Planar Translational Cable Direct Driven Robots

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Planar Translational Cable Direct Driven Robots
Thesis Defense

• By
• Jigar Vadia

Advisor Dr. Bob Williams
08/12/2002
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Introduction

• Robots
• Electromechanical device with multiple
  degrees-of-freedom (DOF)
• Programmable to accomplish a variety of tasks
• Serial Robots
• Joints and links are constructed in a serial
  fashion from the base
• Parallel Robots
• Joints and links, supporting the load in parallel
• Can handle higher loads with higher speeds
• Major drawback workspace is severely restricted
  as compared to serial robots

Serial Robot
Parallel Robot
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Cable Direct Driven Robots (CDDR)

• Parallel manipulator
• End effector link is supported by n cables with
  n tensioning motors
• Lower mass and better stiffness compared to other
  parallel robots
• Dr Bob Williams and Dr Paolo Gallina introduced
  parallel/serial wrist manipulator architecture
• Translational freedom provided by CDDR
• Rotational freedom provided by Serial Wrist
  Mechanism

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Accomplished work

• Introduce square end effector with cross cable
  architecture to provide reaction at end effector
• Provide additional rotational degree of freedom
  and control rotational angle f to zero The robot
  would have one degree of actuation redundancy (4
  cables- 3 d.o.f.) with this change.

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Objectives

• Derive Kinematics,Statics and Dynamics modeling
  of new design.
• Determination of Statics workspace.
• Designing,building,interfacing of hardware
• Simulate the robot using Simulink and Matlab
• Real-time hardware implementation

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Kinematics

• Forward Pose Kinematics
• Newton-Raphson numerical solution was used for
  the solution of over constrained coupled
  nonlinear equations.

• Inverse Pose Kinematics

• Forward Rate Kinematics
• Forward rate solution can be derived by simply
  inverting inverse rate solution
• Solution only exist if inverse jacobian matrix M
  has full rank.

• Inverse Rate Kinematics

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Static Modeling

• The sum of external forces and moments exerted on
  the end effector by the cables must equal the
  resultant external wrench

Third row is derived by assuming f0
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Dynamics

• Dynamic model for end effector

Motor Shaft Pulley Cable Dynamic Equations
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Dynamics

• Motor Shaft Pulley-Cable Dynamic Equations

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Statics Workspace Determination

• The workspace wherein all cables are under
  positive tension while exerting all possible
  Cartesian wrenches is called the statics
  workspace.
• Cable Tension can be for CDDR with one degree of
  actuation redundancy can be expressed as

• Where the particular solution is

• The homogeneous solution is expressed as the
  kernel vector N of S ( )
  multiplied by arbitrary scalar a.

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CDDR Hardware
Base Plate
Pulleys
DC Motors

• Made of Aluminum
• 3 diameter

• 24-V
• Gear ratio-19.71
• Encoders with 500 C.P.R.

• 0.25 x 3 x 3 Aluminum base
  plate
• 4- Vibration control leveling mounts

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CDDR Hardware
Amplifier
Transformer
MultiQ PCI-Board

• DC Supply Voltage20V-80V
• Peak Current- 25 A
• Max. Continuous Current- 12.5 A

• 8 Analog I/O
• 4 Digital I/P
• 6 Encoder I/P

• Input Voltage- 120V
• Output voltage- 30 V

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Simulation

• Dynamics of CDDR was simulated using control
  architecture presented by Dr. Bob and Dr. Gallina

Control Architecture
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Minimum Torques
With Online Torque Estimation
Without Online Torque Estimation
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Cable Tensions
Without Online Torque Estimation
With Online Torque Estimation
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Hardware Implementation

• Only kinematics was implemented for the real time
  hardware implementation due to software
  limitation of Matlab real time workshop.
• Robot was commanded to follow linear and circular
  trajectory.

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Linear Trajectory(0,0) to (0.10,0)

• Robot was commanded to move from origin (center
  of the base plate) to (0.10,0) in 1 second time.
• End-effector was placed to the origin manually.
• Kp7500 , Ki0 , Kd 1

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Results
Length Control
Cartesian Control
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Results
Cartesian Control Errors
Trajectory Generation
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Linear Trajectory(0,0) to (0.10,0.10)

• Robot was commanded to move from origin (center
  of the base plate) to (0.10,0.10) in 1 second
  time.
• End-effector was placed to the origin manually.
• Kp15000 , Ki0 , Kd 10

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Results
Length Control
Cartesian Control
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Results
Cartesian Control Errors
Trajectory Generation
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Circular Trajectory

• Robot was commanded to trace a circle of 0.15
  meter radius keeping the origin as a center.
• End-effector was placed to the origin manually.
• Kp15000 , Ki0 , Kd 10

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Results
Length Control
Cartesian Control
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Results
Cartesian Control Errors
Trajectory Generation
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Conclusion

• Online Dynamic Torque estimation is required for
  dynamic CDDR with high velocities and
  acceleration, otherwise, the simulation revealed
  that some cables become slack during the motion
  and the control is lost.
• Hardware results had more errors as compared to
  simulated results because dynamics was not
  implemented in real time control.
• The whole theoretical statics workspace could not
  be used in hardware.It was difficult to move the
  end-effector in the region close to the edges of
  the statics workspace as it needs very large
  force to move the end-effector. It approaches to
  singularity on the edge.
• Method to maintain positive cable tensions using
  statics was implemented for hardware
  implementation . Method to maintain positive
  cable tensions using dynamics was implemented for
  simulation.
• A planar translational cable direct driven robot
  with 3 d.o.f. (f commanded to 0 ) and one degree
  of actuation redundancy(4-cables-3 d.o.f.) was
  designed,constructed,simulated and controlled in
  real time.

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Future Work

• Performance of the robot can be improved
  drastically if the dynamics can be implemented
  for real time control.
• Coordinated Cartesian controller could be
  implemented instead of independent length
  controller for better performance.
• Future work should focus on the real time
  application as well as commercialization of the
  robot.