Three-Dimensional Construction with Mobile Robots and Modular Blocks

Written By: Justin Werfel and Radhika Nagpal

Presented By: Russell Winkler

Self-Reconfigurable Mobile Robots

• Designed For– Frequent Reconfiguration• Locomotion over different terrains• Three-dimensional playback

• Not Designed For– Static Structures• Bridges• Tables

Goal

“To be able to deploy an unspecified number of robots into an obstacle-free workspace, along with a supply of free blocks and a single-block ‘seed’ for the structure, and have construction

proceed without further intervention.”

Assumptions

• Weightless environment• Active units may move freely in any direction

and in three dimensions• All blocks are cubic• Blocks contain self aligning connectors• Once a block is attached it is never detached

The Units

• Passive Units– No mobility– Limited communication• Locally with physically attached neighbors• To active units

– Optimized for structural stability• Active Units– Manipulators of passive units– Do not communicate with other active units

The Passive Units (Blocks)

“seed” block

• The “seed” block• Knowledge of “shape map”• Coordinates (0,0,0)

I need blocks here• The seed block knows where blocks need to be attached in the local reference of it’s 6 sides and communicates this to the active units (robots)

• When the robots connects a new block, the block receives the shape map, it’s coordinates, and other relevant block information

Other Blocks placed in its row

Other Blocks placed in its plane

Information is passed back to other blocks regarding the newly filled position

Block Rules

• The Shape Map Rule – A block cannot be placed at any site that does not

match the shape map (duh)

Block Rules

• The Row Rule– A contiguous group of blocks in the same row can

start with its first block attached anywhere, but successive blocks must be attached contiguously from there

Blocks can be attached to EITHER of these spots, but not both

More Block Rules

• The Plane Rule– A contiguous group of blocks in the same plane

can originate anywhere but thereafter must grow from that point of origin

If this entire face has been designated to add blocks to, A block may be added to ANY of the faces, but after the first addition, blocks must be added from that first block

The Rules in ActionThe Desired Shape

ILLEGAL!

ILLEGAL!

ILLEGAL!

The shape map does not specify that a block should be placed here

Violates the row rule

Violates the plane rule

The Rules in Action

• Following these rules will provably result in the reliable construction of any structure meeting these criteria– There are no loops

– No more than two “couches”• Kind of

– Any close parts• Like a U shape

Back to Blocks• Seed block with 6 open faces• Add an additional block, now both

blocks have 5 open faces• Faces with an attached block are

designated as done• Add more blocks, the center four

have 4 open faces and the outer blocks have 5 open faces

• Add a block in another row and the blocks send signals informing other blocks that their faces are no longer open.

• Faces that are not involved in the shape map are immediately designated as closed

Faces are now “closed”

Faces are now “corners”

Back to Blocks• Each block maintains information

about all 6 faces• Each face maintains information on 3

state variables– A plane “P” that is parallel to the face– Two rows that extend out from where a

block attached to the face would go

• Information and updates are only passed to blocks that are involved in the change of a particular row or plane to minimize communication traffic– This is based on the blocks coordinates

• If all three state variables for a particular face are “open” or “corner” then a block may be attached to that face

The Cost of Communication

• Communication further than a single block is rare– Only when the first block is placed in a new row is there a

need to update more than just the neighboring blocks

• Communication time grows linearly with the size of the project

Thusly!

Enough About Blocks!

A robot algorithm is required to place blocks in such a way that

Every face is visited at least oncePreviously closed faces are re-visitedAttempt to reduce communication costsAttempt to reduce robot movement costs (time)

• Algorithms must me measured according to• Total distance travelled by all robots• The number of messages sent from blocks to robots• The number of messages sent from physically connected blocks

Robot Algorithms – Random Walk

• While the structure is not complete, bring a block to the structure

• If the current face is closed, randomly move to another adjacent face

• Repeat until block has been placed• Go get another block

Robot Algorithms – Random Walk

• Pros– Guaranteed to finish (if left long enough)– Requires little inter-block communication

• Cons– Extremely time intensive– Requires more robot movement than the other

algorithms– Requires a lot of block-robot communication

Robot Algorithms – Systematic Search

• Robots move systematically along the perimeter of the structure

• Robots first move along the perimeter on a single plane

• If no open or corner face was found on that plane, the robot navigates to the next plane

• When the robot finds a face for the block, it will retrieve another block and return to the previous position to continue its new search

Robot Algorithms – Systematic Search

• Pros– Guarantees the structure will be complete– Involves less revisiting of previously covered faces

potentially reducing the required time– Requires little inter-block communication

• Cons– Much more complicated algorithmically– Requires more communication between block and

robot– Requires state memory on the Robot

Robot Algorithms – Gradient-Following

• When a robot with a block approaches the structure, the robot queries the block for the closest available open face

• The block provides the robot with a coordinate for the closest open face

• The robot navigates to the open face and attaches the block

Robot Algorithms – Gradient-Following

• Pros– Requires the least amount of total distance for the

robots to travel– Requires the least amount of communication

between robot and block• Cons– Requires increased inter-block communication– Requires blocks to track gradient information

The Comparison

D – Distance

M1 – Block-Robot Communication

M2 – Inter-Block Communication

How Many Robots?

• It depends…– Size of the project– Size and ability of the robot being used

• To many and they interfere with each other• To few and time is wasted• Depending on the Project– Develop a density of how many robots should be working on

the particular project according to how many open faces are available

– The more open faces on the structure, the more robots can be deployed

Conclusions

• Rules make programming simple• Subdividing the problem into separate tasks

handled by unique pieces makes life easier• Future possibilities– Include structures that are currently unavailable

(loops, couches, etc)– Specialized systems could require specialized rules

that allow the row and plane rule to be less restrictive

Questions?