Footstep Planning Among Obstacles for Biped Robots

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 ModelAssumptions

• The environment floor is flat
• Obstacles are not moving and their positions and
  heights are known
• Footstep positions and motions are pre-computed
• Only the floor surface is allowed for foot
  placement

4
Biped Navigation ModelStatically-stable Footstep
5
Biped Navigation ModelStatically-stable Footstep

• Select placements along the edge of the reachable
  region at different relative foot angles
• Select a few interior placements to move in tight
  areas
• A few backward foot placements
• ? 15 placements for each foot

6
Biped Navigation ModelFootstep 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 ModelFootstep Transition
Trajectory

• Statically-stable intermediate postures, Qright
  and Qleft, are introduced to reduce
• the number of transition trajectories.
• ? 15 for each foot

Q1 ? Qright ? Q2
8
Footstep Planning AlgorithmDynamic Programming

• Forward dynamic programming
• Greedy heuristic search instead of exhaustive
  search
• Priority queue of Search nodes
• (footprint placement heuristic cost)

9
Footstep Planning AlgorithmDynamic Programming

• Fail
• if No more valid successor nodes
• if number of nodes in search tree exceeds
  pre-defined maximum limit

Obstacle Collision
10
Footstep Planning AlgorithmCost Heuristic
Function

• D(NQ) depth of NQ in the tree
• ?(NQ) penalty to orientation change or
• backward step
• ?(NQ) 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 AlgorithmObstacle
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 AlgorithmObstacle
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 AlgorithmOverview of Planner
14
Experiments

• 15 footsteps
• 20 floor obstacles
• 6,700 nodes in the search tree
• ? Computed in 12 sec on 800MHz Pentium II
• wd 1.0
• wp 0.2
• wg 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