1. Generalized Standard Foot Trajectory for a Quadruped Walking Vehicle (Shigeo Hirose, Osamu Kunieda - 1991) Presentation: Guillaume Poncin

2. Titan IV

3. Titan VII

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

5. Previous work Assumed that: Body remains horizontal Reachable range is a rectangular prism Each leg trajectory passes through the center C i

6. 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

7. 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

8. 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

9. Generalized Standard Foot Trajectories Method 1.Project the gait scheme on a horizontal plane 2.Select effective searching areas 3.Select the walking type 4.Produce stroke contours graph 5.Select the longest stroke 6.Determine the foot trajectories Let’s look at an example…

10. 1. Projection of reachable areas

11. 2.Effective areas

12. 3.Walking type (crab-walking gait, x-type)

13. 4. Getting the stroke contour graph Center regions of the graph are the potential Exchange Points that allow the longest strokes

14. 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

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

16. Slope Climbing We use the same planner Called the “reversed trapezoid gait”

17. 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

18. 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)

19. More difficult environment Some regions are impossible to cross.

20. 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.

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