Planning Among Movable Obstacles with Artificial

Constraints

Presented by: Deborah Meduna and Michael Vitus

by: Mike Stilman and James Kuffner

Motivation

http://www.cs.cmu.edu/~mstilman/mov/WAFR06-Planning.avi

Outline

• Problem Definition

• Main Topics– TRANSIT– TRANSFER

• Algorithm Overview– Artificial Constraints– Obstacle Identification– Constraint Resolution

• Results

Problem Definition

• Separate configuration spaces for different obstacle locations

• Obstacle movement restricted to robot motion• Motion planning restricted to the robot subspace

TRANSIT

• Moves the robot along a path while obstacles remain fixed

• Valid if and only if path is in the robot’s collision-free space

• Moves the robot and ONE obstacle along a path to a new state

• Valid if and only if:– The robot and obstacle paths are in collision-

free space– The robot and obstacle do not collide along

the path

TRANSFER

Problem Scope

• Monotone vs. Non-monotone– Monotone: each movable obstacle only needs

to be moved once– Non-monotone: can be broken into multiple

monotone plans

• Presented Planner is Linear-Monotone

Algorithm Overview (1)

• Plan a path through the cluttered environment– Allow translation through movable obstacles

• Determine the last obstacle that has to be moved

Algorithm Overview (2)

• Plan a path to Transfer the last obstacle and Transit the robot to the goal– Adds artificial constraints for earlier timesteps

• Resolve conflicts between movable obstacles and artificial constraints

Artificial Constraints

• Robot Transit operations create constraints on all obstacle configurations:– Robot motion along path sweeps volume V

Artificial Constraints

• Robot Transfer operations create constraints on non-moving obstacle configurations

Reverse Search - Motivation

• Assembly planning:– Much smaller branching factor due to actual

constraints

• Movable obstacles:– Final configuration not pre-determined

• Must use forward search

– Use reverse search for the ordering of which obstacles to move

– Transfer of the last obstacle is performed first• Adds artificial constraints

Obstacle Identification

• Identifies last obstacle to be manipulated prior to reaching the goal or sub-goal

• Utilize relaxed planner, Plast, allowing paths through movable obstacles

• Select OL, last obstacle in collision with path

Constraint Resolution

• Plans a Transfer path for OL and the following Transit path to the goal

• The two paths form artificial constraints– No obstacles scheduled earlier in time than OL

can be within the two swept volumes

Example

• Show movie from CMU

http://www.cs.cmu.edu/~mstilman/mov/WAFR06-Execution.avi

Results

• Figures 1, 2 and 4 not solve-able by existing planners

1

2

4

3

Conclusions

• Future Work:– Include accessibility constraints– Incorporate heuristics for generating Transfer

paths