Planning with differential constraints for LAGR

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Planning with differential constraints for LAGR

• Paul Vernaza

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Problem definition

• Given an obstacle map, current position, goal
  position, plan a path to goal satisfying
  differential constraints
• Solution must operate in real-time
• Robot wheeled, differential drive

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Current approach

• Combination of A and elastic band potential
• Advantage speed

• Disadvantage no consideration of dynamics

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Investigated approaches

• Coupled approach
• Incrementally build search graph from sampled
  controls, dynamics simulator
• Choose expansion points in A-like manner
• Decoupled approach
• Find collision-free path
• Track path via controller that satisfies
  differential constraints
• Advantages, disadvantages

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Decoupled path planning

• A elastic band a little awkward
• Can we directly and efficiently minimize elastic
  potential? Possibly
• Careful choice of obstacle potential
• Simulated gradient descent
• Alternatively, A with roadmap

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Path tracking with differential constraints

• Length-optimal vs. time-optimal
• Vehicle BVP solvers Reeds-Shepp, Balkcom-Mason,
  Chitsaz-LaValle
• Too unrealistic? No acceleration
• Other steering methods
• Learning a controller

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Planned deliverables

• New path planning approach
• Path tracker with differential constraints
• Hopefully, trial on real robot