View
223
Download
0
Tags:
Embed Size (px)
Citation preview
Generalized Standard Foot Trajectory for a Quadruped Walking
Vehicle
Generalized Standard Foot Trajectory for a Quadruped Walking
Vehicle(Shigeo Hirose, Osamu Kunieda - 1991)(Shigeo Hirose, Osamu Kunieda - 1991)
Presentation: Guillaume Poncin
Titan IVTitan IV
Titan VIITitan VII
GoalsGoals
•Find a motion plan for quadruped walking robots
•Arbitrary reachable range of the legs
•Uneven surfaces
•Inclined surfaces
Previous workPrevious work
• Assumed that:
Body remains horizontal
Reachable range is a rectangular prism
Each leg trajectory passes through the center Ci
Instead: more complex modelInstead: 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
AnalysisAnalysis
• 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
Diagonal Triangle ExchangeDiagonal 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
Generalized Standard Foot Trajectories Method
Generalized Standard Foot Trajectories Method
1. Project the gait scheme on a horizontal plane2. Select effective searching areas3. Select the walking type4. Produce stroke contours graph5. Select the longest stroke6. Determine the foot trajectories
Let’s look at an example…
1. Projection of reachable areas
1. Projection of reachable areas
2.Effective areas2.Effective areas
3.Walking type3.Walking type
(crab-walking gait, x-type)
4. Getting the stroke contour graph
4. Getting the stroke contour graph
Center regions of the graph are the potential Exchange Points that allow the longest strokes
5. Selection of the longest stroke
5. Selection of the longest stroke
• For all possible yoke angles :
Look for longest stroke feasible by each pair of opposite feet
Compare the two longest, take the smaller
6. Determination of foot trajectories
6. Determination of foot trajectories
Here choose for 1 and 3, then 2 and 4 are somewhat free
Slope ClimbingSlope Climbing
• We use the same planner
• Called the “reversed trapezoid gait”
Conclusion of the paperConclusion of the paper
•General method to generate foot trajectories for quadruped robots
•Validated by computer simulation
•Applied on actual robots: Titan III and IV
Extensions ?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)
More difficult environmentMore difficult environment
Some regions are impossible to cross.
Idea: different planning levelsIdea: 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.
ResultResult
Top view of a plan for a six-legged robot in the previous configuration space