Positional Encoding by Robots with Non-rigid Movements
Consider a set of autonomous computational entities, called robots, operating inside a polygonal enclosure (possibly with holes), that have to perform some collaborative tasks. The boundary of the polygon obstructs both visibility and mobility of a robot. Since the polygon is initially unknown to the robots, the natural approach is to first explore and construct a map of the polygon. For this, the robots need an unlimited amount of persistent memory to store the snapshots taken from different points inside the polygon. However, it has been shown by Di Luna et al. [DISC 2017] that map construction can be done even by oblivious robots by employing a positional encoding strategy where a robot carefully positions itself inside the polygon to encode information in the binary representation of its distance from the closest polygon vertex. Of course, to execute this strategy, it is crucial for the robots to make accurate movements. In this paper, we address the question whether this technique can be implemented even when the movements of the robots are unpredictable in the sense that the robot can be stopped by the adversary during its movement before reaching its destination. However, there exists a constant \(\delta > 0\), unknown to the robot, such that the robot can always reach its destination if it has to move by no more than \(\delta \) amount. This model is known in literature as non-rigid movement. We give a partial answer to the question in the affirmative by presenting a map construction algorithm for robots with non-rigid movement, but having O(1) bits of persistent memory and the ability to make circular moves.
KeywordsAutonomous robots Map construction Non-rigid movement Polygon with holes Look Compute-Move cycle Distributed algorithm
The first three authors are supported by NBHM, DAE, Govt. of India, CSIR, Govt. of India and UGC, Govt. of India, respectively. We would like to thank the anonymous reviewers for their valuable comments which helped us improve the quality and presentation of the paper.
- 1.Agathangelou, C., Georgiou, C., Mavronicolas, M.: A distributed algorithm for gathering many fat mobile robots in the plane. In: ACM Symposium on Principles of Distributed Computing, PODC 2013, Montreal, QC, Canada, 22–24 July 2013, pp. 250–259 (2013). https://doi.org/10.1145/2484239.2484266
- 3.Bose, K., Adhikary, R., Kundu, M.K., Sau, B.: Arbitrary pattern formation on infinite grid by asynchronous oblivious robots. In: Das, G.K., Mandal, P.S., Mukhopadhyaya, K., Nakano, S. (eds.) WALCOM 2019. LNCS, vol. 11355, pp. 354–366. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-10564-8_28CrossRefGoogle Scholar
- 4.Bose, K., Adhikary, R., Kundu, M.K., Sau, B.: Positional encoding by robots with non-rigid movements. CoRR abs/1905.09786 (2019). http://arxiv.org/abs/1905.09786
- 10.Luna, G.A.D., Flocchini, P., Santoro, N., Viglietta, G., Yamashita, M.: Meeting in a polygon by anonymous oblivious robots. In: 31st International Symposium on Distributed Computing, DISC 2017, pp. 14:1–14:15, Vienna, 16-20 October 2017. https://doi.org/10.4230/LIPIcs.DISC.2017.14