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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
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
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