator's inverse kinematics are also analyzed to relate its joint variables to the end effector pose.
This document provides an overview of the key topics that will be covered in a Control Systems course, including:
1) Definitions of open-loop and closed-loop systems and how they differ.
2) Modeling of mechanical systems using Newton's laws and differential equations.
3) Analysis of systems using transfer functions, block diagrams, and signal flow graphs.
4) Time response analysis including steady state errors and classification of systems.
5) Stability analysis using the s-domain and tools like Routh's criterion and frequency response.
6) State space representation including state variables, state space, controllability, and observability.
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 describes genetic algorithm experiments with the Traveling Salesman Problem. It implemented different representations, selection methods, crossover operators, and mutation operators in MATLAB. Key results include:
1. Path and adjacency representations had similar solution quality and speed, with adjacency slightly faster.
2. K-tournament selection with continuous K values performed well, allowing adjustment of selection pressure. It was used in subsequent experiments.
3. Order crossover and sequential constructive crossover had strong performance. Heuristic edge recombination crossover also did well. Simple inversion mutation worked best.
4. Automating experiments in MATLAB and processing results with Perl scripts enabled efficient evaluation of many parameter combinations. This revealed best performing operators.
4 solar refrigeration and elecricity generationMd Irfan Ansari
This document discusses refrigeration and solar energy conversion systems. It describes vapor compression and solar vapor absorption refrigeration cycles. It explains how photovoltaic cells work by converting solar radiation into electricity via the photoelectric effect. Key components of PV systems like solar panels, batteries, and inverters are outlined. Advantages and limitations of solar energy conversion are also summarized. Solar lanterns are provided as a simple application of solar PV technology for rural lighting needs.
This document discusses robot kinematics and position analysis. It covers forward and inverse kinematics, including determining the position of a robot's hand given joint variables or calculating joint variables for a desired hand position. Different coordinate systems for representing robot positions are described, including Cartesian, cylindrical and spherical coordinates. The Denavit-Hartenberg representation for modeling robot kinematics is introduced, allowing the modeling of any robot configuration using transformation matrices.
1. The document describes a 2 link planar manipulator with 2 rotational joints and specifies the link lengths and coordinate frames.
2. It covers the forward kinematics to find the endpoint using homogeneous transformations by composing individual coordinate transforms between frames.
3. As an example, it shows the coordinate transforms between Frame 0 to Frame 1 which is a rotation of 30 degrees and translation of (1,1) and between Frame 1 to Frame 2 which is a rotation of 60 degrees and translation of (1/2,√3/2).
Solar refrigeration uses solar energy to power refrigeration systems for food and medicine preservation and comfort cooling. There are three main types of solar refrigeration: photovoltaic operated vapor compression, solar mechanical vapor compression using a Rankine cycle, and absorption refrigeration. Absorption refrigeration replaces the compressor with a thermal compression system using ammonia as the working fluid and a generator powered by solar collectors to desorb the ammonia, providing refrigeration without large mechanical energy inputs. While solar refrigeration has benefits of being environmentally friendly and not relying on power grids, its high initial costs and low coefficient of performance currently limit widespread adoption.
The document discusses robot kinematics and control. It covers topics like coordinate frames, homogeneous transformations, forward and inverse kinematics, joint space trajectories, and cubic polynomial path planning. Specifically:
1) Kinematics is the study of robot motion without regard to forces or moments. It describes the spatial configuration using coordinate frames and homogeneous transformations.
2) Forward kinematics determines end effector position from joint angles. Inverse kinematics determines joint angles for a desired end effector position.
3) Joint space trajectories plan motion by describing joint angle profiles over time using functions like cubic polynomials and splines.
4) Cubic polynomials satisfy constraints like initial/final position and velocity to generate smooth motion profiles for a single revol
1) The document discusses the fundamentals of robotic manipulators, including their classification, parts, motions, and work envelopes.
2) The major types of robot configurations are Cartesian, cylindrical, spherical, SCARA, and articulated, which are defined by their joint types and resulting work spaces.
3) Robotic manipulators consist of links connected by joints and powered by electric, hydraulic, or pneumatic drives to position an end effector through programmed motions.
Robotic Arm using flex sensor and servo motorjovin Richard
The document describes the design and functioning of a robotic arm that can be controlled through hand gestures. The robotic arm has several degrees of freedom and uses sensors like accelerometers and flex sensors to capture hand movements. The analog sensor signals are processed by a microcontroller to generate PWM signals that control servo motors for joint movement. A DC motor is used for the gripper part to pick and place objects. The robotic arm has applications in industrial automation and medical procedures.
This document provides an overview of robots and robotics. It defines a robot as a re-programmable machine that can perform tasks automatically in place of humans, especially in hazardous environments. The document then discusses the history and origins of the words "robot" and "robotics." It also outlines some of the key parts of industrial robots like sensors, effectors, actuators, controllers, and arms. Finally, it briefly describes different types of robots and their applications as well as some advantages and disadvantages of robotics.
Research on The Control of Joint Robot TrajectoryIJRESJOURNAL
ABSTRACT: This paper relates to a Robot that belongs to the category of Joint Robot.In the article,we analyze the path planning and control system of the robot,specifically speaking,it involves the interpolation of the robot trajectory, the analysis of the inverse kinematics, the introduction of the method to reduce the trajectory error, the optimization of the trajectory and in the end, the corresponding control system is designed according to the relevant parameters. This research project first introduces the importance of the robot, and then analyzes the whole process of the robot from the grasping pin, the screw to they are delivered to the designated position,finally, the process is introduced in detail, and the simulation result is displayed.
Modeling, Simulation, and Optimal Control for Two-Wheeled Self-Balancing Robot IJECEIAES
Two-wheeled self-balancing robot is a popular model in control system experiments which is more widely known as inverted pendulum and cart model. This is a multi-input and multi-output system which is theoretical and has been applied in many systems in daily use. Anyway, most research just focus on balancing this model through try-on experiments or by using simple form of mathematical model. There were still few researches that focus on complete mathematic modeling and designing a mathematical model based controller for such system. This paper analyzed mathematical model of the system. Then, the authors successfully applied a Linear Quadratic Regulator (LQR) controller for this system. This controller was tested with different case of system condition. Controlling results was proved to work well and tested on different case of system condition through simulation on matlab/Simulink program.
Inverse Kinematics Analysis for Manipulator Robot with Wrist Offset Based On ...Waqas Tariq
This paper presents an algorithm to solve the inverse kinematics for a six degree of freedom (6 DOF) manipulator robot with wrist offset. This type of robot has a complex inverse kinematics, which needs a long time for such calculation. The proposed algorithm starts from find the wrist point by vectors computation then compute the first three joint angles and after that compute the wrist angles by analytic solution. This algorithm is tested for the TQ MA2000 manipulator robot as case study. The obtained results was compared with results of rotational vector algorithm where both algorithms have the same accuracy but the proposed algorithm saving round about 99.6% of the computation time required by the rotational vector algorithm, which leads to used this algorithm in real time robot control.
Robot trajectory generation involves planning smooth trajectories to move a robot arm or mobile robot between initial and final postures. Trajectories are preferred over jerky motions because smooth trajectories do not violate joint drive limits, excite resonant modes of the mechanical structure, or require sudden changes in joint angles. Trajectory generation approximates a planned path by curve functions that satisfy constraints like continuity and joint velocity/acceleration limits to produce smooth motion profiles in both the joint and operational spaces.
Robotics Simulation by Wireless Brains - ROBOKDC'15 ProjectSurya Chandra
Final project for the graduate course of robotics at Colorado School of Mines. Nuclear fuel rods are moved from specified locations in a pallet and is placed into an elevator by a robot . The elevator takes the rods to the reactor room. A second robot places each of the fuel rods into a specified slot of the reactor.
The document discusses manipulator kinematics, which refers to the position and orientation of a robot's end effector as a function of time, without regard to forces or mass. It describes different methods for representing an end effector's position, including joint space and world space methods. The key difference between forward and backward transformations is that forward transformation maps from joint space to world space, while backward transformation maps from world space to joint space. Accuracy refers to how well a robot can reach a desired location, while repeatability refers to how well it can return to a previously taught point.
This work presents the kinematics model of an RA-
02 (a 4 DOF) robotic arm. The direct kinematic problem is
addressed using both the Denavit-Hartenberg (DH) convention
and the product of exponential formula, which is based on the
screw theory. By comparing the results of both approaches, it
turns out that they provide identical solutions for the
manipulator kinematics. Furthermore, an algebraic solution of
the inverse kinematics problem based on trigonometric
formulas is also provided. Finally, simulation results for the
kinematics model using the Matlab program based on the DH
convention are presented. Since the two approaches are
identical, the product of exponential formula is supposed to
produce same simulation results on the robotic arm studied.
Keywords-Robotics; DH convention; product of exponentials;
kinematics; simulations
simuliton of biped walkinng robot using kinematicsReza Fazaeli
This document describes simulation and control of a biped walking robot using kinematic and dynamic modeling. It presents the dynamic equations of motion for a 2D model of the robot with 5 degrees of freedom. It then describes how impacts are modeled when the swing foot makes contact with the ground. A linear control method is developed using selected outputs to control the robot's motion along a straight line. Simulation results are shown for both 2D and 3D dynamic models of the robot, with angles, velocities, accelerations, and torques calculated. The robot is able to walk stably along a straight line by maintaining balance during single support phases, demonstrating the effectiveness of the control approach.
Path Planning of Mobile aco fuzzy-presentation.pptxssuserf6b378
The document describes a study on path planning for mobile robots using fuzzy logic and ant colony algorithms in complex dynamic environments. It proposes a new approach that combines these methods. The study models the robot's workspace as a grid with fixed and moving obstacles. It explains how the ant colony algorithm and fuzzy logic are applied to determine optimal paths between start and end points while avoiding obstacles. Simulation results show the combined approach finds shorter paths in less time compared to using each method individually.
A fuzzy logic controllerfora two link functional manipulatorIJCNCJournal
This paper presents a new approach for designing a Fuzzy Logic Controller "FLC"for a dynamically multivariable nonlinear coupling system. The conventional controller with constant gains for different operating points may not be sufficient to guarantee satisfactory performance for Robot manipulator. The Fuzzy Logic Controller utilizes the error and the change of error as fuzzy linguistic inputs to regulate the system performance. The proposed controller have been developed to simulate the dynamic behavior of A
Two-Link Functional Manipulator. The new controller uses only the available information of the input-output for controlling the position and velocity of the robot axes of the motion of the end effectors
Robot forward and inverse kinematics research using matlab by d.sivasamySiva Samy
The document discusses developing forward and inverse kinematic models of a Scorbot era 5u plus industrial robot using MATLAB. It begins by introducing the Denavit-Hartenberg parameters for representing robot kinematics. Then it describes modeling the specific Scorbot era 5u plus robot in MATLAB, including defining its link lengths and joint ranges using DH parameters. Forward kinematics analysis is performed by varying the joint angles to find the end effector position and orientation. Validation is done by comparing the results to a commercial robot simulator and LabVIEW. Inverse kinematics analysis is also developed to determine required joint angles to achieve a desired end effector pose.
4 solar refrigeration and elecricity generationMd Irfan Ansari
This document discusses refrigeration and solar energy conversion systems. It describes vapor compression and solar vapor absorption refrigeration cycles. It explains how photovoltaic cells work by converting solar radiation into electricity via the photoelectric effect. Key components of PV systems like solar panels, batteries, and inverters are outlined. Advantages and limitations of solar energy conversion are also summarized. Solar lanterns are provided as a simple application of solar PV technology for rural lighting needs.
This document discusses robot kinematics and position analysis. It covers forward and inverse kinematics, including determining the position of a robot's hand given joint variables or calculating joint variables for a desired hand position. Different coordinate systems for representing robot positions are described, including Cartesian, cylindrical and spherical coordinates. The Denavit-Hartenberg representation for modeling robot kinematics is introduced, allowing the modeling of any robot configuration using transformation matrices.
1. The document describes a 2 link planar manipulator with 2 rotational joints and specifies the link lengths and coordinate frames.
2. It covers the forward kinematics to find the endpoint using homogeneous transformations by composing individual coordinate transforms between frames.
3. As an example, it shows the coordinate transforms between Frame 0 to Frame 1 which is a rotation of 30 degrees and translation of (1,1) and between Frame 1 to Frame 2 which is a rotation of 60 degrees and translation of (1/2,√3/2).
Solar refrigeration uses solar energy to power refrigeration systems for food and medicine preservation and comfort cooling. There are three main types of solar refrigeration: photovoltaic operated vapor compression, solar mechanical vapor compression using a Rankine cycle, and absorption refrigeration. Absorption refrigeration replaces the compressor with a thermal compression system using ammonia as the working fluid and a generator powered by solar collectors to desorb the ammonia, providing refrigeration without large mechanical energy inputs. While solar refrigeration has benefits of being environmentally friendly and not relying on power grids, its high initial costs and low coefficient of performance currently limit widespread adoption.
The document discusses robot kinematics and control. It covers topics like coordinate frames, homogeneous transformations, forward and inverse kinematics, joint space trajectories, and cubic polynomial path planning. Specifically:
1) Kinematics is the study of robot motion without regard to forces or moments. It describes the spatial configuration using coordinate frames and homogeneous transformations.
2) Forward kinematics determines end effector position from joint angles. Inverse kinematics determines joint angles for a desired end effector position.
3) Joint space trajectories plan motion by describing joint angle profiles over time using functions like cubic polynomials and splines.
4) Cubic polynomials satisfy constraints like initial/final position and velocity to generate smooth motion profiles for a single revol
1) The document discusses the fundamentals of robotic manipulators, including their classification, parts, motions, and work envelopes.
2) The major types of robot configurations are Cartesian, cylindrical, spherical, SCARA, and articulated, which are defined by their joint types and resulting work spaces.
3) Robotic manipulators consist of links connected by joints and powered by electric, hydraulic, or pneumatic drives to position an end effector through programmed motions.
Robotic Arm using flex sensor and servo motorjovin Richard
The document describes the design and functioning of a robotic arm that can be controlled through hand gestures. The robotic arm has several degrees of freedom and uses sensors like accelerometers and flex sensors to capture hand movements. The analog sensor signals are processed by a microcontroller to generate PWM signals that control servo motors for joint movement. A DC motor is used for the gripper part to pick and place objects. The robotic arm has applications in industrial automation and medical procedures.
This document provides an overview of robots and robotics. It defines a robot as a re-programmable machine that can perform tasks automatically in place of humans, especially in hazardous environments. The document then discusses the history and origins of the words "robot" and "robotics." It also outlines some of the key parts of industrial robots like sensors, effectors, actuators, controllers, and arms. Finally, it briefly describes different types of robots and their applications as well as some advantages and disadvantages of robotics.
Research on The Control of Joint Robot TrajectoryIJRESJOURNAL
ABSTRACT: This paper relates to a Robot that belongs to the category of Joint Robot.In the article,we analyze the path planning and control system of the robot,specifically speaking,it involves the interpolation of the robot trajectory, the analysis of the inverse kinematics, the introduction of the method to reduce the trajectory error, the optimization of the trajectory and in the end, the corresponding control system is designed according to the relevant parameters. This research project first introduces the importance of the robot, and then analyzes the whole process of the robot from the grasping pin, the screw to they are delivered to the designated position,finally, the process is introduced in detail, and the simulation result is displayed.
Modeling, Simulation, and Optimal Control for Two-Wheeled Self-Balancing Robot IJECEIAES
Two-wheeled self-balancing robot is a popular model in control system experiments which is more widely known as inverted pendulum and cart model. This is a multi-input and multi-output system which is theoretical and has been applied in many systems in daily use. Anyway, most research just focus on balancing this model through try-on experiments or by using simple form of mathematical model. There were still few researches that focus on complete mathematic modeling and designing a mathematical model based controller for such system. This paper analyzed mathematical model of the system. Then, the authors successfully applied a Linear Quadratic Regulator (LQR) controller for this system. This controller was tested with different case of system condition. Controlling results was proved to work well and tested on different case of system condition through simulation on matlab/Simulink program.
Inverse Kinematics Analysis for Manipulator Robot with Wrist Offset Based On ...Waqas Tariq
This paper presents an algorithm to solve the inverse kinematics for a six degree of freedom (6 DOF) manipulator robot with wrist offset. This type of robot has a complex inverse kinematics, which needs a long time for such calculation. The proposed algorithm starts from find the wrist point by vectors computation then compute the first three joint angles and after that compute the wrist angles by analytic solution. This algorithm is tested for the TQ MA2000 manipulator robot as case study. The obtained results was compared with results of rotational vector algorithm where both algorithms have the same accuracy but the proposed algorithm saving round about 99.6% of the computation time required by the rotational vector algorithm, which leads to used this algorithm in real time robot control.
Robot trajectory generation involves planning smooth trajectories to move a robot arm or mobile robot between initial and final postures. Trajectories are preferred over jerky motions because smooth trajectories do not violate joint drive limits, excite resonant modes of the mechanical structure, or require sudden changes in joint angles. Trajectory generation approximates a planned path by curve functions that satisfy constraints like continuity and joint velocity/acceleration limits to produce smooth motion profiles in both the joint and operational spaces.
Robotics Simulation by Wireless Brains - ROBOKDC'15 ProjectSurya Chandra
Final project for the graduate course of robotics at Colorado School of Mines. Nuclear fuel rods are moved from specified locations in a pallet and is placed into an elevator by a robot . The elevator takes the rods to the reactor room. A second robot places each of the fuel rods into a specified slot of the reactor.
The document discusses manipulator kinematics, which refers to the position and orientation of a robot's end effector as a function of time, without regard to forces or mass. It describes different methods for representing an end effector's position, including joint space and world space methods. The key difference between forward and backward transformations is that forward transformation maps from joint space to world space, while backward transformation maps from world space to joint space. Accuracy refers to how well a robot can reach a desired location, while repeatability refers to how well it can return to a previously taught point.
This work presents the kinematics model of an RA-
02 (a 4 DOF) robotic arm. The direct kinematic problem is
addressed using both the Denavit-Hartenberg (DH) convention
and the product of exponential formula, which is based on the
screw theory. By comparing the results of both approaches, it
turns out that they provide identical solutions for the
manipulator kinematics. Furthermore, an algebraic solution of
the inverse kinematics problem based on trigonometric
formulas is also provided. Finally, simulation results for the
kinematics model using the Matlab program based on the DH
convention are presented. Since the two approaches are
identical, the product of exponential formula is supposed to
produce same simulation results on the robotic arm studied.
Keywords-Robotics; DH convention; product of exponentials;
kinematics; simulations
simuliton of biped walkinng robot using kinematicsReza Fazaeli
This document describes simulation and control of a biped walking robot using kinematic and dynamic modeling. It presents the dynamic equations of motion for a 2D model of the robot with 5 degrees of freedom. It then describes how impacts are modeled when the swing foot makes contact with the ground. A linear control method is developed using selected outputs to control the robot's motion along a straight line. Simulation results are shown for both 2D and 3D dynamic models of the robot, with angles, velocities, accelerations, and torques calculated. The robot is able to walk stably along a straight line by maintaining balance during single support phases, demonstrating the effectiveness of the control approach.
Path Planning of Mobile aco fuzzy-presentation.pptxssuserf6b378
The document describes a study on path planning for mobile robots using fuzzy logic and ant colony algorithms in complex dynamic environments. It proposes a new approach that combines these methods. The study models the robot's workspace as a grid with fixed and moving obstacles. It explains how the ant colony algorithm and fuzzy logic are applied to determine optimal paths between start and end points while avoiding obstacles. Simulation results show the combined approach finds shorter paths in less time compared to using each method individually.
A fuzzy logic controllerfora two link functional manipulatorIJCNCJournal
This paper presents a new approach for designing a Fuzzy Logic Controller "FLC"for a dynamically multivariable nonlinear coupling system. The conventional controller with constant gains for different operating points may not be sufficient to guarantee satisfactory performance for Robot manipulator. The Fuzzy Logic Controller utilizes the error and the change of error as fuzzy linguistic inputs to regulate the system performance. The proposed controller have been developed to simulate the dynamic behavior of A
Two-Link Functional Manipulator. The new controller uses only the available information of the input-output for controlling the position and velocity of the robot axes of the motion of the end effectors
Robot forward and inverse kinematics research using matlab by d.sivasamySiva Samy
The document discusses developing forward and inverse kinematic models of a Scorbot era 5u plus industrial robot using MATLAB. It begins by introducing the Denavit-Hartenberg parameters for representing robot kinematics. Then it describes modeling the specific Scorbot era 5u plus robot in MATLAB, including defining its link lengths and joint ranges using DH parameters. Forward kinematics analysis is performed by varying the joint angles to find the end effector position and orientation. Validation is done by comparing the results to a commercial robot simulator and LabVIEW. Inverse kinematics analysis is also developed to determine required joint angles to achieve a desired end effector pose.
Robust Control of a Spherical Mobile RobotIRJET Journal
This document summarizes a research paper about controlling a spherical mobile robot using sliding mode control. It begins with an abstract that describes the challenges of controlling spherical robots due to their underactuated systems. It then provides background on previous control methods for spherical robots. The document presents the kinematic model of a 2-DOF spherical robot and describes how sliding mode control can be used to provide robust control and path following for the robot. It provides the equations for the sliding mode controller design. Finally, it presents simulation results showing the robot following a desired trajectory with minimal tracking error using the sliding mode controller.
Determination of the Operational Parameters of a Planar Robot with Three JointsWaqas Tariq
Robots are currently made in numerous types and are used in diverse roles such as production lines, daily living activities and some security fields. These types of robots are well designed and successfully applied in many areas requiring high sensitivity and stability. The aim of this study was to determine the optimum values of several operational parameters for a planar robot with respect to robot design and construction. With this aim, a small planar robot with a three-jointed arm activated by hydraulic cylinders in each segment was evaluated using a technical design drawing. The arm motions of the planar robot are rotary and parallel within a vertical plane. The resulting optimal operational parameters of the planar robot were determined as starting and target positions of 31.5 cm and 55 cm, respectively, on the x-axis and 17.18 cm and 118.44 cm on the y–axis. Time-position and time-velocity graphs were constructed corresponding to the orbit-planning parameters, resulting in Cartesian velocities for the terminal processor of 13.98 m/sec on the x-axis and 20.16 m/sec on the y-axis at 1.5 seconds after initiation. The maximum power consumption of the robot was determined as 1 kW according to the outer load and arm weights.
ROBOT HYBRID AND FORCE CONTROL IN MULTI-MICROPROCESSOR SYSTEM AnuShka Yadav
This document discusses a multi-microprocessor system for controlling the position and force of a walking robot in real time. It presents the implementation of an open architecture system that uses forward and inverse kinematics to control the robot's position in Cartesian coordinates. Experimental results showed that the open architecture control system ensured flexibility, short execution time, precision targeting and repeatability of movement programs compared to a single microprocessor system.
This document describes the development of a mechanism for transplanting rice seedlings using a self-propelled transplanter. The mechanism uses a four-bar linkage to pick up rice seedlings from a tray and plant them into the soil at the proper depth and orientation. The linkage is analyzed using graphical and analytical methods to optimize the path of the planting finger for continuous and efficient transplanting as the machine moves forward. Link dimensions, inclination angle, and forward speed are varied to refine the mechanism's performance. The developed mechanism aims to mechanize the labor-intensive transplanting process while mimicking manual transplanting methods.
Business Proposal Presentation in Purple Monochrome Corporate Style.pptxJOHN35307
Trajectory planning is moving from point A to point B while avoiding collisions over time. This can be computed in both discrete and continuous methods. Trajectory planning is a major area in robotics as it gives way to autonomous vehicles.
Trajectory planning is sometimes referred to as motion planning and erroneously as path planning. Trajectory planning is distinct from path planning in that it is parametrized by time. Essentially trajectory planning encompasses path planning in addition to planning how to move based on velocity, time, and kinematics.
Problem Constraints
Holonomicity
Holonomicity is the relationship between the controllable degrees of freedom of the robot and the total degrees of freedom of the robot. If the number of controllable degrees of freedom are greater than or equal to the total degrees of freedom a robot is said to be holonomic. By using a holonomic robot many movements are much easier to make and return to a past pose is much easier.
A car would be non-holonomic, as it has no way to move laterally. This makes certain movements, such as parallel parking, difficult. An example of a holonomic vehicle would be one using mecanum wheels, such as the new Segway RMP.[1]
Dynamic Environments
In dynamic environments, such as the real world, many possible collision objects are not stationary. This makes trajectory planning more difficult as time is constantly changing and objects are moving. A robot cannot simply move backward in time as it might simply back away from a stationary collision. In addition to this many choices are completely irreversible due to terrain, such as moving off of a cliff.
Concepts
Concepts of Trajectory Planning
Trajectory planning gives a path from a starting configuration S to a goal configuration G avoiding collisions in a 2D or 3D space.
A configuration is the pose of a robot describing its position. Configuration Space C, is the set of all configurations. For instance, in two dimensions a robot's configuration would be described by coordinates (x, y) and angle θ. Whereas in three dimensions a robot's configuration would be described by coordinates (x, y, z) and angles (α, β, γ).
Free space Cfree is the set of all configurations that are collision-free. Computing the shape of Cfree is not efficient, however, computing if a given configuration is a collision free is by simply using kinematics and collision detection from sensors.
Target space is a linear subspace of free space which we want robot go there. In global motion planning, target space is observable by robot's sensors. However, in local motion planning, robot cannot observe the target space in some states. To solve problem, robot assume several virtual target space which is located in observable area (around robot). The virtual target space is called sub-goal.[2]
Planning Algorithms
Artificial Potential Field
Example of a Potential Field
Artificial Potential Field Planning places values over the map with the goal having the low
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.
The document describes the forward kinematics analysis of a 6 degree of freedom arc welding robot. It discusses assigning coordinate frames to each link using the Denavit-Hartenberg convention. The forward kinematics problem is to determine the position and orientation of the end effector given the joint variable values. The methodology develops a kinematic model in Matlab using the link transformations. For example joint values, the model outputs the end effector position and orientation as represented by a homogeneous transformation matrix. The analysis can determine the end effector pose for any given joint configuration.
The document discusses the mathematical structure of kinematic models for manipulators. It defines that a manipulator consists of rigid links connected by joints, with an arm for mobility, wrist for orientation, and end-effector for tasks. Degrees of freedom refer to independent movements in 3D space, with 6 total - 3 for translation and 3 for rotation. Kinematic modeling involves direct and inverse kinematics - direct finds end-effector position from joint parameters, inverse finds joint values for a given end-effector position. Denavit-Hartenberg notation assigns reference frames, and transformation matrices relate positions between adjacent links based on joint-link parameters to define the kinematic model.
2. Abstract
The two link robotic arm manipulator analyzed in this report is required to be accurate and achieve great precision when
moving from the home position (position 1) to reachable positions within the workspace. The applications of two link
robots are continuously developing. For example they are utilized in the medical field and manufacturing which are
very different industries. In this study the two link manipulator was analyzed to develop the relationship between the
ideal motion as it relates to the actual motion of the joints and end effector in the xy plane. Linearized equations of
motion (EOM) were used to develop proportional controllers for each joint. The full EOM are used to simulate the
manipulator as it moves in the xy plane. Using the coefficients of the cubic polynomial that moves the manipulator from
position 1 to position 2, plots were generated to visualize the changes in the robot’s position, velocity and acceleration
over 0.5 seconds. The polynomials of the two-segment continuous-acceleration trajectory were found and used to
compare the desired x versus y path to the actual x versus y path. It was found that the error occurred when the end
effector reached position 2 which was outside of the linearized region around position 1. The inertial and mass effects
significantly influenced the end effectors precision. It is observed that the end effector’s error is large as it moves from
position 3 to the via point and increase to the position once the end effector reaches its stopping position 5 it entirely
missed the desired location.
Purpose
This two link robotic arm study is intended to analyze
the relationship between the desired and actual motion
and path taken by the robot during operation. Using the
linearized EOM and the coefficients of the cubic
polynomial, the simulation of the manipulator to move
from position 1 to position 2. The polynomials for the
two-segment continuous-acceleration trajectory of the
manipulator can be used to analyze the comparison
between the desired and actual x versus y path. The
analysis in this study creates a visualization of the
robot’s physical constraints and how they affect its
operation. One can employ this analysis to understand
when and why error associated with the manipulator
occurs during the robot’s operation.
Approach
Using the MATLAB program a code was written to
analyze the robot’s motion in the xy plane and changes
in the angular velocity and acceleration of both joints
and the end effector. The MATLAB code is designed to
develop the various graphs that follow to simulate the
location on both joints and end effector with respect to
time and determine the true effects of the robot’s
physical constraints as they relate to the actual motion
versus the ideal motion of the robot. The transformation
matrices are designed to capture the relationship
between the reference frames of the links of the robot.
The associated kinematic equations of the robot are used
to determine the joint parameters that provide a desired
position for the end effector. The positions of motion,
constant variables, gains of each joint’s proportional
controller and transfer functions are defined prior to the
development of the linear and nonlinear EOM. The
respective plots which follow are developed to illustrate
how the two link robot moves in 2D space and what
region in its workspace does it encounter error
associated with the end effector not reaching the desired
end position. Some plots are developed to identify
causes of error related to the robot’s operation and
physical constraints.
Results
The two-link manipulator shown is motionless at the
home position P1 = (θ1=15o
, θ2=135o
).
-
The objective of this project is to model a two link
robot using MATLAB.
Use linearized EOM for the manipulator and
develop proportional controllers for each
joint. Use position 1 (θ1 = 15o
, θ2 = 135o)
Using EOM to simulate the manipulator as it
moves from rest to position two.
Determine the coefficients of the cubic
polynomial that move the manipulator from
rest at position one to position 2 in 0.5 sec.
3. Find the two-segment continuous-
acceleration trajectory desired polynomials
for the motion from position 3 through a “via
point” at position 4 to the final position 5.
Parts 1 & 2: Plot θ1 vs Time and θ2 vs Time
Graph 1 below plots θ1 and θ1 versus time. The desired
plot was developed using the link parameters and
proportional controller’s joint constraints of ωn = 3 Hz
and ζ = 0.707. The angles provided can be seen in
Graph 3. When developing this graph, proportional
controllers were utilized for each joint together with the
full equation of motion (EOM).
Graph 1: Simulated Thetas vs Time
Part 3: Plot X vs Y Path
The previous graph is useful to see how the angles
respond over time. To observe how the robot moves in
space, it is necessary to look at graph 2 that plots the X
versus Y position of the end effector as it moves from
rest at position 1 to the destination at position 2. When
comparing (actual motion) graph 2 with (desired
motion) graph 6 it is observed that they don’t follow the
same path. Their stopping position is roughly at the
same. They don’t have the same path because of the
physical constraints of the robot’s links. This is due to
the fact that the robot’s links have inertia and mass that
needs to be taken into account. The end position error is
a result of the fact the proportional controller is designed
to work in the linearized region around position 1. The
error will increase the farther the end position is from
that area at position 1. Position 2 is close enough to
position 1 that the error is very small, but larger errors
are expected at larger extensions of the arm.
Graph 2: Trace of X vs Y Path
Part 4: Plot Desired Position vs Time
Graph 3 below shows the desired position versus time
in joint space. After finding the coefficients of the cubic
polynomial that moves the manipulator from rest at
position 1 to position 2 (θ1 = 90o
θ2 = 10o
) change in both
angles was plotted with respect to time. It creates a
visualization of a smooth continuous curve. This was
generated using positions 1 and 2 with the cubic
polynomial and a time of 0.5 seconds.
Graph 3: Desired Angles of Theta vs. Time
Part 5: Plot Angular Velocity vs Time
Graph 4 below demonstrates the desired angular
velocity versus time for the two joints. These joints are
moving from position 1 to position 2 (θ1 = 90o
θ2 = 10o
)
in 0.5 sec. The coefficients of the cubic polynomial
4. were found to create the visualization of how the
angular velocities of both joints change over time.
Graph 4: Desired Velocities of Thetas versus Time
Part 6: Plot Desired Acceleration vs Time
Graph 5 below shows the desired acceleration versus
time for the robot in joint space. The straight line
suggests a constant jerk on both joints. It is a derivative
of the velocity curve that was developed with taking the
derivative of the velocity equation.
Graph 5: Desired Acceleration of Thetas vs. Time
The desired x y path is shown in Graph 6 below. This is
the desired path generated from the cubic polynomial
displayed in Cartesian space.
Graph 6: Desired Path Trace
Graph 7 below is a visualization of what motion the
robot actually performed when moving from position 1
to position 2 (θ1 = 90o
θ2 = 10o
). Graph 7 takes into
account the errors in the controls.
Graph 7: Simulated Trace of Path
Part 7: Plot Desired Position vs Time
Graph 8 below shows in Cartesian space the desired
position vs time of x and y of the manipulator from
position 1 to position 2 over a time of 0.5 sec.
5. Graph 8: Position Y vs Time and Position X vs Time
Graph 9 below shows the step response. The lines that
represent theory (green and purple) would be the
electrical impulses that drive the robot’s motors. Due to
losses, gravity and errors the electrical impulses needed
are larger than the theory. The blue and red lines on the
step response graph represent the electrical impulse
applied. They are intended to create a visualization of
the actual movement of the robot in MATLAB.
Graph 9: Step Responses
Part 8: Plot the Desired X vs Y and the Actual X vs
Y Moving from Position 3 - Position 4 – Position 5
Graph 10 below demonstrates the desired X vs Y path
of the robot’s end effector. The curves are smooth and
efficient with some arcs connecting the start position,
via point and stop position.
Graph 10: Desired XY Path Trace (P3-P5)
Graph 11 below demonstrates the actual path of the
robot in the xy plane of the robot’s end effector. The
error deviation from the desired path starts out rather
large as the end effector moves from position 3 (θ1 =
90o
, θ2 = 45o) in the lead up to the “via point” to position
4 (θ1 = 60o
, θ2 = 60o). As the end effector moves farther
away from the via point the error increases. Once the
end effector reaches position 5 (θ1 = 30o
, θ2 = 20o) the
error is so large that the robot misses the final position
that is desired.
Graph 11: Simulated XY Path Trace (P3-P5)
6. Future Work
The proportional controller should be replaced by a
proportional-integral-derivative (PID) controller. This
type of a controller is a control loop feedback controller.
They are designed to continuously calculate an error
value as the difference between a desired set point and
the process variable measured. The PID controller over
time works to minimize the error by adjusting the
control variable.
Conclusion
Comparing graph 2 (actual motion) to graph 6 (desired
motion) the two link robot’s path is not equivalent. The
ending position is roughly the same, but the path they
follow is not because the robots links have inertia and
mass that should be considered. Although, those
physical characteristics are not know. There is
significant end position error because the proportional
controller is designed to work in the linearized region
around position 1 (θ1 = 15o
θ2 = 135o
). The error is
expected to increase the farther the end position is
laterally from the area at position 1. The inertial and
mass effects do not influence the error as severe because
the distance from position 1 to position 2 is only 20 cm.
The absolute value of angular velocity and angular
acceleration for joint 2 was larger than that of joint 1.
When considering the error associated with the controls
it is clear that graph 7 (actual path) demonstrates how
the robot’s path differs from graph 6 (desired path).
Graph 8 demonstrates the need for a larger input of
electrical impulses than the theoretical requirements to
meet the power requirement. Finally, graph 10 and 11
simulate the path taken by the robot from position 3 (θ1
= 90o
, θ2 = 45o
) through the “via point” position 4 (θ1 =
60o
, θ2 = 60o
) and stopping at position 5 (θ1 = 30o
, θ2 =
20o
). When designing a two link robot the physical
constraints associated with the motors and the inertia
and mass of the components must be considered to
ensure optimal precision of the robot’s end effector. A
major design consideration when selecting motors for
the robot is determining the linearization constraints
associated with different motors. As seen in this study
there were significant errors associated with the
proportional controller because it is designed to operate
in the linearized region around position 1.
7. Two Link Robot MATLAB Code
%% Travis John Heidrich
%% Two Link Robot Analysis
%% May 1, 2016
%% Clean Up
clear all
close all
clc
%% Define Parameters
% Define Robot Dimensions
Izz1 = 0; %N*m*s^2
Izz2 = 0; %N*m*s^2
% this is the motor armature inertia, already reflected thru the gear ratio
M1 = 0.035; % kg
M2 = 0.067; % kg
L1 = 0.2; % m
L2 = 0.3; % m
% Create Transforms
syms ai alphai di thetai theta1temp theta2temp
Tx=[1 0 0 0;0 cos(alphai) -sin(alphai) 0;0 sin(alphai) cos(alphai) 0;0 0 0 1];
Dx=[1 0 0 ai;0 1 0 0;0 0 1 0;0 0 0 1];
Tz=[cos(thetai) -sin(thetai) 0 0;sin(thetai) cos(thetai) 0 0;0 0 1 0 ;0 0 0 1];
Dz=[1 0 0 0;0 1 0 0;0 0 1 di;0 0 0 1];
%Concatenate in one homogeneous transform
AtB=Tx*Dx*Tz*Dz;
ai = 0;
alphai = 0;
thetai = theta1temp;
di = 0;
T01 = subs(AtB);
ai = L1;
alphai = 0;
thetai = theta2temp;
di = 0;
T12 = subs(AtB);
ai = L2;
alphai = 0;
thetai = 0;
di = 0;
T2E = subs(AtB);
T02 = T01*T12;
T0E = T01*T12*T2E;
% Define Motor Variables
Km1 = 0.00767;
Km2 = 0.0053;
Kg1 = 14;
Kg2 = 262;
Ke1 = 0.804*(60/(2*pi))*(1/1000);
Ke2 = 0.555*(60/(2*pi))*(1/1000);
Rm1 = 2.6;
Rm2 = 9.1;
Jm1 = 3.87e-7;
Jm2 = 6.8e-8;
g = 9.81; % m/s^2