Self-Reconfiguration in Two-Dimensions via Active Subtraction with Modular Robots

Matthew D. Hall, Anil Ozdemir, Roderich Gross


Modular robotic systems comprise groups of physically connected modules which can be reconfigured to create morphologies that suit an environment or task. One method of reconfiguration is via subtraction, where extraneous modules disconnect from an initial configuration, before being removed by external intervention. In this paper, we consider an approach to reconfiguration in two dimensions, here termed active subtraction, in which unwanted modules traverse a configuration in order to remove themselves safely, without the need for external intervention, making it a form of self-reconfiguration. We present a sequential solution that selects suitable extraneous modules that then remove themselves, one by one. We also present a parallel solution that, while being more computationally demanding, allows multiple modules to move simultaneously. Both solutions are proven to (i) be correct for any given non-hollow structure, and (ii) require, in the worst case, quadratic time proportionally to the number of modules. Simulation studies demonstrate that both solutions work effectively for specified and randomly generated desired configurations with hundreds of modules, and reveal a non-monotonic dependence between the performance and the percentage of modules to be removed. This work demonstrates active subtraction as a viable method of self-reconfiguration, without the need for heuristics or stochasticity, and suggests its potential for application in real-world systems.

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This is a paper describing self-reconfiguration by subtraction for sliding cube module style motion. Overall it is interesting and a good contribution, but the authors need to be more explicit about assumptions made. Stability of structure during reconfiguration? You say there is gravity and a floor, but there is nothing about the stability of the structure during reconfiguration. -need to add assumption of known coordinates/sensors. You use a leader to generate a cooridnate system via message passing, but the election of that leader needs to know some position information (it is west most on ground) How is west sensed? How is direction (n,s,e,w) known? Is it able to sense that it is contacting / communicating to the ground? -be clear that you are looking at 2d case. -how is synchronization implicit with the assumptions you made? Message latency and delay could still cause asynchronization even if all robots have an internal clock. “ We hypothesize that the problem of determining an optimal order is NP hard” is not justified, please remove or justify -how is timing enforced with parallel active subtraction? This requires all modules to move according the the leaders clock, but they only have a communication channel to the leader with unknown latency, and no synchronization mechanism or assumption has been made. What are your assumptions about initial configuration? I think you need to assume a fully packed rectangle, otherwise robots not connected to the ground could be disconnected who are not connected to the ground. For example, in figure 6 left, if we added 2 modules to the top row of the initial configuration on the right side, forming a cantilever. The leftmost of these 2 modules would move first, disconnecting the second module from the shape and not on the ground. -- on a second read it looks like you do make the assumption, but it is not clearly stated, you say : “A modular robot of rectangular shape is situated (i.e., standing) on the ground, extending upwards”.. Please reword to be “a group of modules in a filled rectangular shape” - this is a strong assumption, and you need to make it clear.