1. Presented By: Huy Nguyen Kevin Hufford
Humanoid Robots
Presented By:
Huy Nguyen
Kevin Hufford

3. Two problems
Given two statically-stable configurations, qinit and qgoal, generate a dynamically stable, collision-free trajectory from qinit to qgoal.
Kuffner, et. al, Dynamically-stable Motion Planning for Humanoid Robots, 2000.
In an obstacle-cluttered environment, walk toward a goal position.
Kuffner, et. al, Footstep Planning Among Obstacles for Biped Robots, IROS 2001

4. Dynamically-stable Motion Planning for Humanoid Robots
Kuffner, et. al; 2000.

5. Statically-stable postures
area of support
gravity vector
center of mass X(q)
projection of X(q)
A configuration q is statically-stable if the projection of X(q) along the gravity vector lies within the area of support.

6. Modified Rapidly-exploring Random Tree (RRT)
RRT introduced by LaValle ’98.
Similar to SBL.
Randomly extend two trees from the start and goal configurations towards each other.
Bias exploration towards unexplored portions of the space.
Not clear how this is done in high-dimensional space.
Modified version similar to nonholonomic planning.
Path must obey dynamic constraints.

7. Modified RRT q
qinit
qgoal
Randomly select a collision-free, statically stable configuration q.

8. Modified RRT Select nearest vertex to q already in RRT (qnear). q
qinit
qnear
qgoal
Select nearest vertex to q already in RRT (qnear).

9. Modified RRT q
qtarget
qinit
qnear
qgoal
Make a fixed-distance motion towards q from qnear (qtarget).

10. Modified RRT q
qtarget
qinit
qnew
qnear
qgoal
Generate qnew by filtering path from qnear to qtarget through dynamic balance compensator and add it to the tree.

11. Distance Metric
Don’t want erratic movements from one step to the next.
Encode in the distance metric:
Assign higher relative weights to links with greater mass and proximity to trunk.

12. Random statically-stable postures
It is unlikely that a configuration picked at random will be collision-free and statically-stable.
Solution: Generate a set of statically-stable collision-free configurations, and randomly sample from this set at run time.

13. Random statically-stable postures
Generate a random configuration.
Fix head and arm positions to reduce dimensionality and improve planning efficiency.
Fix right leg and use inverse kinematics to position left foot. If successful (stable and collision-free), save this point.
Repeat step 2 for the left leg.
Double the number of samples by leveraging the symmetry of the humanoid, and mirroring the configurations generated in steps 2 and 3.

14. Statically-stable postures

15. Results Dynamically-stable planned trajectory for a crouching motion
Performance statistics (N = 100 trials)

16. Footstep Planning Among Obstacles for Biped Robots
Kuffner, et. al;
IROS 2001

17. Simplifying Assumptions
Non-moving obstacles of known position and height
Foot placement only on floor surface (not on obstacles)
Pre-computed set of footstep placement positions (15)

18. Simplifying Assumptions
Statically-stable transition trajectories
Statically-stable intermediate postures
Thus, problem is reduced to best-first search of foot placements (while considering environment collision)

19. Best-First Search Tree
qinit 2 5 8 12
Generate successor nodes from qinit
Assign cost to each node

20. Best-First Search Tree
qinit 2 5 8 12 8 6
Generate successor nodes from lowest cost node
Assign costs for successor nodes
Prune nodes that result in collisions
Continue until a generated successor node falls in goal region

21. Cost Heuristic Cost of path taken so far Cost estimate to reach goal
Depth of node in the tree
Penalties for orientation changes and backward steps
Cost estimate to reach goal
Straight-line steps from current to goal
Empirically-determined weighting factors

22. Obstacle Collision Checking
Two-levels
2D projections of foot and obstacle on walking surface
3D polyhedral minimum-distance determination (V-clip)

23. Results

24. Future Work Allow stepping on obstacles
Environments with uneven terrain
Incorporate sensor feedback
Different heuristics
Run algorithm on real humanoid
Dynamic stepping motions (including hopping or jumping)

25. Conclusions General task involves a high-dimensional space
Use random planning [Kuffner 2000]
Restrict motion to a finite set [Kuffner 2001]
Randomized planner is more general, and could solve [Kuffner 2001] problem, but would take more time
Could integrate the two planners to form a more efficient, comprehensive planner
Use 2001 planner to move to goal location, and 2000 planner to achieve final posture