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 , • Humanoid with uniform docking interfaces that allow transfer robots of mechanical forces and moments, electrical power, and communication throughout the robot. • Modular Beyond conventional actuation, sensing, and robots control typically found in fixed-morphology robots, self-reconfigurable robots are also able to deliberately change their own shape by • Educational rearranging the connectivity of their parts in order to adapt to new circumstances, perform new tasks, toy robots or recover from damage. • Sports The field of modular self-reconfigurable robotic systems addresses the design, fabrication, motion robots planning, and control of autonomous kinematic machines with variable morphology .
A taxonomy of architectures Lattice Chain / Tree Units are arranged and • Units are connected together • connected in some regular in a string or tree topology. pattern. This chain or tree can fold up • Control and motion can be • to become space filling, but executed in parallel. the underlying architecture is serial. Simpler reconfiguration, as • modules move to a discrete Continuity of articulation make • set of neighboring locations. them more versatile but computationally more difficult to represent and analyze and Easy to scale. • more difficult to control.
A taxonomy of architectures Self-assembly and the like Mobile Units do not move on their Units can autonomously • • maneuver around. own. They can individually execute They attach, communicate, • • coordinated movements and detach within fluidic or (including hook up to form agitated environments. complex chains or lattices).
Potential advantages 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).
Envisaged application areas 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.
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.
Challenges for the future 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 of 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.
How can CG help The problems The algorithms • Reconfiguring • Deterministic or stochastic • Locomotion • For specific prototypes or for general models • Self-repairing • With or without restrictions • (Self-organizing) on strength and velocity • Centralized o distributed With and without obstacles – With or without communication – Syncronous or asynchronous
How can CG help Main difficulties Main contributions Of theoretical nature: • Deadlocks • Possible strategies and their • Collisions applicability range • Characterization of solvable • Strategies in 3D problems / configurations • Complexity bounds: – Number of (synchronous) steps – Number de moves per module/unit – Amount of communication – Memory and computation requirements per unit
LATTICE-BASED ROBOTIC SYSTEMS
Abstract setting Moves of the units Connectivity Shape of the lattice • Pivoting • Square • Edge • Sliding • Vertex • Hexagonal • Squeezing • Triangular 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)
Abilities Tunneling Moving along the boundary
SOME RESULTS
EXPLOITING TUNNELING
The combing algorithm 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 spanning tree algorithm Specific for Crystalline-Telecube robots • Centralized • 2D and 3D • Proves universal reconfiguration • O ( n ) parallel steps and ϴ ( n 2 ) 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
Distributing the spanning tree algorithm Specific for Crystalline-Telecube robots • Distributed • 2D and 3D • Proves universal reconfiguration • O ( n ) parallel steps and ϴ ( n 2 ) 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 Total number of moves, Total number of messages, as a function of the number of as a function of the number of modules modules
How fast can the reconfiguration be?
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?
Boundary strategies
Recommend
More recommend
