Generalized Standard Foot Trajectory for a Quadruped Walking Vehicle

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Generalized Standard Foot Trajectory for a
Quadruped Walking Vehicle

• (Shigeo Hirose, Osamu Kunieda - 1991)

Presentation Guillaume Poncin
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Titan IV
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Titan VII
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Goals

• Find a motion plan for quadruped walking robots
• Arbitrary reachable range of the legs
• Uneven surfaces
• Inclined surfaces

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Previous work

• Assumed that
• Body remains horizontal
• Reachable range is a rectangular prism
• Each leg trajectory passes through the center Ci

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Instead more complex model

• Arbitrary reaching range
• Horizontal reachable area between 2 planes
• Each foot supports the robot at least 75 of the
  time
• Center of gravity moves at constant speed

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Analysis

• Static Stable Condition
• The projection of the center of gravity is in
  the polygon of support of the legs
• Evaluation criterion
• Maximize the stroke length of each foot

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Diagonal Triangle Exchange

• Ideas
• Exchange the supporting foot triangle
  successively during motion
• Keep the center of gravity inside the triangles
• Individual foot trajectories of same length and
  direction
• crab walk

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Generalized Standard Foot Trajectories Method

• Project the gait scheme on a horizontal plane
• Select effective searching areas
• Select the walking type
• Produce stroke contours graph
• Select the longest stroke
• Determine the foot trajectories
• Lets look at an example

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1. Projection of reachable areas
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2.Effective areas
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3.Walking type
(crab-walking gait, x-type)
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4. Getting the stroke contour graph
Center regions of the graph are the potential
Exchange Points that allow the longest strokes
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5. Selection of the longest stroke

• For all possible yoke angles q
• Look for longest stroke feasible by each pair of
  opposite feet
• Compare the two longest, take the smaller

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6. Determination of foot trajectories
Here choose for 1 and 3, then 2 and 4 are
somewhat free
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Slope Climbing

• We use the same planner
• Called the reversed trapezoid gait

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Conclusion of the paper

• General method to generate foot trajectories for
  quadruped robots
• Validated by computer simulation
• Applied on actual robots Titan III and IV

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Extensions ?

• This was only about getting the gait right on a
  fairly flat surface
• How do we plan for complete motion in more
  difficult environment ?
• (See Motion planning of legged vehicles in an
  unstructured environment, C. Eldershaw M. Yim)

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More difficult environment
Some regions are impossible to cross.
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Idea different planning levels

• High level PRM / Configuration Space
• (using cell decomposition)
• Foot-level planner (using a heuristic)
• Loop back from low to high if the path is found
  to be impossible.

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Result
Top view of a plan for a six-legged robot in the
previous configuration space