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