1. Planning for Humanoid Robots Presented by Irena Pashchenko CS326a, Winter 2004

2. What is different? High Dimensionality ( >30 DOF ) Requires careful control to maintain static and dynamic stability.

3. Two problems ( I ) Given two statically-stable configurations, q init and q goal, generate a dynamically stable, collision-free trajectory from q init to q goal. Kuffner, et. al, Dynamically-stable Motion Planning for Humanoid Robots, 2000.

4. Two problems ( II ) In an obstacle-cluttered environment, walk toward a goal position. Kuffner, et. al, Footstep Planning Among Obstacles for Biped Robots, IROS 2001

5. Dynamically-Stable Motion Planning for Humanoid Robots, Kuffner, et. al, 2000. q init q near q target q new  q

6. Restricted Configuration Space C valid = C stable  C free C stable - set of statically stable configurations Given q init  C valid and q goal  C valid find find trajectory  s.t.  (t)  C valid Justification – statically stable trajectory can be transformed into dynamically-stable by arbitrarily slowing down the motion. gravity vector center of mass X(q) projection of X(q) area of support

7. Random-Exploring Trees ( LaValle ’98) Efficient randomized planner for high- dim. spaces with Algebraic constraints (obstacles) and Differential constraints (due to nonholonomy & dynamics) Biases exploration towards unexplored portions of the space Rendering of an RRT by James Kuffner

8. Modified RRT Build two trees from the start and goal configurations To obey dynamic constraints – introduce dynamic balance compensator in Connect/Extend phase q goal q init

9. Modified RRT - EXTEND( T, q ) Randomly select a collision-free, statically stable configuration q. q goal q init q

10. Modified RRT - EXTEND( T, q ) Select nearest vertex to q already in RRT (q near ). q goal q init q near q

11. Modified RRT - EXTEND( T, q ) Make a fixed-distance motion towards q from q near (q target ). q goal q init q near q target  q

12.  q Modified RRT - EXTEND( T, q ) Generate q new by filtering path from q near to q target through dynamic balance compensator and add it to the tree. q goal q init q near q new

13. RRT_CONNECT_STABLE( q init, q goal ) 1. T a.init( q init ); T b.init( q goal ); 2.For k = 1 to K do 3. q rand  RANDOM_STABLE_CONFIG (); 4.if not( EXTEND ( T a, q rand = Trapped ) 5.if( EXTEND ( T b, q new ) = Reached ) 6.return PATH( T a, T b ); 7. SWAP ( T a, T b ); 8.return Failure;

14. Distance Metric To avoid erratic movements from one step to the next. Encode in the distance metric:  (q, r ) =  w i ( q i – r i ) Higher relative weights to links with greater mass and proximity to trunk.

15. Random Static Postures It is unlikely that a configuration picked at random will be collision-free and statically-stable. Solution: generate a set of configurations, and randomly sample this set at run time.

16. Experimental Results Dynamically-stable planned trajectory for a crouching motion. Performance statistics ( N = 100 trials ). Task Description Computation Time Crouch near table minmaxavgstd 176620304133  3-12 min

17. Footstep Planning Among Obstacles for Biped Robots, Kuffner, et. al, 2001.

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

19. Simplifying Assumptions Statically-stable transition trajectories, pre-calculated Statically-stable intermediate postures  fewer trajectories Thus, problem is reduced to best-first search of feet placements (collision-free)

20. Best-First Search Initial Configuration Generate successor nodes from lowest cost node 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 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-level: 2D projections of foot and obstacle on walking surface 3D polyhedral minimum-distance determination (V- clip)

23. Experimental Results Path Computed in 12 seconds on an 800 MHz Pentium II

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

25. Conclusion 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 takes longer 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