Motion Control

1
Motion Control
2
Motion Control

• Determine the time history of the generalized
  forces to be developed by the joint actuators so
  as to guarantee execution of the commanded task
  while satisfying given transient and steady-state
  requirements

3
The Control Problem

• The goal
• reference tracking disturbance rejection
• Negative feedback control
• System parameters variations
• Nonmeasurable disturbance

4
The Control Problem

• Joint space control problem

Open loop
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The Control Problem

• Operational space control problem

Difficult to measure directly
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Joint Space Control

• Your control theory textbook
• Linear time-invariant SISO system
• Robot manipulator
• MIMO
• Nonlinear
• Strong coupling

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Joint Space Control

• Motion equations of manipulator
• Let qm denote the joint actuator displacement
• Let tao_m denote the actuator driving torques

where Kr is diagonal
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Joint Space Control
Diagonal constant matrix
Configuration dependent term
Linear de-coupled
Nonlinear coupled
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Nonlinear coupled
linear decoupled
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Joint Space Control

• Decentralized control
• treat nonlinear interacting term d as disturbance
• high gear reduction ratio and/or
• limited performance in terms of velocity and
  acceleration
• Centralized control
• compensate for nonlinear coupling terms
• direct drive and/or
• large operational speeds required

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Two-Link Planar Robot
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Independent Joint Control

• Regard the manipulator as formed by n independent
  systems (n joints)
• control each joint as a SISO system
• treat coupling effects as disturbance

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Independent Joint Control

• Assuming that the actuator is a rotary dc motor

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Feedback Control
15
Position and Velocity Feedback
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Position and Velocity Feedback

• Choose the zero of the controller to cancel the
  real pole by setting

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Position and Velocity Feedback

• Root locus

Kp determines the radius, Kv can be chosen to set
the location
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Position and Velocity Feedback

• The closed loop transfer function

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Position and Velocity Feedback

• The closed loop disturbance transfer function
• disturbance rejection factor
• output recovery time

20

Two-Link Planar Robot
Determine Kp and Kv and Tv