SwarmCom: An infra-red-based mobile ad-hoc network for severely constrained robots
Stefan M Trenkwalder, Inaki Esnaola, Yuri Kaszubowski Lopes, Andreas Kolling and Roderich Groß
Abstract
Swarm robotics investigates groups of relatively simple robots that use decentralised control to achieve a common goal. While the robots of many swarm systems communicate via optical links, the underlying channels and their impact on swarm performance are poorly understood.
This paper models the optical channel of a widely used robotic platform, the e-puck. It proposes SwarmCom, a mobile ad-hoc network. SwarmCom has a detector that, with help of the channel model, was designed to adapt to the environment and nearby robots.
Experiments with groups of physical e-pucks show that SwarmCom outperforms the state-of-the-art infra-red communication software (libIrcom) in range (up to three times further), bit error rate (between 50%--63% lower), and throughput (up to 8 times higher). Using channel coding, the bit error rate can be further reduced at the expense of throughput.
SwarmCom could have profound implications for swarm robotics, contributing to system understanding and reproducibility, while paving the way for novel applications.
Channel coding in SwarmCom
Per default, SwarmCom provides three forms of channel coding that detects and corrects up to 0, 1, and 7 errors. To correct up to 0, 1, and 7 bits, a [n = 15, k = 15], [15, 11], and [15, 1] BCH code has been implemented, respectively. BCH codes allow a fast encoding with a generator matrix and fast decoding with syndrome decoding [1].
A codeword c ∈ Fn2 is a vector of n elements of a Galois field of two elements [F2 = GF(2)], which is sent between nodes of a network. Each codeword is generated by
c = G d
where d ∈ Fk2 and G ∈ Fk2×n are the transmission data vector and the generator matrix, respectively.
In this work, c is a systematic codeword that means that d is directly accessible. Therefore, no decoding is required to obtain the data, d, if it is error-free. To detect/correct potential errors, syndrome decoding is used.
A syndrome, s, is generated from a received codeword, r=c+e, by
s = H r,
0
⏞
s = H c + H e,
s = H e,
where H is a parity check matrix and e is an error vector. Because a syndrome is solely dependent on e, a syndrome-error translation table can be generated that indicates which errors need correcting (i.e., 0 = e + e and c = r + e).
Detection and correction of 0 errors
SwarmCom operates on a channel with small throughput and, therefore, it uses no channel coding as default to prioritise throughput.
As a result, the generator matrix is an identity matrix and no syndrome-error translation table is needed.
Detection and correction of one error
To correct up to one error, a [15, 11] BCH code has been implemented.
The generator matrix is
The parity check matrix is
The syndrome-error table is
Detection and correction of seven errors
To correct up to seven errors, a [15, 1] BCH code has been implemented. This code is also called repetition code as it repeats the same bit 15 times.
The generator matrix is
To avoid a longer execution time, a repetition code can be decoded by a majority decision, which reduces memory requirements and computation time in comparison to a syndrome decoding. If more bits are 11 than 00, the detector is deciding for 11 and vice versa.
Mobile robot experiments
Additional experiment results are presented that could not be included in the paper due to length restrictions.
Variation on the bit rate
As stated in the paper, Pi is not affected by the bit rate as shown in the graph.
The predictions p̂i are aligned with pi with a small offset, which does not indicate a systematic prediction error based on the bitrate.