Web Enabled Robot Design and Dynamic Control Simulation Software Solutions From Task Points Descript

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Web Enabled Robot Design and Dynamic Control
Simulation Software Solutions From Task Points
Description

• Tarek Sobh, Sarosh Patel and Bei Wang
• School of Engineering
• University of Bridgeport

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Table of Content

• Research Summary
• Task Point Description
• Theory
• The Software Package
• Results
• Conclusion
• Future Development
• Current Project Status

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Research Summary

• A web-based solution for robot design and dynamic
  control simulation based on given task point
  descriptions
• The software combines and utilizes the
  computational power of both the Mathematica and
  Matlab packages

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Research Summary (cont.)

• Given the location and velocity of each task
  point, our approach formulates the complete
  design of a 3 DOF robot model by computing its
  optimal dynamic parameters such as link length,
  mass and inertia
• Suggests the optimal control parameters (Kp, Kv)
  for the dynamic control simulation

Puma560 3 DOF robot
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Task Point Description

• A set of desired positions of an end-effector
• Velocities at a particular instant of time
• Problem definition to obtain the optimal robot
  design and dynamic control strategy in such a way
  that the task can be carried out with maximum
  manipulability and minimum error in reaching the
  desired positions and velocities

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Theory

• Manipulability
• The Cost Function
• Optimizing the Cost Function
• Calculations of Dynamic Parameters
• Trajectory Generation
• PD Control Loop
• Optimization of Kp and Kv

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TheoryManipulability

• Manipulability the ability of the manipulator to
  accelerate in all directions from that point
• Yoshikawa

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TheoryThe Cost Function

• The criteria used to form the cost function
• Manipulability
• Accuracy
• Distance from the point.
• K is the DH parameter of the robot
• q1,q2..qm are the joint vectors of the task
  points

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TheoryOptimizing the Cost Function

• Uses the steepest descent algorithm, which finds
  the minima by searching in the direction
  opposite, to the gradient
• Minimizing the function provides the optimal
  values for the DH table

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TheoryCalculations of Dynamic Parameters

• Calculates manipulator DH table on the following
  assumptions
• The manipulator links are solid and cylindrical
  in shape
• All links have uniform density (uniform mass
  distribution)
• All the links are made of the same material
• There are a finite number of actuators and
  sensors with known specifications that can be
  used in the design

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TheoryCalculations of Dynamic Parameters (Cont.)

• Mass
• Center of Gravity The center of gravity is
  calculated geometrically with respect to the link
  coordinate frame

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TheoryCalculations of Dynamic Parameters (Cont.)

• Inertia Since the links are considered to be
  cylindrical, the Inertia about the axis of a
  cylinder is given by
• Using the perpendicular axis theorem the Inertia
  along the other two axes is given by

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TheoryTrajectory Generation

• A seven-degree polynomial to generate the
  trajectory
• The control loop is implemented over to support
  this trajectory

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TheoryPD Control Loop

• It is advantageous to use a PD control loop
• Simple to implement
• Involves few calculations ideal for real time
  control provided with optimum Kp and Kv
• System behavior can be controlled by changing the
  feedback gains
• Can be implemented in parallel for each link

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TheoryPD Control Loop (cont.)

• Torque to be applied to the manipulator Forward
  Dynamics
• The feedback loop Inverse Dynamics
• In the case of real time control the sensors
  provide the feedback

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TheoryPD Control Loop (cont.)
a block diagram commonly found in robot
prototyping research
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TheoryPD Control Loop (cont.)

• Kp proportional gain
• Kv derivative gain
• e error in position
• e error in velocity

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TheoryOptimization of Kp and Kv

• Sum of the Square of Errors about the desired
  trajectory should be less than a specified
  threshold

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The Software Package

• Web Interface
• Kinematic Design Module
• Dynamic Design Module
• Dynamic Control Simulation Module

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The Software Package (Cont.)
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Web Interface

• JSP, Servlet, JLink and JMatservlet
• Central control module

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Kinematic Design Module

• Generate best kinematics robot configuration with
  max manipulability
• Modified kinematics synthesis package build on
  top of Robotica
• Input set of task points description
• Output a robot configuration in the form of DH
  table (optimal kinematics properties of the
  three-link robot)

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Kinematic Design Module (Cont.)

• DesignRobot task_points, configuration,
  precision, file_name
• Task_points a matrix with xyz coordinates of
  task points
• Configuration a string of Rs and Ps
  describing prismatic or rotational joints
• File_name the location in which the DH
  configuration file is stored

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Dynamic Design Module

• Input file (DH table) generated by Kinematic
  model radii of the links (mass of the links is
  pre-assumed)
• Output Dynamic parameter matrix dyn
• Running in the MATLAB environment

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Structure of the DYN matrix
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Dynamic Control Simulation Module

• MATLAB environment
• Input coordinates of points with respect to a
  time frame and velocities at those points
  specified range of values for Kp and Kv and the
  step increment
• Output optimum value of Kp and Kv, and update
  frequency

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Results User login Screen
sample run video
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User specifies number of task points
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User specifies the coordinates and velocities of
each task points with respect to a time scale
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User specifies link radii for dynamic model
generation, and Kp, Kv initialization for dynamic
PD control simulation
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DH table, Dynamic Parameter Matrix and optimal
Kp, Kv values for each link
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A standard PPP model
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Desired Trajectory for link 1, 2, 3
Desired Vs. obtained link displacement for link 1
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Desired Vs. obtained link displacement for link 2
Desired Vs. obtained link displacement for link 3
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Desired velocity trajectory for link 1, 2 and 3
Desired Vs. Obtained velocity for link 1
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Desired Vs. Obtained velocity for link 2
Desired Vs. Obtained velocity for link 3
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Conclusion

• Web-enabled
• Generates the basic configuration of a
  manipulator based on user specified task points,
  in order to attain the greatest manipulability in
  the workspace.
• Provides the optimum values of Kp, Kv for optimum
  dynamic control.

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Future Development

• Building better cost functions
• Customizable objective functions
• Advanced trajectory generation algorithms
• Faster algorithms for calculation of inverse
  kinematics
• A numerical solution package for inverse
  kinematics for a few common robot models
• Implementation of PID control in addition to PD
  control, to further minimize the error

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Current Project Status

• The following paper
• A MOBILE WIRELESS AND WEB BASED ANALYSIS TOOL FOR
  ROBOT DESIGN AND DYNAMIC CONTROL SIMULATION FROM
  TASK POINTS DESCRIPTION has been accepted by the
  Journal of Internet Technology

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References

• Proceedings Lloyd J., Hayward V. A Discrete
  Algorithm for Fixed-path Trajectory Generation at
  Kinematic Singularities, IEEE Int. Conf. on
  Robotics and Automation, Minneapolis (1996)
• Proceedings Sobh T. and Toundykov D. Kinematic
  Synthesis of Robotic Manipulators from Task
  Descriptions, to appear in IEEE magazine on
  Robotics and Automation, summer (2003).
• Journal Yoshikawa T. Manipulability of Robot
  Mechanisms. International Journal of Robotics
  Research, vol.4, pp.3--9 (1985)
• Proceedings Pires E., Machado J. and Oliveira P.
  "An Evolutionary Approach to Robot Structure and
  Trajectory Optimization", 10th International
  Conference on Advanced Robotics, pg. 333-338,
  Budapest, Hungary, August (2001)
• Journal Sobh, T., Dekhil, M., Henderson T., and
  Sabbavarapu A. Prototyping a Three Link Robot
  Manipulator, International Journal of Robotics
  and Automation, Vol. 14, No. 2 (1999)
• Report Dekhil, M., Sobh T., Henderson T.,
  Sabbavarpu A. and Mecklenburg R. Robot
  manipulator prototyping (Complete design
  review), University of Utah (1994)
• Books Spong M. and Vidyasagar. Robot Dynamics
  and Control, Wiley, New York (1989)
• Images obtained from lthelix.gatech.edu/Classes/ME
  4451/2002S3/ Lectures/03TwoSerialRobots.pdf gt

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Thank You