1. Footstep Planning Among Obstacles for Biped Robots James Kuffner et al. presented by Jinsung Kwon

2. Objective Planning safe navigation strategies for biped robots moving in obstacle- cluttered environments.

3. Biped Navigation Model Assumptions 1.The environment floor is flat 2.Obstacles are not moving and their positions and heights are known 3.Footstep positions and motions are pre-computed 4.Only the floor surface is allowed for foot placement

4. Biped Navigation Model Statically-stable Footstep

5. 1.Select placements along the edge of the reachable region at different relative foot angles 2.Select a few interior placements to move in tight areas 3.A few backward foot placements  15 placements for each foot

6. Biped Navigation Model Footstep Transition Trajectory Set of statically-stable motion trajectories for transitioning between footsteps are pre-calculated. 15x14 = 210 trajectories needed for each foot?

7. Biped Navigation Model Footstep Transition Trajectory Statically-stable intermediate postures, Q right and Q left, are introduced to reduce the number of transition trajectories.  15 for each foot Q 1  Q right  Q 2

8. Footstep Planning Algorithm Dynamic Programming Forward dynamic programming Greedy heuristic search instead of exhaustive search Priority queue of Search nodes (footprint placement + heuristic cost)

9. Footstep Planning Algorithm Dynamic Programming Obstacle Collision Fail if No more valid successor nodes if number of nodes in search tree exceeds pre- defined maximum limit

10. Footstep Planning Algorithm Cost Heuristic Function D(N Q ) = depth of N Q in the tree ρ(N Q ) = penalty to orientation change or backward step Х(N Q ) = min steps to traverse the straight- line distance to the center of the goal region w = weighting values  The heuristics favors straight path with less steps to the goal.

11. Footstep Planning Algorithm Obstacle Collision-checking Two-level collision checking 1. 2D polygon-polygon intersection test Outline of obstacle projection  Outline of footstep 2. 3D polyhedral minimum distance Check for footstep and trajectories

12. Footstep Planning Algorithm Obstacle Collision-checking Lazy-evaluation : Insert all successors and perform the minimum distance calculation after a node is removed from the priority queue  Reduce the num of collision check which is very expensive in calculation

13. Footstep Planning Algorithm Overview of Planner

14. Experiments 15 footsteps 20 floor obstacles 6,700 nodes in the search tree  Computed in 12 sec on 800MHz Pentium II w d = 1.0 w p = 0.2 w g = 1.0 determined experimentally

15. Experiments

16. Future works 1. Step upon the surface of obstacles 2. Handle environments with uneven terrain 3. Incorporate visual or sensor feedback during planning 4. Investigate different heuristics 5. Running on a real humanoid 6. Include dynamic stepping motions