Controlling modular robotic systems: some ideas from Computational - - PowerPoint PPT Presentation

Controlling modular robotic systems:

some ideas from Computational Geometry

Vera Sacristán

March 2015

If you ask Wikipedia what a robot is:

If you get to the section on modern robots:

And then read the section on the future of robotics (for civil use): Modular robots are usually composed of multiple building blocks of a relatively small repertoire, with uniform docking interfaces that allow transfer

• f mechanical forces and moments, electrical

power, and communication throughout the robot. Beyond conventional actuation, sensing, and control typically found in fixed-morphology robots, self-reconfigurable robots are also able to deliberately change their own shape by rearranging the connectivity of their parts in order to adapt to new circumstances, perform new tasks,

• r recover from damage.

The field of modular self-reconfigurable robotic systems addresses the design, fabrication, motion planning, and control of autonomous kinematic machines with variable morphology.

• Humanoid

robots

• Modular

robots

• Educational

toy robots

• Sports

robots

Lattice

• Units are arranged and

connected in some regular pattern.

• Control and motion can be

executed in parallel.

• Simpler reconfiguration, as

modules move to a discrete set of neighboring locations.

• Easy to scale.

A taxonomy of architectures

Chain / Tree

• Units are connected together

in a string or tree topology.

• This chain or tree can fold up

to become space filling, but the underlying architecture is serial.

• Continuity of articulation make

them more versatile but computationally more difficult to represent and analyze and more difficult to control.

• Units do not move on their
• wn.
• They attach, communicate,

and detach within fluidic or agitated environments.

Self-assembly and the like

A taxonomy of architectures

• Units can autonomously

maneuver around.

• They can individually execute

coordinated movements (including hook up to form complex chains or lattices).

Mobile

Versatility

Potentially more adaptive than conventional systems. The ability to reconfigure allows to adapt their morphology to tasks and environments.

Robustness

Units are interchangeable. Therefore, robots can replace faulty parts autonomously (self-repair).

Low cost

Scale economy on massive production of a few unit typologies A range of complex machines can be made from one set of modules (reuse).

Potential advantages

Replace human work and fixed-structure fixed-task robots

• Solving unpredicted tasks in unknown environments.
• Reusability in contexts of restricted volume and mass.
• Self-repairing in long term missions.

Bucket of stuff

Consumers of the future could have a container of self-reconfigurable

• modules. When needed, the consumer would call forth the robots to

achieve a task such as “clean the car” or “replace a bulb”. The robot would assume the shape needed and do the task.

Envisaged application areas

Challenges for the future

[1]

• M. Yim, W.-M. Shen, B. Salemi, D. Rus, M. Moll, H. Lipson, E.

Klavins, G. S. Chirikjian Modular Self-Reconfigurable Robot Systems: Challenges and Opportunities for the Future IEEE Robotics & Automation Magazine, 14(1):43-52, 2007. [2]

• S. Murata, H. Kurokawa

Self-Organizing Robots Springer Tracts in Advanced Robotics, Vol. 77, 2012.

Hardware design [1]

• Strength, precision, and robustness of bonding between modules.
• Motor power and precision, energetic efficiency of the modules.
• Dexterity of units and, therefore, flexibility of the system.

Planning and control algorithms [1]

• Massive and parallel locomotion, with and without obstacles.
• Optimal reconfiguration, both in time and energy.
• Handling failure modes: misalignments, dead units, erratic behavior of units.
• Computing optimal configurations for a given task and environment.
• Efficient and scalable asynchronous communication.

Mixed soft-hard [1]

• Fusing distributed access information from unit sensors for decision making.
• Interaction with obstacles in unknown environments.

Challenges for the future

Module size [2]

• Specially motors and sensors, both in speed and size.

Number of modules [2] Current maximum: 50 units of M-TRAN, 100 of ATRON.

• Production costs.
• Reliability of connections, communication, and power supply.
• Extend distributed strategies to be able to deal with such errors.

Self-reconfiguration o Self-assembly? [2] 1. Modules are already connected in the initial state, and the reconfigurations

• f the whole system are realized by incremental changes in the connections.

Advantages: reduced degrees of freedom. Disadvantages: algorithmic difficulties. 2. The system is assembled through random collisions among parts, induced by agitating a container. Advantages: desirable to face faults or unpredicted

• situations. Disadvantages: in 3D, unlikely to obtain the desired shape.

Challenges for the future

How can CG help

The problems

• Reconfiguring
• Locomotion
• Self-repairing
• (Self-organizing)

With and without obstacles

The algorithms

• Deterministic or stochastic
• For specific prototypes or

for general models

• With or without restrictions
• n strength and velocity
• Centralized o distributed

– With or without communication – Syncronous or asynchronous

Main difficulties

• Deadlocks
• Collisions
• Strategies in 3D

Main contributions

Of theoretical nature:

• Possible strategies and their

applicability range

• Characterization of solvable

problems / configurations

• Complexity bounds:

– Number of (synchronous) steps – Number de moves per module/unit – Amount of communication – Memory and computation requirements per unit

How can CG help

LATTICE-BASED ROBOTIC SYSTEMS

Abstract setting

Shape of the lattice

• Square
• Hexagonal
• Triangular

Moves of the units

• Pivoting
• Sliding
• Squeezing

The 3-dimensional setting is analogous We are currently working on a systematic analysis and classification of 3D prototypes (joint work with Irene de Parada) Connectivity

• Edge
• Vertex

Tunneling

Moving along the boundary

Abilities

SOME RESULTS

EXPLOITING TUNNELING

• Specific for Crystalline-Telecube robots
• Centralized
• 2D and 3D
• Proves universal reconfiguration
• O(n) parallel steps and ϴ(n) moves per module
• Within the union of the BB of the initial and goal shapes
• Requires linear strength
• Inspired in the sweep-line/plane paradigm
• G. Aloupis, S. Collette, M. Damian, E. D. Demaine, R. Flatland, S. Langerman, J.

O’Rourke, S. Ramaswami, V. Sacristán, S. Wuhrer. Linear reconfiguration of cube- style modular robots, Computational Geometry: Theory and Applications, 42(6- 7):652–663, 2009.

The combing algorithm

The combing algorithm

• Specific for Crystalline-Telecube robots
• Centralized
• 2D and 3D
• Proves universal reconfiguration
• O(n) parallel steps and ϴ(n2) moves per module
• Within the union of the initial and goal shapes
• Uses only constant strength
• Relays on spanning trees (main difficulty: deadlocks)
• G. Aloupis, S. Collette, M. Damian, E. D. Demaine, R. Flatland, S. Langerman, V.

Pinciu, J. O’Rourke, S. Ramaswami, V. Sacristán, S. Wuhrer. Efficient constant- velocity reconfiguration of crystalline robots, Robotica, 29(1):59-71, 2011.

The spanning tree algorithm

The spanning tree algorithm

• Specific for Crystalline-Telecube robots
• Distributed
• 2D and 3D
• Proves universal reconfiguration
• O(n) parallel steps and ϴ(n2) moves per module (but many less)
• Within the union of the initial and final shapes
• Uses only constant strength
• Grows the spanning tree in parallel (main difficulty: decrease

unnecessary moves)

• V. Sacristán, manuscript (simulation phase).

Distributing the spanning tree algorithm

Distributing the spanning tree algorithm

Distributing the spanning tree algorithm

Total number of moves, as a function of the number of modules Total number of messages, as a function of the number of modules

How fast can the reconfiguration be?

• Specific for Crystalline-Telecube robots
• Centralized
• 2D and 3D
• Proves universal reconfiguration
• O(log n) parallel steps and O(n log n) moves per module
• Within O(1) added to the union of the BBs initial and goal shapes
• Requires linear strength
• Geometric D&C strategy (main difficulty: keeping connection)
• G. Aloupis, S. Collette, E. D. Demaine, S. Langerman,, S. Ramaswami, V. Sacristán, S.
• Wuhrer. Reconfiguration of cube-style modular robots using O(log n) parallel moves,
• Proc. 19th International Symposium on Algorithms and Computation (ISAAC2008),

LNCS 5369, pp. 342-353, Springer-Verlag, 2008.

How fast can the reconfiguration be?

How fast can the reconfiguration be?

Boundary strategies

A general framework

• Abstract setting: (pivoting), sliding, and squeezing 2D tiles
• Centralized
• Proves universal reconfiguration except for edge-connected pivoting

tiles

• ϴ(n) moves per module
• Uses only constant strength
• Within the disjoint union of the initial and goal shapes +1
• Strongly sequential
• Extension to 3D?
• Inspired in the labyrinth strategy. Main difficulty: deadlocks.
• N. Benbernou, P. Bose, D. Bremner, E. Demaine, M. Demaine, F. Hurtado, V. Sacristán, P.
• Talaskian. Manuscript.
• C. Sung, J. Bern, J. Romanishin, D. Rus. Reconfiguration Planning for Pivoting Cube Modular

Robots, IEEE International Conference on Robotics and Automation (accepted), 2015.

Staying in-place

• Abstract setting: squeezing squares
• Centralized
• ϴ(n) moves per module
• Within the union of the initial and goal shapes +1 + melting BB

subset

• Uses only constant strength
• Strongly sequential
• Extension to 3D?
• Inspired in the labyrinth strategy. Main difficulty: holes.
• S. Ramaswami, V. Sacristán. Manuscript.

• Abstract setting: sliding cube
• Distributed
• 2D and 3D
• Proves universal reconfiguration
• O(n) parallel steps and ϴ(n) moves per module
• Within the union of the BB of the initial and goal shapes
• Requires linear strength
• Strictly synchronous (strong communication)
• Does not seem to extend to other shapes
• Inspired in the combing strategy
• O. Aichholzer, T. Hackl, V. Sacristán, B. Vogtenhuber, R. Wallner. Manuscript.

Distributed approach (1)

• Abstract setting: squeezing edge-connected squares and hexagons
• Distributed
• Proves universal reconfiguration
• ϴ(n) parallel steps
• ϴ(n) moves and O(n) communication per module
• Uses only constant strength
• Within the disjoint union of the initial and the goal shape
• Only in 2D
• Inspired in the labyrinth strategy (main difficulty: collisions and

deadlocks)

• F. Hurtado, E. Molina, S. Ramaswami, V. Sacristán. Distributed reconfiguration of 2D

lattice-based modular robotic systems. Autonomous Robots, 2015.

Distributed approach (2)

Distributed approach (2)

• 1. Self Organizing phase (static)

– Elect a leader (or have it from start) – Detect holes and elect a leader for each hole – Compute a spanning tree:

• Scan tree: all leaves lie in the boundary

– Assign DF-distance values (val, min, max)

• To distinguish the branches of the tree

– Activate leafs

• And cut them from the tree

Forwards (initial to strip)

– Follow the right hand rule – Never climb on active modules – Advance only on decreasing DF-values to get to the leader

• 2. Reconfiguring phase (movement)

Backwards (strip to goal)

+ Fill in DF-order. Obtain goal destination from leader, update relative position while advancing, stop when goal position is reached

Distributed approach (2)

Forwards (initial to strip)

– Activation conflicts

• Solution: priorities in rules

– Collisions

• Solution: priority by DF value

– Deadlocks

• Solution: jumping rules

Backwards (strip to goal)

+ Temporary bottlenecks + Closing holes

Conflicts!

Distributed approach (2)

http://www-ma2.upc.edu/vera/local-reconfiguration

Simulations

Dimension Parallel steps Moves per module Space Strength Combing 2D & 3D O(n) Θ(n) BBs O(n) Spanning tree 2D & 3D O(n) O(n2) In place O(1) Distributed ST 2D & 3D O(n) O(n2) but << In place O(1) Fast 2D & 3D O(log n) O(n log n) BBs+O(1) O(n)

Exploiting tunneling

Boundary strategies

Strategy Dimension Shapes Strength Space Moves per module Parallel steps General framework Centralized 2D All O(1) Disjoint union Θ(n)

• Flooding

Centralized 2D Square

• and

more? O(1) Union +1 + portion

• f BB

Θ(n)

• Combing

Distributed 2D & 3D Square O(n) Union

• f BBs

Θ(n) O(n) General 2d Distributed 2D All O(1) Disjoint union Θ(n) O(n)

• Boundary strategies in 3D

– Specially for the non-cubic case

• Extend and improve distributed algorithms

– Reduce communication (and deal with collisions!) – Forget synchrony

• Deal with faults
• The non-homogeneous setting
• Locomotion solutions not shape-dependent
• Explore discretization for chain robots
• Mobile robots

Still plenty to do

Controlling modular robotic systems:

some ideas from Computational Geometry

Thank you!

Vera Sacristán

March 2015