1. Multi-Limb Robots on Irregular Terrain

2. NASA/JPL’s LEMUR Robot

3. Only friction and internal degrees of freedom are used to achieve equilibrium

4. Other Climbing Robots Cutkosky, Stanford, 2004 NINJA II
Hirose et al, 1991
Free-climbing vs. aid-climbing
Talk about applications
Yim, PARC, 2002

5. Free climbing is a problem-solving activity
Each step is unique
Where to make contact?
Which body posture to take?
Which forces to exert?
Decisions at one step may affect the ability to perform future steps

6. ATHLETE (NASA/JPL)

7. HRP-2 (AIST, Japan)

8. Motion-Before-Stances Approach
Suitable when the terrain is mostly even and horizontal
Stances-Before-Motion Approach

9. Overview Given a terrain model and a goal location
Compute a motion path to reach the goal
Sensing
Planning
waypoint 1
candidate
contacts
non-gaited motion path
Robot

10. Overview Given a terrain model and a goal location
Compute a motion path to reach the goal
waypoint 2
Sensing
Planning
Execution
waypoint 1

11. Key Concept: Stance Set of fixed robot-environment contacts
3-stance of LEMUR
Set of fixed robot-environment contacts
Fs: space of feasible robot configurations at stance s
Contacts
Quasi-static equilibrium
No (self-)collision
Torques within bounds
Feasible motion at 4-stance

12. Inverse Kinematics Problem

13. Forward Kinematics q2 q1 d2 (x,y) d1 x = d1 cos q1 + d2 cos(q1+q2)
y = d1 sin q1 + d2 sin(q1+q2)

14. Inverse Kinematics q2 q1 d2 (x,y) d1 x2 + y2 – d12 – d22 q2 = cos-1
-x(d2sinq2) + y(d1 + d2cosq2)
y(d2sinq2) + x(d1 + d2cosq2)
q1 =

15. Inverse Kinematics Two solutions d2 (x,y) d1 x2 + y2 – d12 – d22
q2 = cos-1
x2 + y2 – d12 – d22
2d1d2
-x(d2sinq2) + y(d1 + d2cosq2)
y(d2sinq2) + x(d1 + d2cosq2)
q1 =
Two solutions

16. More Complicated Exampleq2
(x,y) d3 d2 q3 d1 q1
Redundant linkage
Infinite number of solutions
Self-motion space

17. More Complicated Exampleq2
(x,y) d3 d2 q3 d1 q1

18. More Complicated Exampleq2
(x,y) d3 d2 q3 d1 q1

19. Challenge
High-dimensional configuration space C (11 LEMUR, 42 for ATHLETE, 36 for HRP-2, 16 for Stanford robot)
Many possible contacts, hence many stances C Fs

20. Equilibrium ConstraintCM
Spend some time here explaining your problem in a bit more technical detail. (Basically, take this from Section 3.1 of your ISRR paper, leading up to the description of the One-Step Climbing Problem, which you can state with the next slide.)
Also, here is where you can mention the similarities to re-grasping in a multi-finger hand, and to motion-planning methods for track and legged robots.

22. backstep
highstep
lieback

23. Equilibrium Test in 3D Assuming infinite torque limits:
 Center of mass above convex support polygon

24. Equilibrium Test Assuming infinite torque limits:
 Center of mass above convex support polygon CM

25. Equilibrium Test Assuming infinite torque limits:
 Center of mass above convex support polygon

26. Transition Configuration
Zero force

27. Lazy Search

28. Lazy Search

29. Lazy Search

30. Lazy Search

31. Lazy Search

32. Lazy Search

33. Lazy Search

34. Configuration Sampling
Sample position/orientation of the chassis at random in restricted area
Solve IK for each limb making contact
Sample DOFs in free limb at random
Test equilibrium constraint

36. Need for Sensor Feedback