Generic Smooth Motion For Robotics by Matthew Bott

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Generic Smooth Motion For RoboticsbyMatthew
Bott
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What does the title actually mean?
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What Is Meant By Generic?

• Any Robotic System
• The System Will Require
• Initial and goal configurations
• Knowledge of the current state of all variables
  in the initial and goal configurations
• Control variables which allow the current
  configuration state to be changed
• Forward kinematics

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What Is Meant By Smooth Motion?

• Smooth changes made to configuration variables at
  all times
• Smooth undulatory smooth

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How about an basic example?
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The Rolling Disc
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Hasnt this already been done?
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Advantages Over Rivals

• Does not require Inverse Kinematics
• These can be unknown or unreliable
• Does not use pre-set path segments
• Increases flexibility
• Produces a smooth path
• Generally a good thing
• Generic
• Can be used on most robots
• Handles Drift
• Dynamic path alterations

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What makes this difficult?
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Issues

• The end conditions do not define the solution
• Inverse kinematics unknown
• A planned path is insufficient
• We deal in control changes as opposed to controls
• Non-Holonomics
• Movement is restricted by physical
  characteristics
• Path planning restricted

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How do we aim to produce the system?
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Gradient Descent

• Smoothness may be used as a cost
• Any configuration can be assigned a cost value
• A control can then be changed by a small amount
• Giving a new configuration
• Giving a new cost value
• A cost vs. control gradient can then be
  calculated for that control

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• This process may be repeated for each control
• The controls may then be changed by an amount
  proportional to the gradient
• This changes the configuration to a more
  desirable one
• This process is in turn repeated until the goal
  is reached.
• We Do Not Need To Solve Equations
• The choice of cost measure is vital to the
  success of any gradient descent based method.

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Thats a lot to take in.
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(No Transcript)
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What will be used as Cost?
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Strain As A Cost Measure

• We are using strain as a cost measure
• Why?
• Strain is effectively curvature2
• Gradient descent requires a minimum
• A path of high curvature will be less smooth than
  one of low curvature
• Therefore a low strain path is a smooth path.

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How Does It Work?

• We can place a spline through the initial,
  current and goal states for each configuration
  variable
• And then take the sum of the strains of each
  spline
• This cost is then minimised and the path is
  improved

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Example Splines
Good
Bad
Goal
Current Attempt
Initial
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Where is all this going?
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The Grand Plan

• Prove theory on Rolling Disc
• Prove theory on more advanced problem
• Different Robots
• Physics such as Momentum
• Introduce Time Restraints
• Individual robot characteristics

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Acknowledgements

• Code and concept contributions from Dr Jon Lewis
• Supervised by Dr Mike Weir

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Any Questions?