Three-Dimensional Construction with Mobile Robots and Modular Blocks presents a system for constructing 3D structures using mobile robots and modular blocks. Passive blocks contain self-aligning connectors and communicate locally to maintain a "shape map" for construction. Active robots manipulate blocks and do not communicate. The system uses simple rules for block placement to reliably build any structure meeting criteria of no loops and limited overhangs. Various robot algorithms are evaluated for building structures with the lowest costs.

2. Three-Dimensional Construction with Mobile Robots and Modular Blocks Written By: Justin Werfel and RadhikaNagpal Presented By: Russell Winkler

3. Self-Reconfigurable Mobile Robots Designed For Frequent Reconfiguration Locomotion over different terrains Three-dimensional playback Not Designed For Static Structures Bridges Tables

4. 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.”

5. 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

6. 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

8. Knowledge of “shape map”

10. Block Rules The Shape Map Rule A block cannot be placed at any site that does not match the shape map (duh)

11. 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

12. 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

13. The Rules in Action The Desired Shape The shape map does not specify that a block should be placed here ILLEGAL! Violates the plane rule ILLEGAL! ILLEGAL! Violates the row rule

14. 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

16. Add an additional block, now both blocks have 5 open faces

17. Faces with an attached block are designated as done

18. Add more blocks, the center four have 4 open faces and the outer blocks have 5 open faces

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

20. Faces that are not involved in the shape map are immediately designated as closedFaces are now “closed” Faces are now “corners”

21. 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

22. 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!

24. Total distance travelled by all robots

25. The number of messages sent from blocks to robots

27. 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

28. 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

29. 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

30. 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

31. 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

32. The Comparison D – Distance M1 – Block-Robot Communication M2 – Inter-Block Communication

33. 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

34. 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

35. Questions?