Footstep Planning Among Obstacles for Biped Robots

James Kuffner et al.

presented by Jinsung Kwon

Objective

Planning safe navigation strategies

for biped robots moving in obstacle-

cluttered environments.

Biped Navigation ModelAssumptions

1. The environment floor is flat2. 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

Biped Navigation ModelStatically-stable Footstep

Biped Navigation ModelStatically-stable Footstep

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

Biped Navigation ModelFootstep Transition Trajectory

Set of statically-stable motion trajectories for transitioning between footsteps are pre-

calculated.

15x14 = 210 trajectoriesneeded for each foot?

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

Footstep Planning Algorithm

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

Footstep Planning Algorithm

Dynamic Programming

ObstacleCollision

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

Footstep Planning Algorithm

Cost Heuristic Function

D(NQ) = depth of NQ in the treeρ(NQ) = penalty to orientation change or backward stepХ(NQ) = min steps to traverse the straight- line distance to the center of the goal regionw = weighting values

The heuristics favors straight path with less steps to the goal.

Footstep Planning Algorithm

Obstacle Collision-checkingTwo-level collision checking1. 2D polygon-polygon intersection

test Outline of obstacle projection Outline of footstep2. 3D polyhedral minimum distance Check for footstep and trajectories

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

Footstep Planning Algorithm

Overview of Planner

Experiments

15 footsteps20 floor obstacles6,700 nodes in the search tree Computed in 12 sec on 800MHz Pentium II wd = 1.0 wp = 0.2 wg = 1.0determined experimentally

Experiments

Future works

1. Step upon the surface of obstacles2. Handle environments with uneven terrain3. Incorporate visual or sensor feedback during planning4. Investigate different heuristics5. Running on a real humanoid6. Include dynamic stepping motions