Immuno-inspired robotic applications: a review
Ali Razaa,b, Benito R. Fernandeza
aDepartment of Mechanical Engineering, University of Texas at Austin, USA
bDepartment of Mechatronics & Control Engineering, University of Engineering & Technology, Lahore, Pakistan
Abstract
Artificial immune systems primarily mimic the adaptive nature of biological immune functions.
Their ability to adapt to varying pathogens makes such systems a suitable choice for various
robotic applications. Generally, AIS-based robotic applications map local instantaneous sensory
information into either an antigen or a co-stimulatory signal, according to the choice of repre-
sentation schema. Algorithms then use relevant immune functions to output either evolved anti-
bodies or maturity of dendritic cells, in terms of actuation signals. It is observed that researchers,
in an attempt to solve the problem in hand, do not try to replicate the biological immunity but
select necessary immune functions instead, resulting in an ad-hoc manner these applications
are reported. Authors, therefore, present a comprehensive review of immuno-inspired robotic
applications in an attempt to categorize them according to underlying immune definitions. Im-
plementation details are tabulated in terms of corresponding mathematical expressions and their
representation schema that include binary, real or hybrid data. Limitations of reported applica-
tions are also identified in light of modern immunological interpretations. As a result of this
study, authors suggest a renewed focus on innate immunity and also emphasize that immuno-
logical representations should benefit from robot embodiment and must be extended to include
modern trends.
Keywords:
Artificial immune systems, Mobile robots, Idiotypic network, Clonal selection, Danger theory
1. Introduction
The biological immune system (BIS), consisting of a large number of cells and molecules,
works to protect its host from invading infectious agents, known as pathogens. Immune responses
to invading pathogens are triggered by the recognition of antigen. Adaptive part of BIS handles
the invading bacterium or viruses by adapting to varying pathogens, in an antigen-specific man-
ner. Whereas, the innate immune system handles common bacteria in a non-antigen-specific
manner. Immunologists are still trying to fully interpret the working of BIS, which is based on a
wide range of cells and molecules and their interconnections. Resultantly, a number of models
have been presented over the years to describe its working as a whole along with the functions of
each cell-type. It is because of the fact that BIS exhibits intelligence in terms of self-organization,
Email addresses: ali.raza@utexas.edu (Ali Raza), benito@mail.utexas.edu (Benito R. Fernandez)
Preprint submitted to Applied Soft Computing
November 14, 2018
arXiv:1202.4261v1  [cs.RO]  20 Feb 2012
learning, adaptation, recognition, robustness and scalability[1], researchers are trying to imple-
ment its computational interpretations in various applications. Artificial immune system (AIS) is,
therefore, defined as an adaptive system that is inspired by theoretical immunology and observed
immune models, which are applied to problem solving [2, 3].
However, intelligence demands embodiment to exhibit itself, just as humans use bodies to
show their brains. Robotic systems are, therefore, a common choice among researchers to ex-
hibit intelligent nature of their algorithms. Robotic systems can be wide ranging but in most of
artificially intelligent systems, mobile robots are used to navigate through different environments
and scenarios. Robot navigation can be classified as either using global path planning or local
reactive approach [4]. Global path planning needs prior knowledge of the environment in which
robot has to navigate. It means that shape, location and orientation of walls, obstacles, food
items and/or targets is required to be known. However, most real world problems are inherently
unstructured and thus all the knowledge may not be known ahead of time. On the other hand,
local reactive navigation approach uses the local instantaneous information from sensors to help
navigate the robot. It gives directives to handle the local situation in terms of steering directions,
thus eliminating the need of a-priori knowledge of environment. However, this approach does
not necessarily guarantees the solution nor its optimality.
A robot, in a typical navigation experiment, has to arbitrate different behaviors of wander,
obstacle avoidance, target seeking, etc. Brook’s subsumption architecture [5] defines a behavior
based reactive approach to control mobile robotic systems allowing intelligence to emerge from
behavior arbitration. Like other approaches of neural networks and reinforcement learning, AIS
can also be used in conjunction with this architecture to design effective sense-act algorithms. A
successful AIS-based robotic system should, therefore, be able to perform behavior arbitration
on the basis of underlying immune functions. These immune functions can be based on one of
many computational interpretations of BIS, ranging from earlier clonal selection to most recent
danger model.
In context of navigating robot(s) in unstructured environments and making them exhibit mul-
tiple behaviors, AIS presents a biologically inspired framework that can solve such problems
because BIS can adapt to handle unknown pathogens. A number of robotic applications has been
published over the years albeit questions on validity of older immune models (e.g. idiotypic net-
work). Recent BIS definitions (e.g. danger theory) are also required to be looked into. Current
trends in mobile robotics are also more inclined towards heterogeneity and consequent problem
of coordination/cooperation among robots of various capabilities [6, 7, 8], over and above the
classic problem of navigation in unknown environments. Other problems include, but are not
limited to, conflict resolution in multiple behaviors [9, 10], probabilistic robotics [11] and be-
havior evolution [12]. Such problems are testing the extents of control/navigation algorithms.
It is, therefore, important to review immuno inspired robotic applications in light of emergent
aspects of BIS and newer trends in robotics.
Castro [2] defined a layered framework in which an AIS undergoes the processes of repre-
sentation, affinity measures and immune algorithms to solve a problem in application domain,
as shown in fig. 1. Robotic applications, using AIS as a core algorithm, generally use the same
framework. This review uses Castro’s framework as a selection guideline for the reported lit-
erature by tabulating details in a structured format. However, some applications do not follow
the framework by either avoiding the underlying details or using AIS only as a metaphorical
explanation of their algorithms; those are resultantly skipped in this review.
This report is also an effort to analyze the literature in terms of underlying AIS definitions,
representation schema, application type and corresponding results. Report also discusses the
2
Figure 1: AIS-based framework for problem solving, adapted from Castro [2].
implementation issues in such applications. Subsequent section detail out computational inter-
pretation of various AIS models along with their corresponding general algorithms. Section 3
categorizes the reported robotic applications in terms of their AIS definitions and underlying
mathematical details. Section 4 presents a discussion to identify the established results as well
as the areas that require further investigation.
2. AIS Definitions:
There are a number of explanations of BIS and a lot of research is still being done by immu-
nologists all over the globe. The goal of immuno inspired computational research, on the other
hand, is to translate such definitions to solve problems. Clonal selection theory [13] is the oldest
definition that interprets the working of B cells in a BIS. It was augmented by negative selec-
tion to describe the phenomenon when BIS chooses not to respond, to give rise to self-nonself
theory [14]. Immune network theory [15], most commonly used in robotic applications, defined
the working of antibody network that enables antibodies to recognize each other. Recent major
development in immunology is the inclusion of danger theory [16] to construct a three signal
approach to handle invading pathogens in dangerous/stressed situations. Following subsections
briefly define the AIS models that are used in robotic applications.
2.1. Clonal Selection:
Clonal selection (CS) theory is one popular explanation of how B and T lymphocytes improve
their response to presented-antigens in order to acquire immunity through affinity maturation.
Selection is inspired by the antigen-antibody-affinity. It states that B-cells divide when an affinity
is present between stimulating antigen’s epitope and B-cell receptors. These cells then mature
into plasma cells and secrete antibodies. Antibodies with higher affinities are then reproduced
through somatic hypermutation of B-cells. Paratopes on antibodies and epitopes on antigens
work as key-lock mechanism (complement cascade) to help other cells to eliminate antigens.
Immune system retains some matching B-cells as memory cells. Moreover, it adapts by building
3
up concentrations of B-cells as well as maintains a diversity in mutating these cells in the bone
marrow [17]. Figure 2, constructed from various sources including [18, 19, 16], provides a
description on the working of B-cells once antigen is presented to it.
Figure 2: Working of B-cells in a biological immune system
2.1.1. Computational Interpretation of Clonal Selection
It is important to mathematically interpret affinity between antigen and antibody. Selection,
ordering and subsequent reselection of antibodies or mutated antibodies is solely done on the
basis of affinity scores. It acts similar to fitness function in genetic algorithms (GA). Affinities
Afi are application specific but generally can take the following form.
Afi =
A
PN
i=1 (di + cβi)
(1)
Where di is distance between presented antigen and selected antibody and βi can be defined in
terms of available auxiliary data. Commonly, the distance is translated in terms of euclidean
or hamming distances based on real or binary representations, respectively. Clonal selection is
adaptive and works on the principle of antibody evolution through somatic hypermutation. The
results of affinity computations, using Eq. 1, are sorted in ascending order which is followed
by reselection on basis of best-population-size and subsequent maturation using Eq. (2). Each
antibody in selected-and-ordered-best-population is then cloned as described in Eq. 3. These
clones are projected within the solution bounds. Affinities are computed again and resulting best
clones are selected. Selected best clones then replace the antibodies in initial antibody matrix.
µi
=
K1e−K2·A fi
(2)
Ci
=
Ai + γ µi · rand(.)
(3)
4
In this expression, µi is antibody maturation rate, K1 is maturation constant and K2 is matura-
tion decay factor. Whereas, Ci and Afi are clones and affinity of ith selected antibody respectively.
γ is scaling factor for random number generator for the cloning expression. There can be other
variants of maturation and cloning expressions (Eq. 2 & 3) on the basis of corresponding repre-
sentation schema.
For a comprehensive computational detail on clonal selection, reader is referred to White and
Garrett [20]. Garrett [21] also presented an alternative representation to combine several B-Cell
representations in an attempt to combine the clonal selection and immune network approaches
in a generic network.
2.1.2. General Algorithm of Clonal Selection
Although there are a number of variants of CS-based algorithms, following table 1 is one
generic algorithm. It starts with the initialization of antibody parameters. An antibody matrix
is specified at this stage by including the initial solution candidate as well as randomly gener-
ated antibodies. Best antibodies are then selected on the basis of affinity evaluation. Affinity
function uses the information of antibody & antigen and calculates the affinity on the basis of
selected function e.g. boolean operators, euclidian /hamming distance or a user defined func-
tion. A number of string matching rules are listed by Dasgupta [1] for interested readers. The
premise of these definitions is to use a function that best incorporates the key-lock mechanism of
antigen-antibody interaction. The rest of algorithm follows the procedure described in previous
subsection.
Table 1: General Clonal Selection Algorithm
Algorithm
Input: Antigen: Ag
Output: Evolved antibodies Ab (Memory)
1. Initialize: Random population of Ab
2. While ¬ goal do
• for all Antigens Ag do
– Affinity computation: for each Ab
– Selection: according to affinities
– Cloning: proportional to respective affinity
– Maturation: mutate clones, inversely proportional to cor-
responding affinities
– Reselection: according to affinities
– Update Memory
– Metadynamics
• end
• repeat
3. end
5
2.2. Immune Network:
Clonal selection theory does not explain the working BIS in absence of invading pathogens
or suppression of certain immune functions. Jerne’s idiotypic-network theory [15], also known
as immune network (IN), proposes the possible explanation. It suggests that an antibody pos-
sesses a unique idiotope, similar to epitope, so that other antibodies can recognize it. The group
of antibodies that share common idiotope belongs to one idiotype. This theory also states that
once an antibody’s idiotope is recognized by paratopes of other antibodies, it is suppressed. Con-
sequently, antibody concentration is reduced. Similarly, once an antibody’s paratope recognizes
idiotopes of other antibodies or epitopes of antigens, it is stimulated. Antibody concentration
is increased as a result of this stimulation. In other words, this theory tries to explain the com-
munication between antibodies via collective dynamic network of stimulative and suppressive
interactions, suggesting a continuous communication even in absence of antigens. This is in
contrast to the antibody −antigen −only interactions of clonal selection theory. It is because of
this notion that cells within an immune system can recognize each other, in addition to recogniz-
ing antigens, this theory is applied on a number of different applications ranging from internet
security to mobile robotic systems. Figure 3 illustrates the network of antibodies using idiotypic
connections.
Figure 3: Working of idiotypic stimulations and suppressions in an Immune Network
2.2.1. Computational Interpretation of Immune Network
Jerne’s idiotypic network theory [15] was translated into a computational model by Farmer
et al. [22]. Following differential equation was proposed by Farmer et al. for antibody concen-
tration Ai with respect to all the stimulatory and suppressive effects as well as the natural death
rate.
˙Ai =
αa
Na
X
j=1
mijaj −αs
Na
X
j=1
mjia j +
Ng
X
k=1
nikyk −λi
ai
(4)
ai = σ(Ai) =
1
τi + exp(−Ai),
∀i = 1, . . . , Na.
(5)
It is defined for Na antibodies and Ng antigens. First sum in Eq. (4) represents the stimula-
tion of antibody Ai in response to the other antibodies Aj (idiotope-paratope connection). It is
6
termed as stimulus1 in subsequent sections. Second sum represents suppression of antibody Ai
in response to all other antibodies (paratope-idiotope connection). Third sum models the stimu-
lation of antibody Ai in response to all antigens (paratope-epitope connection) and is termed as
stimulus2. Last term in the expression shows antibody death rate. The resulting antibody concen-
tration rate depends on the collisions between antibody Ai and antibody A j that is proportional
to aiaj. Eq. (5) is a squashing function that controls the size of ai.
Jerne’s network theory has some critics as well. It is argued that a very large antibody popu-
lation limits the network size in idiotypic suppressions [23]. Similarly, the network structure in
terms of its symmetry has its own share of arguments [24].
2.2.2. General Algorithm of Immune Network
There can be a number of variants of IN based algorithms. Following table 2 is the core
algorithm that generally is common to all variants.
Table 2: General Immune Network Algorithm
Algorithm
Input:
• Definitions: Antigen, Antibody
• Antigen: Ag
Output: A network of Antibodies: Ab
1. While ¬ goal do
• Collect Antigen
• Affinity: between Antigen and Antibody
• Network: Stimulations and Suppressions (Some or all)
– Stimulus 1: between antibodies
– Stimulus 2: between antigen and antibodies
– Suppression: between antibodies
• Antibody Network Dynamics
• Cloning
• Metadynamics
• Return Network
2. repeat
3. end
2.3. Danger Theory:
Newer definitions of self-nonself models and danger theory are extensions of earlier clonal
selection theory of antibody production of activated B-Cells. Matzinger [16], in her danger the-
ory (DT), explains how immune response is initiated. It presents a three signal model to explain
the working of biological immunity in stressed situations. It describes that a co-stimulatory signal
from dendritic cells activates the T-helper cells. These dendritic cells of the immune system, also
termed as antigen presenting cells (APCs), are themselves activated by danger signals emitted
7
by the injured/stressed cells. Once activated, they provide a co-stimulatory signal to exhibit in-
nate/adaptive immune response. Furthermore, dendritic cells can be immature, semi-mature and
mature. Immature dendritic cells collect antigens along with safe and danger signals from its lo-
cal environment like pathogen associated molecular patterns signals (PAMPS) and inflammatory
cytokines. If environment is safe, the dendritic cell becomes semi-mature and upon presenting
antigen to T-cells it causes the T-cell-tolerance. On the other hand, if environment is dangerous,
it becomes mature and causes T-cell-reactivity. Figure 4 illustrates the maturity of APCs in case
of a danger signal that results in co-stimulation of T-cells.
Figure 4: Initiation of biological immunity according to danger theory
2.3.1. Computational Interpretation of Danger Theory
Computational interpretations and consequent algorithms, inspired by danger theory, are still
in their infancy. There are two interpretations following introductory work of Aickelin et al.
[25]; one is dendritic cell algorithm (DCA) by Greensmith et al. [26] while the other is toll like
receptor algorithm (TLR) by Twycross [27]. Both use different aspects of danger theory. DCA
introduces the underlying translations of PAMPS, safe and danger signals resulting from maturity
of dendritic cells with the help of co-stimulatory molecule (CSM). These signals are buffered as
well as the antigen. DCA, on the basis of dendritic cell maturity and migration threshold, sets
the cell context. Equation 6, in one possible configuration of output (Op), thus contextualizes the
environment which then arbitrates the immune responses. Also see table 3 for the algorithm.
Op = β
WP
3
X
i=1
Pi + WD
3
X
i=1
Di + WS
3
X
i=1
S i
,
∀p
(6)
2.3.2. General Algorithm of Danger Theory
At the heart of danger model of immunology is the antigen presenting cells (APC)/dendritic
cells. The core of DCA is presented here in table 3. It is a population based algorithm that uses
the concept of immune function initialization in a three signal model.
3. AIS-based Robotic Applications:
In literature, AIS-based robotic applications tend to simulate robot control around small, ar-
tificial environments, generally addressing the problems of behavior arbitration and autonomous
navigation (e.g. [28, 29]). These environments are generally programmed as fixed and depicted
as arenas where robots have to perform. Subsequent discussion categorizes the reported immuno-
inspired robotic applications in four categories. First category lists the applications using clonal
8
Table 3: General Dendritic Cell Algorithm, from [26]
Algorithm
Input: Sorted antigen and signals (PAMP,DS,SS)
Output: Antigen and their context (0/1)
1. Initialize: DC
2. While CSM output signal < migration threshold do
• Collect Antigen
• get signals
• calculate interim output signals
• update cumulative output signals
• update cell location to lymph-node
• if semi-mature output > mature output then
– cell context is assigned as 0
• else
– cell context is assigned as 1
• end
• arbitrate the behavior
• Invoke innate / adaptive immune response
• kill cell
• replace cell in population
3. end
selection as central algorithm, second details those with immune network, third describes those
with danger theory and fourth category details those with hybrid/implicit definitions under other
approaches in both innate and adaptive immunities. Figure 5 shows a genealogical chart of these
categories according to their parent immune categories; innate or adaptive. The discussion is
further augmented with underlying mathematical expressions of different approaches in tables 4,
5 & 6.
3.1. Robotic Applications using Clonal Selection:
There are different versions of CS algorithms being used by researchers. The variations are
mainly due to definitions of antigen-antibody strings, affinity computations and auxiliary func-
tions. Computational efficiencies are also important but mainly depend on the string lengths and
population size of mutated antibodies during the process. Subsequent discussion details salient
features of reported literature with major criticism on underlying immunological interpretation
and should be read in conjunction with table 4.
Hu [30] used a CS-based approach for global path planning of a robot. Antibodies are defined
as a set of nodes that represent line segments from starting point to end point. Interestingly, this
representation does not use antigen definition. Fitness function (affinity) is defined in terms of
euclidean distance di and obstacle information βi in the arena. Paths that intersect obstacles affect
the fitness function.
9
Figure 5: Genealogical Chart of AIS-based Robotic Applications
Wang & Hirsbrunner [31] developed an immune mechanism based evolution algorithm (IMEA)
in an off-line robot navigation task, in an attempt to avoid premature convergence during naviga-
tion, and compared it with genetic algorithm approach. IMEA combines the concepts of genetic
algorithms (crossover and mutation) with those of clonal selection (memory updation and selec-
tion). It is noted that this approach uses the concept of vitality νi to compute fitness function
and is based on least mean squared error between selected two paths. IMEA does not use the
concepts of somatic hypermutation and cloning to evolve the solution but relies on the concepts
of GA, instead.
Li et el. [32] presented a CS-inspired approach for concurrent mapping and localization in
order to search the space for possible robot maps. This approach does not use the metaphors of
antigen or antibody but chooses chromosomes to represent change in distance and orientation as
in genetic algorithms. It then uses CS for mutation purpose only. In fitness function, described
in table 4, w1 and w2 are real numbers in range of (0, 1) and if Oi j > 0.5 then δi j = 1 else δi j = 0;
and if Eij > 0.5 then ζij = 1 else ζij = 0.
Hur, J. [33] developed a multi robot system, for a bomb disposal task, using CS-based anti-
body evolution to update a lookup table (memory) that lists solutions corresponding to different
states. Diffuser-bot, scanner-bot and inspector-bot maximize the number of bombs diffused,
number of bombs found and number of bombs inspected, respectively, in addition to maintaining
energy levels through affinity computation. The underlying definitions are given in table 4 in
which affinities are computed through assigning weights (wi) to a number of certain soft con-
straints (ni). Number of clones (Nc) is proportional to the affinity of individual antibodies in
population N. The maturated and reselected antibodies then update the lookup table.
There are some robotic applications that use clonal selection principle as an auxiliary function
or as a metaphor only. Chingtham and Nair [34] tried a two robot line tracking system using two
10
concentric tracks. Outer robot uses the innate immune system to help inner robot to avoid sway
and inner robot uses CS to adjust its speed on track. Literature does not describe the mathematical
representation of underlying principles. Jun et al. [35] used CS metaphors to augment immune
network, only to transfer strategy between individual robots.
3.2. Robotic Applications using Immune Network:
Immune network is widely used AIS-based approach in robotics, more than any other model,
because it explicitly defines all the interactions between antibodies and antigen and their resulting
network. The applications are subdivided in terms of their parent technique. The representation
schema of antigen and antibody, affinity computation, antibody selection criterion is presented in
table 5 along with the details of experiment. Table 6 provides mathematical expressions for stim-
ulations and suppressions in network along with the details of corresponding auxiliary functions,
cloning and metadynamics.
3.2.1. Ishiguro-Watanabe Stream:
This subcategory deals with binary representations for antigen and antibody. Resultant net-
work uses hamming distance as primary criterion for affinity computation. Consequent antibod-
ies are then selected on the basis of their respective concentrations. The underlying principle of
suppressions and stimulations remain similar with minor differences.
Ishiguro et al. [36], in 1995, implemented an IN-based approach on a six legged robot in
order to acquire a gait. Each leg is incorporated with a local immune system (LIN) having four
antibodies. Each antibody represents gait behaviors; namely backward, retract, forward and
protract. Paratopes and idiotopes of all the antibodies are pre-assigned as to either support or
transfer. These LIN are evolved using GA in which ”winner takes all” approach is used to select
antibodies. Two types of antigen are incorporated; one to input situation, other to represent
coordination among local networks. Experimentation is limited to forward movement in which
18 iterations of GA establish a no fall situation. This work by Ishiguro et al. is considered
as a first attempt towards physical application of idiotypic network but ad-hoc antibody/antigen
allocation restricts such systems to low complexity.
Ishiguro et al. [37, 38], in 1996, also proposed a decentralized behavior arbitration scheme
to navigate a mobile robot to replenish energy, avoiding obstacles in an arena. It is noted that
paratopes are modeled as desirable actions with preassigned definition of action. Idiotopes are
modeled as identification numbers that are assigned according to the results of an adjustment
mechanism (reinforcement). Antigen are pre-massaged in terms of object information, direction
of object and current energy state. Experimental results, however, show limited results of an
18 antibody network that enables the robot to avoid one obstacle to reach the charging station.
Antibody selection is done on a ”roulette wheel” method. Moreover, the network does not make
use of antibody metadynamics but uses an adjustment mechanism to select an idiotope ID.
It should be noted that Jerne’s idiotypic theory defines the idiotype in terms of physical con-
nection, like that of a key lock, to identify each other. However, a BIS can open a number of
locks with one key. Although this analogy is weak, antigen/antibody allocation in Ishiguro’s ini-
tial work, however, does not incorporate this phenomenon. Moreover, this approach also avoids
use of unstructured environment in simulations. Ishiguro’s work was extended by Watanabe et
al. [39] to include an off-line innovation function. This innovation function is based on a genetic
algorithm with a mixing pot method for crossover operator. It is noted that antibodies are re-
tained as behavior modules. The problem was also extended to add garbage collection behavior
11
in addition to existing obstacle avoidance and energy replenishment behaviors. The drawback of
this approach, as well as of Ishiguro’s, is the definition of antibodies as behavioral modules. This
approach forces one to define behaviors ahead of time with no possibility of behavior evolution.
Michelan and Von Zuben [40] improved Ishiguro’s model by incorporating a GA-based anti-
body evolution mechanism. Idiotope is modeled as a set of stimulated antibodies for the network.
Antibody affinity is computed on the basis hamming distance evaluation. GA-based adjustment
mechanism uses a 40% crossover and 1% mutation with an elitist selection. Fitness function
is based on number of collected and transferred garbage, recharges and collisions. It should be
noted, however, that a BIS has an inherent mechanism to clone antibodies using somatic hyper-
mutation. The above mentioned models use other algorithms for similar purposes. This raises a
question on the degree of AIS implementation.
Vargas et al. [41] attempted the same garbage collection application using learning classi-
fier system in addition to existing platform provided by Michelan and Von Zuben. This model,
named as CLARINET, adds a learning classifier system to classify antigens and antibodies. An-
tibody structure is, for that purpose, restructured in terms of antecedent and consequent parts to
represent paratopes and antibody connections to represent idiotopes. This addition makes anti-
body network more flexible but requires more computation effort as classifiers are updated both
before and after the immune network dynamics. They also implemented the GA-based immune
network on Khepra robots [42].
Krautmacher and Dilger [43] tried to implement a simplified rescue scenario involving single
robot. Antigen are binary coded information of object type and position. Algorithm then uses
coordinate transformations for network dynamics in which no metadynamics is incorporated.
Rest is same as in Watanabe’s approach.
Wang et al. [44] used the immune network approach of Ishiguro in conjunction with obstacle
restriction method (ORM) and reinforcement learning (RL). This application is a single-robot
path-planning exercise in which two types of antibodies are defined: one to represent obstacle
avoidance behavior and other to seek goal. Antigen is defined as a binary coded data of obsta-
cles/goal in terms of task proximity (near or far). An expression similar to T-cell metaphor, as in
Luh et al. [45], is also used to help suppress either of the behaviors. This also replaces the need
to define stimulus2. Moreover, cloning or metadynamics is not defined in network structure.
Tsankova et al. [46], in 2007, applied Ishiguro’s network to implement stigmergy based
foraging behavior. This work uses different scenarios to collect pucks with single/two robot(s),
with one network for goal following behavior and one to pick and drop the pucks. Report also
compares the results with Braitenberg’s 3C and Q-learning robots. This research does not add
to Ishiguro’s interpretation but the experimentation establishes a comparative analysis with two
well known approaches.
3.2.2. Whitbrook’s Stream:
Whitbrook et al. [47] solved the maze-world problem with extensive experimentation using
three approaches: RL, RL with simple idiotypic system and RL with full idiotypic AIS. System
uses 8 predefined antigen having priority levels assigned to pre-massaged data that translates
sensor info into a situation. Sixteen (16) antibodies have predefined behaviors with speed speci-
fications. Idiotopes are fixed while paratopes are predefined that have some adjustment flexibility
through reinforcement. Affinity computation is done as in Vargas et al. [41]. It is noted that anti-
body metadynamics is not implemented. Moreover, system uses a-priori information in antigen,
antibody and idiotope matrices with limited adjustability of paratopes. Although results show
that robot with full feedback performs better in terms of escaping traps by establishing idiotypic
12
network, the system should be able to adjust its internal values automatically either through T-
helper cells or through antibody evolution.
Whitbrook further extended her work by incorporating GA to evolve behaviors [48]. This
GA supported long term learning (LTL) combined with short term learning (STL) of idiotypic
immune network was tested against STL only approach in [49, 50]. The underlying notion
that AIS can only exhibit short term learning can be questioned as it is dependant on system’s
metadynamics that can be adjusted to retain memory for a longer period.
3.2.3. Lee-Sim Stream:
Lee et al. [51] executed the swarm intelligence task involving multiple robots. Task density,
either high, medium, low or nil, is represented as antigen. Antibodies are defined as four behav-
iors of aggregation, random search, dispersion and homing. Sensors detect the task concentration
that is then used in a fuzzy function to output a stimulus-value for Farmer’s equation. Resulting
concentration is then used to stimulate other robots to do the same task. Metaphors of plasma
and deactivated cells are used to incorporate some level of metadynamics. This approach also
suffers from inherent problem of a-priori behavior specification. Jun et al. [35] extended this
work by incorporating T-cell metaphor to represent control parameters. This adds another layer
in the network and resets the antibody concentrations once an antigen is removed.
3.2.4. Li-Wang Stream:
Li and Wang [52] implemented a sheep-and-dog problem using predefined coefficients to
compute affinities. Antibody network dynamics is replaced by an algebraic expression that takes
into account the usual stimulations and suppressions along with a T-cell function and a linear
death rate. Environment is translated into antigen by tabulating positions of dog and sheep in
a matrix X. Antibody matrix Y also has previous information of actions corresponding to each
entry in antigen matrix X. Only five actions are possible. This research does not make any
distinction between sheep and dog in terms of their embodiment. Moreover, the network uses a
manual mechanisms to perform coefficient selection that limits its adaptability.
Duan et al. [53] extended the work of Li and Wang to perform a predator-prey experiment
with 2 predators and one prey, each having a small antibody network that can communicate with
each other except in pursuit domain. Antigen is of two types: one has environment information
in terms of position data and other has communication signal. Two different antibody structures
are implemented for predator and prey robots. Predator has six actions to arbitrate from while
prey has three behaviors to choose from, on the basis of synthesized immune network as in Li
and Wang [52].
3.2.5. Luh’s Work:
Luh has presented three different applications that use different immune metaphors. His ap-
proach is based on real data representation scheme. In 2002, he with Cheng [54] presented a
food foraging application that uses APC module to assess the environment and T-cells as a RL
mechanism. T-helper-cells are used here as an adaptive critic. Luh et al. [45], in 2006, imple-
mented a robot soccer application using immune network. Antigen is sensor information that
is mapped to have three components, one is distance between ball and goal, second is distance
between ball and robot and third is crowd data. Each of these components corresponds to a fuzzy
function to find affinity value. Average of all three affinities, through fuzzy membership func-
tions, is computed in terms of a 6x6 affinity matrix. A T-cell function is incorporated that acts as
13
a reinforcement. Antibody metadynamics is not implemented since there is no repertoire main-
tained as memory. Zhang and Lu [55] reproduced this approach using four antibodies instead of
six for each robot.
Luh and Liu [28], in 2008, solved the robot navigation problem using reactive-IN approach
with fused data representation. Antigen is a vector of azimuthal angle of goal, distance informa-
tion of each sensor and sensor location on the robot periphery. Antibodies are defined as steering
directions (θi). Stimulation and suppression due to antibody-antibody interactions is defined as
cosine of difference between respective antibodies. Stimulation due to antigen interaction is de-
fined in terms of attractive/repulsive forces of goal seeking and obstacle avoidance. In order to
escape robot from trapping in local minima, an adaptive virtual target method is also used. The
weighing mechanism of attractive/repulsive forces is manual. Therefore, it is not clear that how
a robot manages to arbitrate the two behaviors.
Dehuai et al. [56, 57] modified the work of Wang et al. [44] by defining antigen in terms
of task density (high, low or none) and combining antibody structure in one representation. It
is also noted that Farmer’s equation is not solved by an ODE solver but antibody concentration
rate is related directly to behavior modules. Moreover, hamming distance is replaced with Luh’s
expression of cos(∆θ) to define antibody stimulation and suppression. This application is also a
single robot path planning exercise in which two types of antibodies are defined: one to represent
obstacle avoidance behavior and other to seek goal.
3.2.6. Non-Farmer Approach
Mitsumoto et al. [58, 59] presented an IN-based approach to control population of multiple
robots according to assigned task of load transfer from one station to two storage docks. Each
task assignment is treated as an antigen that disturbs the existing population of robots. Algorithm
then reconfigures to attain new stability (homeostatic state) by sharing message-antigen with
other robots. Each robot, treated as a B-cell, has predefined modules to set global states and
behavior strategy. Resultantly, the network is limited only to regulate robot population.
Sathyanath and Sahin [60] and Opp and Sahin [61] used a mine detection task to perform
single objective task with fixed number of robots using a non-idiotypic approach. Antigen are
modeled as mine locations whereas antibodies are defined as robots. The communication be-
tween antibodies is a network that provides antigen-locations. Robots are, resultantly, stimulated
to move toward the mine in order to defuse it. Suppression is implemented when no antigen
is detected and results in random movement. This is unlike Farmer’s interpretation of Jerne’s
idiotypic network theory that ensures communication even in absence of antigen.
Generally, it is because of this notion that cells within an immune network can recognize each
other, in addition to recognizing antigens, IN-approach is applied on mobile robotic systems. Any
change in environment is detected as an antigen. Possible steering directions/behavior-modules
are represented as antibodies. The most stimulated antibody, resulting from immune network
approach and supplementary methodologies, is fed to the system as an actuation signal.
3.3. Robotic Applications using Danger Theory:
Danger theory is a newer definition of BIS working and, therefore, very few robotic ap-
plications are reported in this category. Dendritic cell algorithm by Greensmith [26, 62, 63]
incorporates only the working of antigen presenting cells within a BIS and, therefore, requires
other immuno functions to fully implement a three signal model.
14
Oates et al. [64] used DCA in a mobile robotic security application for classification purpose.
Augmenting the subsumption architecture, the robotic DCA is implemented as a stand-alone
behavioral module. DCA processes the sensor data as antigen and generates signals that are
either safe, dangerous or PAMP [25]. The output of DCA provides a base for subsuming the
behavioral modules. It is to be noted that in subsumption architecture, there is a disagreement
among various behavioral modules e.g. react to bumpers, recover from stall, avoid obstacles
and explore. Brooks [5] suggests that this can be solved by allowing components at one level
to subsume components at a lower level. It is because of this reason the approach is called
subsumption architecture. This application, however, is a classification problem that does not
fully incorporate the behaviors necessary for navigation through a maze.
Prieto et al. [65] implemented a preliminary work that uses DT on a metaphorical level only
and lacks the necessary mathematical interpretations. This application is a soccer goalkeeper
strategy in which APCs are ID of predefined strategy whereas antigen is detection of opponent
and ball in the home side. Signal one, two and three correspond to respective closeness of ball to
the goal.
3.4. Robotic Applications using Other Approaches:
This section lists the robotic applications that do not fall in a single BIS category, lack the
basics of a particular definition, and/or use other AIS definitions. Xiong et al. [66] implemented
a multi-robot system that maps an environment on the basis of market approach. The function of
immunity is limited only to optimize the strategy to select goal points during exploration. Aux-
iliary functions are used for other operations like Bayes theorem for data fusion and diffusivity
for robot distribution in arena.
The approach of Yuan et al. [67] claims to combine artificial potential field (APF) method
of Khatib [68] with Jerne’s idiotypic network theory but fails to specify antibody dynamics.
Representation scheme is binary whereas obstacles and goal are separately coded into it. It also
uses antibody vitality along with a learning strategy to execute path planning task.
4. Findings:
4.1. On using AIS
It is important to understand that some aspects of BIS are still being investigated. Clonal
selection theory, the oldest of considered theories, focused on one signal approach in which
antigen binds with receptors on a B-cell. Danger theory, the newest in self-nonself approach
of BIS, follows a three signal approach as shown in fig. 4. Therefore, year of publication is
important to evaluate an application in terms of validity of its corresponding BIS explanation at
that time. There exists a researcher’s dilemma that what to take and what to leave in order to solve
a problem, especially when a set of theories explain different aspects of a complex phenomenon.
It is of no use that the whole BIS is replicated to solve a relatively simple problem but, at the
same time, one should not fall victim to a single aspect of BIS as well.
Literature indicates that some auxiliary functions or subsystems are also required to support
the core algorithm, like reinforcement learning, fuzzy systems and/or genetic algorithms. It
would be more appropriate to use a computational equivalent from BIS, if available. For example,
nature uses somatic hypermutation to evolve antibodies but some researchers have used GA
instead (e.g. [40, 41]). It would have been logical to use what nature has chosen for a particular
purpose. Similarly, some researchers have used RL (e.g. [38, 44]) when nature uses similar
15
approach of T-helper-cells. It is, therefore, identified that the degree of biological inspiration
can be deeper than some applications show it to be. Moreover, there should be investigations to
establish that BIS-inspired auxiliary function(s) can be as effective as some other.
Following subsections indicate the findings pertaining to afore-mentioned AIS approaches as
well as the robotic applications.
4.1.1. Using Clonal Selection
Wang & Hrisbrunner [31] and Li et al. [32] used GA-based crossover operators in their
applications. In nature, however, BIS does not use crossover. Without sounding like a purist, this
raises a question on validity of such auxiliary functions. Especially when it has been established
that CS-algorithm and it variants are equally effective, if not better, in optimization tasks (e.g.
[20]). A framework for establishing convergence of immune algorithm is also presented in [69]
and a comparative analysis is presented in [70] for various test functions. The representation of
antigen and antibody is not explicitly defined and justified in some of applications. The benefit
of using a robotic application lies in its embodiment and it should be reflective in corresponding
representation schema.
4.1.2. Using Idiotypic Network
The major chunk of publications fall under the idiotypic network theory. A generic structure
of IN is shown in fig. 6 in context of idiotypic connections in a typical robotic application. Anti-
bodies are either evolved or generated by evaluating affinity functions. Mapping schema, affinity
definitions and antibody specifications vary from application to application. The question, how-
ever, is to justify use of a particular theory (idiotypic theory in this case) and to what extent a
theory is applied.
Figure 6: A generalized structure of Antigen-Antibody and Antibody-Antibody interactions in an idiotypic network
Major criticism on Jerne’s idiotypic network theory is in relation to the size of its network
[23]. This criticism arises from a basic argument that how can every antibody recognize every
other antibody in a possible network of millions of cells (with current estimates of more than 1012
16
lymphocytes). These arguments are not countered in the observed robotic applications. It can,
however, be argued that such applications do not require a network of millions of antibodies. In
case of behavior arbitration, the network only requires a handful of antibodies. In case of multi-
robot applications where robots are generally modeled as B-cells, the size of network does not
exceed because of inherent limitations of cost and size of arena.
Farmer’s expression of antibody concentration rate (eq. 4) is common to every application
within idiotypic network theory, barring a few exceptions. It provides an explicit notation to
stimulations and suppressions among antibodies and antigens. It, however, has different im-
plementations in different research streams. Apart from conventional approach to use an ODE
solver, a discretized version using bilinear transform is employed in Krautmacher & Dilger [43]
and an algebraic equivalent, named as synthesized immune network, is used in Li-Wang stream.
The choice of a particular implementation strategy or a solver is normally dictated by compu-
tational requirements of an application. Recently, theoretical issues relating to different AIS
algorithms are being raised. The small size of immune network in case of robotic applications
induces an effect of discreteness, resulting in difficulties to analyze using standard techniques
[71].
Ishiguro-Watanabe stream primarily shares same network structure but differs in the usage
of auxiliary/support functions. It uses reinforcement learning, genetic algorithms, learning clas-
sifiers, etc. as auxiliary functions and does not establish a clonal selection in support to the
network. Jerne’s theory, on the other hand, is built on clonal selection theory. A network-alone
approach, like that of Ishiguro-Watanabe stream, reduces such system to a reactive one that
has no evolution resulting from cloning & hypermutation. It perhaps is a result of behavior-
arbitration/action-selection approach in which there are only a few preprogrammed behaviors to
choose from. Li-Wang and Luh’s streams also lack such implementations.
It is important to devise a way to represent environment into antigen (Ag). Similarly, paratopes
and idiotopes of antibodies (Ai) should be encoded in such a manner that stimulation-suppression
network can be incorporated. Representation of antigen and antibody can be binary (e.g. in
Ishiguro-Watanabe stream) or real (e.g. other streams in IN-approach). A binary representation
scheme such as that of Ishiguro-Watanabe stream structures the external & internal data along
with the binary coded epitope. Similarly, paratopes & idiotopes on antibodies are binary strings
alongside the pre-programmed actions. Subsequent affinity computations are based on Hamming
distances as shown in tables 5 & 6. Real data representation is employed in rest of streams and re-
sulting affinities are computed on the basis of euclidean distance, strength-of-match approach or
string matching. Ishiguro-Watanabe mode of representation has a problem that its network does
not have any information of the robot body but at the same time has a more generic structure.
Luh’s approach, however, makes use of fused data representation that includes some informa-
tion of location of sensors within the network. Selection of representation schema in AIS-based
robotic applications is, therefore, tricky in terms of inclusion of robot embodiment in network
and a consequent loss of generality.
Antibody death is also an important factor in Farmer’s expression. A constant antibody death
rate, as employed by all the applications in this category, does not serve a purpose when no
memory is maintained or when antibody metadynamics is skipped in implementation.
4.1.3. Using Newer Definitions
Danger theory can be considered as an extension of self-nonself models. DCA is based on
one aspect of this theory that relates APCs to their maturity on the basis of danger/stressed sig-
nals in the system. Resultantly, DCA limits itself to the initiation of immuno responses because
17
the theory itself puts limits on that. It can be used in behavior arbitration on the basis of envi-
ronment contextualization but then it should be supplemented with B-Cell and T-Cell algorithms
to complete a three signal immuno function [25]. Only one application is reported in literature
that uses DCA in a robotic application. There is a lot of potential in terms of using innate immu-
nity in conjunction with its adaptive counterpart. As a starting suggestion, conflicting objectives
during robot navigation can be tested with DCA which is currently limited to static data. More-
over, fuzzy weighing in some instances can be replaced with a DCA to co-stimulate different
behavioral modules. The role of T-cells in helping B-cells can also be further refined to a level
of developing adaptive critic as well.
4.2. On immuno-inspired robotics
Current trends in robotics have migrated from reactive paradigm to hybrid and probabilistic
robotics in order to counter uncertainties in sensing and modeling [11]. Moreover, single-robot
applications have gathered more robots to implement swarm intelligence [72]. Heterogeneous
mobile robotic systems, a new trend, involves using robots of different capabilities performing
jobs in unstructured environment. Most of the reported immuno-inspired applications, however,
involve either single robot or multiple robots of same type. Even in case of Li-Wang stream
where predator & prey experiment is implemented, no distinction is made between predator and
prey. In classical predator-prey models, a predator is embedded with higher sensitivities and
a prey is modeled with higher actuation capabilities. For example, a predator may be given
better vision and a prey may have higher speeds to escape an attack. This approach makes such
systems to be heterogeneous mobile robotic systems. This heterogeneity requires a generalized
representation scheme that can handle robots of varying capabilities in terms of their sensing and
actuation.
Reported applications also limit themselves in terms of using predefined behaviors to arbi-
trate from. This poses a problem in case of employing heterogeneous mobile robots because each
robot would then require programming of different behavioral modules ahead of time. Ideally,
intelligence should emerge irrespective of hardware configuration of robots. This leads us to opt
for behavior evolution rather than conventional behavior arbitration because coupling antibodies
to predefined actions or behavior-modules stops inclusion of new behaviors.
The ad-hoc manner in which these applications and their outcomes are reported makes us
suggest benchmarking. Although robotics is ever-changing, there are a number of scenarios
and datasets available. Nowak et al. [73] presented a detailed account of related benchmarks
as part of the European research project BRICS. The benchmarks should be implemented and
compared with other established techniques. Alternatively, some metrics related to utility, cost
and reliability should be implemented to support an algorithm.
Robot trapping in a local minima is the most common drawback of using reactive approach.
In this context, many trap-escaping schemes have been tried and investigated. Potential field
method [74, 75], numerical potential field method [76], virtual target method [77], virtual force
field method [78], vector field method [79] are some of the methods that are used to help lo-
cal minima recovery in robot navigation scenarios. Immuno-inspired methods are also being
designed to handle the issue because of adaptive nature of these algorithms e.g. virtual target
method by Luh and Liu [28] but simple shaped-arenas (e.g. U, W & X) do not fully establish the
trap-escaping capabilities of underlying immunity-based technique.
Most of reported literature uses simulations and do not implement the algorithms on real
systems. It should be noted that there are issues pertaining to non-holonomic nature of most
robotic platforms. In simulations, it is much easier to implement a robot as a dot, irrespective of
18
its dynamics. Similarly, the detection of obstacles, walls or targets is difficult and pose a lot more
implementation issues.
5. Conclusions:
We have reviewed the literature on immuno-inspired robotic applications. In advent of newer
definitions of BIS and current trends in robotics, it is important to categorize these applications
in terms of underlying immune definitions, computational details and deficiencies and conse-
quently point towards future directions. It is concluded that a deeper biological inspiration is
required because a single aspect of AIS may not be sufficient to incorporate a successful robotic
system. Auxiliary functions should be taken from their computational equivalents within BIS,
where available. It is important to highlight here that an AIS can be all-encompassing; one that
combines innate and adaptive immune systems by employing functions of phagocytes, dendritic
cells, T & B lymphocytes, etc. An AIS has functions that provide a distributed network structure
like idiotypic network, reinforcement learning like T-cell algorithms, evolutionary mechanism
like somatic hypermutation, short term learning like metadynamics and weighted sum of attrac-
tive/repulsive forces like dendritic cell algorithm. A two layered approach can be one of the
solutions where one layer corresponds to antigenic data and the other to environment contextu-
alization in terms of safe or dangerous signals.
A network-alone approach reduces robotic system to a reactive one that has no evolution
resulting from cloning & hypermutation. Current trends, on the other hand, are more inclined to-
wards behavior evolution rather than behavior arbitration. It is also concluded that with a deeper
BIS inspiration it is possible to add stochastic nature of clonal selection to the deterministic
approach of idiotypic network. The benefit of using robots as an application is in its embodi-
ment. Fear of unknown environment can be reduced by knowing something about robot. The
information of sensors locations and system dynamics can, therefore, be a part of representation
schema.
Selection of a particular robotic application is also important. Search and rescue scenario
involving heterogeneous robots offers a comprehensive application that uses different robot con-
figurations to accomplish a wide variety of tasks, ranging from single robot navigation through
obstacles to multi-robot coordinated navigation in rescue. Robot taxonomy is important aspect to
be considered as well, especially when one wishes to develop a general algorithm for a number
of robot platforms. It has also been identified that benchmark problems should also be tested to
validate an algorithm. We also emphasize the need of real experiments to minimize the reality
gaps between simulations and actual systems (e.g. issues pertaining to system’s uncertainties,
holonomicity, local minima recovery, conflict resolution etc.).
This review also offers an insight into older work and presents a critique to individual as well
as group works in previous sections. It is evident that AIS-based robotic applications have helped
in establishing immunological computations as a successful approach but there exist a number
of voids that are needed to be filled up, both in terms of theory and experimentation. There are a
number of new directions that can be investigated. A combined framework of neural networks,
endocrinal systems and immune systems can be implemented to establish a homeostasis in an
embodied system. Another novel idea can be to vaccinate a simple robot with specific antibodies
from a specialist/healthy robot. This approach can be used in situations where an untrained robot
is desired to learn faster through vaccination. A robot immune system can also be implemented
that regulates/repairs its internal organs and vital functions, unlike the conventional approach of
using an AIS as a navigation scheme only.
Table 4: Review of Clonal Selection Based Robotic Applications
Antigen
Antibody
Affinity
Auxiliary Functions
Experiment Specifications
Hu
—
Grid points of Robot path,
fitness = A
f , f =
N
X
i=1
(di + cβi)
Roulette wheel selection,
Robot path planning,
X = [ao, a1, · · · , an]
di =
q
(xi −xi−1)2 + (yi −yi−1)2
Mutation, insertion &
ao = start pt, an = end pt
βi =
M
X
j=1
α j (if obstacle, 0 otherwise)
deletion operators
Wang &
Problem
Possible solution
Fi = νi
"
1 + ζ
νi
max(ν) + δDs
 
1 −
νi
max(ν)
!#
GA: crossover & mutation
IMEA for robot path planning,
Hirsbrunner
Ds =
P
i(θ.max(ν) ≤νi ≤max(ν))
µ + φ
no hypermutation or cloning
νi =
M.N
PN
i
q
(xpi −xqi)2 + (ypi −yqi)2
Li et al.
—
Modeled as chromosomes
f =
X
min(1 −Oi j, 1 −Ei j + w1
X
δi j + w2
X
ζi j)
GA: crossover
Single robot performing
X = [X1, X2, · · · , XN]
Oi j →occupancy
Vaccination operator
concurrent mapping &
where Xj =
h
∆dj, ∆θ j
i
Ei j →empty
localization
Hur
Binary coded
Binary coded
f =
1
h
1 + Pk
i wi.ni
i
Memory updation,
Multi robot bomb disposal
{0, 1}2
{0, 1}3, Action
k →no. of soft constraints
Cloning with
system with three robots
ni →no. of constraints within an Ab
Nc =
n
X
i=1
round( β.N
i )
(Scanner, inspector, diffuser)
Table ended
Table 5: Review of Immune Network Based Robotic Applications in Terms of Definitions
Antigen
Antibody
Affinity
Ab Selection
Experiment Specifications
(Ag)
(Ab)
Ishiguro et al.
Pre-massaged Data
Behavior modules (fixed),
Adjustment Mechanism
Roulette Wheel
Single robot,
Seek energy and avoid obstacles
Watanabe et al.
Binary coded, pre-massaged
Behavior modules (fixed),
Hamming distance
Roulette Wheel
Single robot,
Collect garbage, seek energy and avoid
obstacles
Michelan and
Binary coded, pre-massaged
Behavior modules (fixed),
Hamming distance
Roulette Wheel
Single robot,
Von Zuben
Collect garbage, seek energy and avoid
obstacles
Vargas et al.
Ternary, through classifier
Behavior modules (2 part paratope),
Hamming distance
Roulette Wheel
Single robot w/ learning classifier
Collect garbage, seek energy and avoid
obstacles
Krautmacher
Binary encoded, variable
Behavior modules,
Hamming distance
—
Single robot,
and Dilger
Simple rescue scenario
Wang et al.
Binary encoded, pre-massaged,
Binary coded (separate)
Hamming distance
—
Single robot path planning,
Seek goal and avoid obstacles
continued on next page
Table continued
Antigen
Antibody
Affinity
Ab Selection
Experiment Specifications
(Ag)
(Ab)
Tsankova et al.
Binary coded, pre-massaged
Behavior modules (fixed),
Hamming distance
Roulette Wheel
Single/two robot(s),
Stigmergy based foraging behavior with
two networks
Whitbrook et al.
8 predefined situations
16 predefined actions,
Strength of match
feedback
Robot navigation in maze world,
by reinforcement scores
fixed idiotpe and adjustable paratope ma-
trices
Lee and Sim
Real, classification of task density
Real, action strategy,
Combined stimulation
winner take all
Multi robot system,
and suppression
Mine detection using same robots
Jun et al.
Real, classification of task density
Real, action strategy,
Combined stimulation
T-cell assisted
Multi robot system,
and suppression
Mine detection using same robots
Li and Wang
Real, Environment coding
Real, Action strategy,
String matching
Synthesized
Dog and Sheep problem,
immune network
same type of robots
Duan et al.
Real, Environment coding
Separate action strategies,
String matching
Synthesized
Predator and prey problem,
immune network
same type of robots
Luh et al.
Real data
6 predefined behaviors,
Average from FIS
winner take all
Robot soccer application,
in a 6x6 matrix
All 4 robots are of same type
Luh and Liu
Real fused data,
Steering directions,
—
winner take all
Single robot navigation,
using local reactive approach
continued on next page
Table continued
Antigen
Antibody
Affinity
Ab Selection
Experiment Specifications
(Ag)
(Ab)
Dehuai et al.
Real,
Real, Steering directions,
—
ai = (1 −γi)ao
i + γag
i
Car like robot,
γ through distance
path planning with obstacle avoidance
Table ended
Table 6: Details of Network Structure in IN-Based Robotic Applications
Suppression
Stimulus 1
Stimulus 2
Cloning
Metadynamics
Auxiliary Functions
(Ab −Ab)
(Ab −Ab)
(Ag −Ab)
Ishiguro et al.
T
Abi
p
+ T
Abj
r
T
Abi
Abj
T
Ab j
r
+ T
Abi
p
T
Abj
Abi
Hamming distance
—
—
Reinforcement learning to compute
Tx
Watanabe et al.
F

L
X
k=1
(wkIi(k) ⊕P j(k))

F

L
X
k=1
(wkI j(k) ⊕Pi(k))

X
j
F

L
X
k=1
(wkE j(k) ⊕Pi(k))


—
GA based
Mixing pot crossover function
Michelan and Von
Zuben
mij = T
Abi
p
+ T
Ab j
r
T
Abi
Ab j
mji = T
Abj
r
+ T
Abi
p
T
Abj
Abi
Hamming distance
—
—
GA based adjustment scheme with
elitist selection
Vargas et al.
F

L
X
k=1
(wkIi(k) ⊕P j(k))

F

L
X
k=1
(wkI j(k) ⊕Pi(k))

X
j
F

L
X
k=1
(wkE j(k) ⊕Pi(k))


—
—
GA based adjustment and learning
classifier system
Krautmacher
and
Dilger
F

L
X
k=1
(wkIi(k) ⊕P j(k))

F

L
X
k=1
(wkI j(k) ⊕Pi(k))

Hamming distance ∀Ag
—
—
Bilinear transformation for network
dynamics
Wang et al.
L
X
k=1
(Ii(k) ⊕Pj(k))
L
X
k=1
(Ij(k) ⊕Pi(k))
L
X
k=1
(E j(k) ⊕Pi(k))
—
—
Strengthened learning (RL), Obsta-
cle restriction method
Tsankova et al.
L
X
k=1
(Ii(k) ⊕Pj(k))
L
X
k=1
(Ij(k) ⊕Pi(k))
L
X
k=1
(E j(k) ⊕Pi(k))
—
—
a-priori
antibody
idiotopes
and
paratopes
Whitbrook et al.
P[xw1, ym]I[xi, ym]Hi
(1 −P[xi, yp])I[xw1, yp]Hi
P[xi, y j]G(xi) j
Ab concentration
GA (ext.)
RL:
P[xw, yd](t + 1)
=
max(0, P[xw, yd](t) + r ft+0.5)
Lee and Sim
Pre-computed γij
Pre-computed γi j
gi from FIS
Strategy transfer
—
FIS with task density as input
continued on next page
Table continued
Suppression
Stimulus 1
Stimulus 2
Cloning
Metadynamics
Auxiliary Functions
(Ab −Ab)
(Ab −Ab)
(Ag −Ab)
Jun et al.
Pre-computed mij
Pre-computed mi j
gi from FIS
Strategy transfer
—
T-cell concentration: η(1 −gi)Ai
Li and Wang
N
X
k=1
mikgk
N
X
j=1
mi jgj
Affinity: gj
—
—
T-cell: η(1 −gi)
Duan et al.
—
N
X
j=1
mi jgi jk
gj & CAik
—
—
—
Luh et al.
—
—
mcw + mr + mb
3
—
—
FIS is used for mcw, mr, mb
Luh and Liu
cos(θ j −θi)
cos(θi −θ j)
ftarget + fobstacle
—
—
Virtual target method for local min-
ima recovery
Dehuai et al.
h
cos(θo
j −θo
i ), cos(θg
j −θg
i )
i
h
cos(θo
i −θo
j), cos(θg
i −θg
j)
i
potential functions
—
—
—
Table ended
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