Neural Comput & Applic (2003) 12: 200–211 DOI 10.1007/s00521-003-0383-y O R I GI N A L A R T IC L E Catarina Silva Ỉ Bernardete Ribeiro Navigating mobile robots with a modular neural architecture Received: 28 March 2002 / Accepted: July 2003 / Published online: 14 November 2003 Ó Springer-Verlag London Limited 2003 Abstract Neural architectures have been proposed to navigate mobile robots within several environment definitions In this paper a new neural modular constructive approach to navigate mobile robots in unknown environments is presented The problem, in its basic form, consists of defining and executing a trajectory to a predefined goal while avoiding all obstacles, in an unknown environment Some crucial issues arise when trying to solve this problem, such as an overflow of sensorial information and conflicting objectives Most neural network (NN) approaches to this problem focus on a monolithic system, i.e., a system with only one neural network that receives and analyses all available information, resulting in conflicting training patterns, long training times and poor generalisation The work presented in this article circumvents these problems by the use of a constructive modular NN Navigation capabilities were proven with the NOMAD 200 mobile robot Keywords Constructive algorithms Ỉ Mobile robot navigation Ỉ Modular neural networks Ỉ Sensor fusion Introduction There has been an increasing interest in the development of intelligent mobile robots, i.e., robots that are able to learn to navigate and act in complex, possibly unknown, environments This interest grew with the realisation that a mobile robotÕs application environments are usually dynamic, leading to the search for new solutions for mobile robot navigation When attempting to satisfy the requirements of such a control system, it is often difficult to find a unique C Silva (&) Ỉ B Ribeiro ´ Centro de Informatica e Sistemas, Universidade de Coimbra, 3030 Coimbra, Portugal E-mail: catarina@dei.uc.pt control law that applies in all relevant regions of the parameter space [1] and that can evaluate all the information available The overflow of information is indeed a major problem in mobile robot control Neural networksÕ (NNsÕ) adaptive, noise filtering and generalisation capabilities have made them an obvious instrument for controlling mobile robots Traditional approaches use monolithic neural networks Monolithic systems are composed of just one NN that receives all data, learning the solution mapping Monolithic NNs present some problems, due to the usually conflicting tasks that exist in mobile robot navigation These can be handled by following a modular strategy, applying the divide and conquer principle and using functional task division This approach leads to NNs that are known as Modular Neural Networks (MNNs) [2] An MNN consists of a multiplicity of NNs organised in a way that improves both the systemÕs overall performance, and the effectiveness of the training and architecture determination [3] Monolithic NN training is normally a tedious procedure and it is usually difficult to justify the obtained parameters One of the most serious criticisms of NN is the fact that one does not know what is happening inside it In other words, an NN behaves like a black box A considerable benefit that can emerge from MNNs is an interpretable and relevant neural representation of the systemÕs behaviour [4] Another step towards clarifying NNs is the use of constructive algorithms as an approach for the incremental construction of potentially near-optimal NN architectures Such algorithms help overcome the need for the ad hoc and often inappropriate network topology choices that result from the use of algorithms that search for a suitable weight setting in an otherwise a priori fixed network topology [5] This article presents a constructive MNN architecture that performs the navigation control of a real mobile robot Sect states the questions underlying the problem of mobile robot navigation Sect justifies the need for MNN architectures Sect presents the constructive 201 NN algorithms, highlighting the potential improvements obtained by their use Sect describes the modular architecture developed, and Sect 10 presents the constructive method applied Sect 15 reports experimental results for this system, in both a simulated environment and a real mobile robot Sect 16 draws final conclusions and suggests possible extensions Mobile robot navigation As mentioned above, mobile robot navigation consists of the definition and execution of a trajectory to a predefined goal, while avoiding all obstacles, in an unknown environment There are a number of questions that arise when trying to navigate a mobile robot: – – – – how to get information on the environment how to deal with the various types of data what restrictions should be put on trajectory planning how to detect and avoid unknown obstacles Environmental information is usually gathered through sensors in the mobile platform As there are several types of sensors, care has to be taken when receiving online data Once an acceptable data interpretation has been found, the next step is to determine the trajectory There are several approaches to this task, and they can be broadly divided into two groups: The NOMAD 200 is a wheeled cylindrical robot, whose diameter is about 46 centimetres, illustrated in Fig The robot can move forwards or backwards with varying speed and turn right or left a variable number of degrees The robot has also a dead-reckoning system for keeping track of its orientation and position The deadreckoning system determines the robotÕs present position from a previous one with information regarding the path and velocity taken between the two positions This information is gathered by monitoring the platform traction wheels This data can have great relevance, since it is easy to obtain and can be gathered with negligible delay Moreover, it is always available and its update frequency is higher than other sensors The robot has 16 ultrasonic sensors and 16 infrared sensors for observing the surrounding environment Ultrasonic and infrared sensors are evenly distributed around the robot, yielding a 22.5 degree angle between any two adjacent sensors There are two sensors installed in each direction: an ultrasonic and an infrared sensor, distributed according to Fig The redundancy is only apparent, since the sensorsÕ ranges are very different While infrared sensors – global planning-based navigation, where, without having dynamic knowledge of the environment, a trajectory planner determines the best path from the start position to the goal position; – reactive navigation, using sensorial information to determine the robotÕs path online Global planning-based navigation relies on the hypothesis that the robotÕs action environment is sufficiently static to trust an a priori planning However, this hypothesis is rarely true, as the environment is usually much too changeable Examples of these environments are factories or public spaces, like airports Reactive based navigation takes a different approach Assuming that the mobile platform navigates in a truly dynamic environment, as it usually does, this strategy discards global planning, supporting the robotÕs navigation in sensorial information and behaviour patterns that are already known, or that are developed or learned This approach can lead to adaptive systems, with a certain level of learning [6] In this work we focus on the problem of navigating a NOMAD 200 mobile robot in an unknown environment, thus assuming a reactive approach Fig The NOMAD 200 mobile robot 2.1 The NOMAD 200 mobile robot This section describes the mobile robot that was used as a test bed for our experiments We shall first describe the robot, then the simulator Fig The Location of NOMAD 200 sensors 202 detect obstacles up to 60 cm, the ultrasonic sensorsÕ range is from 50 cm to 650 cm Therefore, in every evaluation, for each one of the 16 possible sensorial directions, only one type of sensor will be used, as will be explained in Sect The NOMAD 200 simulator has been used during initial experiments in order to set up the required NN system architecture It accurately models each of the NOMADÕs motion and sensing capabilities It also provides tools to test user-developed programs and recreate specific interactions within a user-defined environment An illustration of the user interface screen is shown in Fig This interface makes it possible to show both the pure simulation environment, and the representation of the robotÕs real trajectory, as will be shown in the results section MNNs The building block of any NN is the neuron The organisation of neurons in layers and the interconnection of these layers are the next steps to be taken in the neural architecture For this concept to be applied, the NN must be provided with sufficient resources (i.e., the correct architecture considering the input space) and, obviously, an algorithm capable of learning the inputoutput mapping by updating the NN weights Unfortunately these requirements are far from being accessible [4] The basic organisation just described can go one step further Specifically, an NN can consist of a multiplicity of networks organised in a modular structure [2] As already mentioned, modularity can be viewed as a manifestation of the principle of divide and conquer, which allows us to solve complex problems, by diving them into smaller sub-problems (modules), easier to solve and combining their individual solutions to achieve the final solution The use of global NNs (as the back propagation NN) and clustering NNs (as the radial basis function NN) can Fig The simulation environment lead to various advantages and drawbacks [4] Combining the two approaches to retain the best of each one is possible using an MNN Nevertheless, the application of the modular concept to an NN has to be systematised, thus: Task decomposition into sub-tasks; Module organisation; Module integration (communication) A global NN, as the multi-layer perceptron (MLP), is characterised by the fact that all its nodes are involved in each pattern processing This is the main difference when comparing with clustering NNs, where only a part of their structure is involved in each pattern processing The use of clustering NNs requires relatively few learning trials and tends to yield interpretable representations, whereas the global NN converges very slowly (or does not converge at all) and still has the black-box problem However, the clustering NN tends to be memory intensive, while global NNs have the advantage of smaller storage requirements and better generalisation performance It therefore seems very interesting to combine the desirable features of each approach, as a way of computing the information to obtain a better neural learning system A modular approach can also be justified on a biological basis In the human brain specific areas have been identified, responsible for specific tasks that not per se solve any particular problem However, in combination, those specific areas accomplish greater tasks, not foreseeable if the particular areas are examined separately An example of this situation is seen in the visual cortex, where the operations it performs are achieved by its division into different regions, each responsible for a smaller sub-task One of the important improvements achieved by MNNs is better generalisation A common approach in neural networks is to use architectures as small as possible to obtain better generalisation, because the ability of feed-forward NNs to generalise is inversely proportional to the number of weights involved [7] 203 Some other advantages are gained by using MNNs Firstly, dividing a task into sub-tasks will avoid the problems of temporal and spatial crosstalk [1] Temporal crosstalk occurs when a single NN is trained with different training sets in two different moments in time to perform two different tasks Usually the net forgets how to execute the first task, altering the previously trained weights Spatial crosstalk occurs when an NN is trained simultaneously for the two tasks, resulting in incoherent training patterns and long training times In either case the outcome is poor generalisation capability Finally, modularity can result in learning economy, since some modules can be reused or modified without altering the other modules, as will be demonstrated in this work in Sect 10 This economy can become crucial when hardware implementations are intended, since MNNs can facilitate the hardware realisation of neural networks [8] There are several types of modular networks: cooperative, competitive, sequential and supervisory [3] In all of them there is an implicit division of tasks They differ in the way the modules interact Whereas in cooperative modular networks all modules cooperate in the final decision, in competitive NNs the modules compete to win the chance to provide the solution In sequential MNNs the modulesÕ solutions are used sequentially to achieve the final solution, the computation of one module depending on the preceding one Supervisory networks have the task of supervising one or more modules [3] Having reflected on the many advantages of using a modular approach to mobile robot navigating problem, emphasising the reasons that led to our choice, we should now look at other successful approaches, whose merit should not be ignored These are: unsupervised learning methods [9], and reinforcement learning procedures [10] Unlike supervised learning, these methods not rely on a training set to learn Instead they learn more autonomously In reinforcement learning the only output that is available is the measure of the performance the NN is achieving: whether it is rewarded or punished This reinforcement signal is much less informative than a set of examples and it can be delayed, i.e., the success or failure obtained can result from past control signals A greater disadvantage of reinforcement learning is the fact that it is a slow process, largely owing to its stochastic nature Unsupervised learning depends on the input distribution to cluster the examples These procedures rely on the possibility that these more autonomous learning methods (non-supervised) can achieve behaviours not foreseeable with a human supervisor Sharkey et al [10] classify the self-learning of autonomous robots as a worthwhile scientific adventure, presenting real-life situations where intelligence emerges both from the interplay with the environment and the gradual development of actionsÕ representations in the world Constructive NNs Recently several NN learning models have been proposed for a wide range of applications Of them, the MLP, trained with the standard back-propagation (BP) algorithm, is the most common The BP algorithm searches for the solution using an a priori determined topology Usually, this procedure is only useful when the topology is correctly determined for the specific problem [11] If the chosen topology is too small, the network will not be able to learn the problem solution; however, if the topology is too large a memorisation process can occur, generating overfitting Research has therefore been conducted with the aim of optimising the NN dimension for each [12, 13] problem Generally, there are two approaches to this optimisation problem One starts with a bigger than necessary network, that is trained until an acceptable solution is found Then, useless hidden units are removed or pruned, using a pruning algorithm [14] The other approach is constructive algorithms, which start with a minimum configuration network and then add hidden units until an acceptable solution is reached Pruning algorithms have several disadvantages [11]: – it is often difficult to determine the appropriate initial network size; – most of the training time is spent with larger than necessary networks; – consequently it is not computationally efficient; – the solution found may not be the smallest possible for the defined performance Constructive approaches avoid most of these problems Thus, a constructive approach was followed to define the modular architecture that best handles the mobile robot navigation problem, which can be classified as a regression problem, whether a constructive modular architecture is used or not Before explaining the constructive approach followed, a formalisation of the regression problem is presented In regression problems, a d-dimensional input space, X, is defined, composed of independent variables, and there is a scalar variable, Y, denominated answer (this is a simplification, because the answer can have one or several dimensions) A regression surface, h, describes the desired relation between the variables X and Y The constructive process tries to find the NN architecture that best represents the h function [2] Determining the NN architecture that is able to approximate the objective function can be seen as a problem of searching in a function space [11], where the search space, the start state, goal state and the control strategy are defined by the constructive process The search space is a sub-space of a function space, which is usually a space where a norm, | |, is defined and satisfies certain conditions: 204 ktk=0, if and only if t=0; kktk=|k|ktk, for any scalar k; kt+xk £ ktk+kxk The generation and test methodology is used in all NN constructive processes to: The norm gives a notion of the distance in the space: if x, t are vectors in the normed space, then the distance from x to t (and vice-versa) will be kt)xk Different norms, and consequently different spaces, are used to represent and solve different kinds of problems As an exhaustive search is computationally prohibitive, the search space is only a sub-space of the function space and is determined by the way new units are generated Notice that, unlike conventional methods with fixedsized networks, constructive algorithms have two search levels The first one searches the best NN architecture and the second searches, within the defined architecture, for the best set of weights The initial state deals with the network before the constructive algorithm takes place Usually this initial network does not have hidden units or connections The training is carried out in this initial structure and hidden units are added and connected as long as the performance is not satisfactory The final states are acceptable problem solutions, good approximations for function h This evaluation depends on the problem on hand The distance measure depends on the defined space norm For two functions h, g, defined in an input space X, a uniform distance can be used, according to Eq 1: kh À gk ¼ maxjhð xÞ À gð xÞj : x2X ð1Þ If h is the objective function and g is the constructive network implemented function, the uniform distance emphasises the x values for which the approximation is worst (with a larger absolute error), using these approximations as a distance measure, assuring the absolute correction for error boundaries Another error measure often used is the Lp distance, in Eq 2: !1=p Z p ; ð2Þ jhð xÞ À gð xÞj dl kh À gkp ¼ X where l is the input space distance and p is a real number, p‡1 If p=2, Euclidean distance is obtained In Eqs and 2, the distance measure is used in all the space, not only in the training patterns, because the greatest interest in the NN test lies not in the training examples, but in its generalisation capabilities There can be several final states, i.e., it is possible that several networks approximate the objective function with the same precision or error The advantage of this fact is that it is only necessary to find one of these networks The main obvious disadvantage is that different network configurations represent different functions, leading to the representation of different realities generate the network according to a control strategy that defines the solution search; test the generated network; if it is acceptable, end the process; if not, return to point The search for the best set of weights can be accomplished through several optimisation algorithms In topology matters, constructive methods always search for the smaller networks first, increasing their size only if necessary Besides having better generalisation capabilities, smaller networks also present other benefits: – computational costs, measured by the number of arithmetic operations, are of O(W), where W represents the number of network weights Therefore, smaller networks are more efficient, not only in training, but also online; – a smaller network is more easily described by a rule set and is easier to interpret In this work we explore a class of constructive algorithms that systematically determine the NN architecture Constructive algorithms aim to improve generalisation and simplify learning through the dynamic creation of problem-specific NN architecture A review of constructive NN algorithms can be found in [11] Modular architecture Mobile robot navigation has a considerable number of issues that can be analysed and studied, as was pointed out in Sect In this work we focus on the problem of navigating a mobile robot to a defined goal in an unknown environment, minimising navigation time and positioning error [15, 16] Navigation systems can be broadly divided into two types of situations: where there is an environment map or where there is not This map can exist prior to the planning, or can be built while the robot navigates in the environment There are several real situations where the existence of a map is not an objective and has little relevance to solving the problem These situations occur when the robotÕs environment is too dynamic, which makes a mapÕs construction too costly to compute In these conditions, the robot may not maintain a map, using its sensorial information to reach the desired objective This is the situation we propose to examine, using an NN The first approach is usually a monolithic network, but a deeper evaluation clouds the effectiveness of this approach [17, 18] In fact, the large amount of available sensorial information can make distinguishing the relevant information a problem Therefore, a monolithic NN that receives all available information can have very long training times and poor generalisation capabilities, as we have corroborated empirically [19] 205 All these factors, and all the MNNÕs features suggested in Sect 5, emphasise the usefulness of MNNs in mobile robot navigation The first step is to functionally divide our proposed task into sub-tasks Mobile robot navigation was divided in two main tasks that proceed directly from the problem definition, presented earlier in this section: – obstacle detection and avoidance; – objective direction This division is easily justifiable, since to fulfil mobile robot navigation one has, firstly, to detect and avoid all obstacles in the way, and secondly, to reach an objective The evidence that these two tasks can be contradictory, i.e., that one can lead the robot in a different direction from the other, strengthens the modular concept application to the problem, because, as was mentioned in Sect 5, temporal and spatial crosstalk can occur when a problem has contradictory objectives These two tasks and the moduleÕs interconnection structure will now be described Figure presents the defined architecture 5.1 The obstacle detection and avoidance module This task has the objective of detecting and avoiding unknown obstacles in the robotÕs environment This module will play a central role in the resolution of the problem, since it will receive and fuse all the sensorial information available 5.1.1 Handling sensorial Information The NOMAD 200 mobile robot has two types of sensors aligned in each of the 16 sensorial directions: an infrared sensor and an ultrasonic sensor The difference in their ranges can be used to optimise the information in each Fig The modular architecture of the 16 possible sensorial directions Ultrasonic sensors are used to give global information about the area, but when the robot is close to obstacles, it uses infrared sensors The reason for this is that an ultrasonic sensor cannot give the distance to an obstacle when it is less than 50 centimetres Thus, when the output of the ultrasonic sensor is 50 centimetres or less, the infrared sensor, in that specific direction, will be used Moreover, an ultrasonic sensor output that exceeds 100 centimetres is always set to 100 centimetres This truncation occurs because objects whose distance is greater are not considered for obstacle avoidance, since they carry little information and are very often the result of multiple reflections of the ultrasonic wave Eq displays these refinements ultrasonic sensor650; < infrared; ð3Þ Sensor ¼ 100; ultrasonic sensor>100; : ultrasonic; otherwise: 5.1.2 Internal structure The obstacle detection and avoidance module has 16 possible inputs, corresponding to the 16 possible sensorial directions presented in Fig As can be inferred, a system of cardinal points has been assigned to the sensorial directions available, dividing the inputs into four quadrants (North, East, South and West) Considering that the robot always faces North, it could be said that it is not a real cardinal system, but a pseudosystem, because our cardinal points are not static Although all the sensors are evenly distributed, the four quadrants not have the same level of imporance In fact, as the robot always faces North, this will be the quadrant with a higher probability of collision, and consequently the most important as far as the obstacle detection and avoidance module is concerned Because 206 Table Codification of the North output Table Obstacle detection and avoidance module codification N1 N2 Direction OD1 OD2 OD3 Direction 0 1 1 N NW NE Other 0 0 1 0 1 0 1 0 N NW NE E S W of its relevance, therefore, the North quadrant will have a specialised module that will monitor and manage the available sensors within its action range The North module uses all available sensors, i.e., the five sensors shaded in Fig (NW, NNW, N, NNE and NE) The training set for the North module was derived from actual trajectories driven by the supervisor in simulated environments It consists of 120 sets of sensorial information and the desired direction associated with it, codified according to Table The test set was derived in the same way and has 38 samples The codification was carried out using two outputs for the North module There are three available output directions, since it is also possible not to consider the North quadrant as an option The output codification was constructed using Gray code1, reducing the error when there is a failure in one output The other three modules (East, South and West) are smaller and identical, making it possible to construct just one module and replicate the other two, taking advantage of the learning economy that underlies the modular structure Each one of these three modules watches one of the other quadrants and has three sensorial inputs that correspond to three sensorial readings of the respective quadrant, as illustrated in Fig There is only one output neuron, which indicates the confidence that there is an obstacle in that quadrant The supervisor used the robotÕs simulator to define the training set by defining trajectories in different scenarios The training set was composed of 30 patterns An integrating module was defined to integrate the four modules (North, East, South and West), (see Fig 4) The integrating module is a neural network with inputs: two from the North module and one from each of the other three modules It has three output neurons, which codify the direction to be followed according to Table The training set for the integrating module was generated by the supervisor and consisted of 32 training examples that constitute all possible combinations of the binary inputs Notice that, although the training set is binary, when the module is online, the inputs will be continuous since they will result from other NNs This integrating module was first tested separately In the test, a goal was not defined and the robotÕs objective was to wander indiscriminately, detecting and avoiding unknown obstacles The results were very satisfactory, Binary code in which only one bit changes from one state to the other Fig Tests with the obstacle detection and avoidance module because, as can be seen in Fig 5, the robot was able to wander without colliding with obstacles 5.2 The objective direction module The objective direction module computes the direction heading to the goal, considering the goal position, the robotÕs actual position (xi,yi) and the robotÕs orientation, hi The desired orientation is computed according to Eq 4: yo À yi ho ¼ at an ; ð4Þ xo À xi where (x0,y0) is the objectiveÕs position and h0represents the angle to the objective The rotation the robot must perform, h, is obtained by Eq h ẳ ho hi : 5ị The direction is also codified according to Table 5.3 The navigation module At this stage, the structures of the obstacle detection and avoidance module and the objective navigation module have been completely defined It remains to be determined how the resulting outputs will be combined To solve this issue, a navigation module was built, as shown in Fig This module receives nine inputs: three outputs derived from each of the two previous modules and three extra sensor values These sensorial inputs are obtained 207 in the objective direction, as a way to introduce more information regarding that specific and important direction For instance if the direction heading to the goal is West, S1 will be the sensorial value in WNW direction, S2 the sensorial value in W direction and S3 the sensorial value in WSW direction (see Fig 2) All these sensorial values are subjected to the handling procedure described in Sect and are further scaled to [0,1], so that all inputs to the navigation module are in this interval This module thus has nine inputs and three outputs that codify the direction to follow according to Table because it is essentially driven by the outputs of the navigation module (see Fig 4) The supervisory module training set was composed of 80 examples, and the test set had 25 examples These examples had two inputs: – one that reflects the degree of convergence between the output of the navigation module and the output of the obstacle detection and avoidance module; – the other presents a probability of the robot having a cyclic behaviour The output of the supervisory module was binary, indicating which functioning mode should be pursued: navigation or obstacle contour mode 5.4 The supervisory and angular memory modules At this stage the systemÕs architecture is defined Most navigation situations presented to the architecture defined in Fig were successfully solved, as will be shown in Sect 15 There are, however, a few situations where the robot exhibited a cyclic behaviour in simulation environments To circumvent these situations, two changes were introduced to deal with the specific situations that were detected when the obstacles were much larger than the robotÕs dimensions or when they presented peculiar configurations Figure presents three examples of these situations, in which the robot is unable to reach the desired objective, exhibiting cyclic behaviour Figure shows a simulator image, where the robot is unable to surmount the obstacle to reach the goal (placed behind it) Thus, two additional modules were defined to cope with situations where the proposed architecture failed: the supervisory module and the angular memory module The addition of these modules further serves to demonstrate the modular approach advantages The supervisory module was developed to detect obstacles whose dimension was much larger than the robotÕs dimension, because a somewhat erroneous behaviour was detected when such obstacles were present The moduleÕs algorithm is represented in Fig Analysing the algorithm, we can conclude that when this neural module detects that the robot is in the presence of a large obstacle, an obstacle contour mode is activated When this is not the case, the normal functioning mode is used This normal mode was called navigation mode, Fig Examples of non-circumventable obstacles Fig A simulation example of the robotÕs cyclic behaviour Fig The supervisory moduleÕs algorithm 208 The obstacle contour mode favours the outputs of the obstacle detection and avoidance module to establish the direction to follow, as a strategy to contour the large obstacle that the robot is faced with With the introduction of the obstacle contour mode the systemÕs architecture abandons its co-operative nature and becomes competitive (see Sect 5), in the sense that there can be two functioning modes that compete to navigate the robot When the functioning mode changes from navigation to obstacle contour and vice versa, there is a possibility of repeatedly making mistakes The angular memory moduleÕs objective is to detect such situations To this, the module keeps track of the angular directions followed when there is a change in the functioning mode, to detect cycles in the trajectory Using a circular memory, the transition points are memorised and when a repetition is found an alternative direction is followed, as a way to break the cycle This module is not an NN, because its main feature is a memorisation one Module construction The topology and parameters of all the NN modules defined so far were constructed and not determined ad hoc This section explains how the NN modules were constructed A dynamic node creation [11] method, initially proposed by Ash [20], was used with a variant of the BP algorithm In this algorithm, sigmoid units are added, one at a time, in the same hidden layer Every time a new unit is added, the training procedure takes place These algorithms are simple, since they are based on the iterative learning algorithm application, maintaining all the advantages of the constructive methods described in Sect The learning algorithm used was a variant of the BP algorithm, with a momentum coefficient, c and a variable learning coefficient, a The learning coefficient, a, was updated according to the expression in Eq 6, where k represents the iteration k ¼ 0; < 0:2; ak ị ẳ ak 1ị=2 k f3; 7; 10; 31g  103 ; ð6Þ : aðk À 1Þ otherwise: As already mentioned, NN constructive algorithms start with an initial configuration and add neurons until some criterion is satisfied Each neural module presented in the architecture had its initial configuration determined by the number of inputs, the number of outputs and the number of initial hidden units Table summarises the results obtained, giving the number of training patterns, the final configuration achieved and the mean square error (MSE) obtained, for each NN module Results This section presents the results for several simulated and real environments In each figure, the robot is represented by a darker circle at the end of the defined trajectory as in [21] The other end is its initial position Figures and 10 show simulated environments, similar to real ones with several small obstacles that interfere with the robotÕs navigation In these examples the objective is reached by the base modular architecture As can be observed, the objective is reached while avoiding all the small obstacles in these cluttered environments Figures 11, 12, 13 and 14 are further examples of simulated navigation that show how the defined architecture deals with some situations through the supervisory module, since the robot was faced with large obstacles In these three examples the supervisory module determines that there is a large obstacle, and the obstacle contour mode is switched on Once the obstacle is overcome, the supervisory module switches back to navigation mode and the objective can be easily reached Figures 15 and 16 show complex environments that are solved by the changes made to the base architecture (Sect 13) It can be seen that the robot does not reach the objective in a straightforward manner In these two examples, the peculiarity of the obstacles misleads the robot in its first attempt, but the angular memory module keeps track of the decisions made and prevents repetition of the mistake when the robot reaches the For the momentum term, c, the test was carried out with values in [0,1], with a 0.05 step Table Results obtained with the dynamic node creation method Module Test set Configuration North East South West Integrating Navigation Supervisory 120 30 30 30 32 396 25 3 fi fi fi fi fi fi fi 1 4 fi fi fi fi fi fi fi 1 3 MSE 0.028 0.001 0.001 0.001 0.001 0.002 0.002 Fig The trajectory defined with the base architecture 209 Fig 10 The trajectory defined with the base architecture Fig 13 Entering an alley (the supervisory module) Fig 11 The trajectory defined by the architecture with the supervisory module (from right to left) Fig 14 The trajectory defined by the architecture with the supervisory module Fig 12 Leaving an alley (the supervisory module) decision point the second time (in both cases it is the point where it turns inside the obstacle) Figures 17, 18 and 19 show simulator images of real trajectories, taken by the NOMAD 200 mobile robot All three snapshots demonstrate that the robot is agile, even in narrow confines Figure 20 presents a real trajectory being performed in a cluttered environment by the NOMAD 200 mobile robot Fig 15 The path defined with the supervisory module and the angular memory module All the situations presented to the robot, in simulation and real environments were successfully dealt with, i.e., the final goal was reached When the supervisory or angular modules had to step in, there was, as mentioned, a cyclic behaviour that was broken 210 Fig 19 The real trajectory taken by the NOMAD 200 mobile robot in a cluttered environment Fig 16 The path defined with the supervisory module and the angular memory module, in an environment like the one illustrated in Fig 6c Fig 17 The real trajectory taken by the NOMAD 200 mobile robot Fig 20 The NOMAD robot performing a real trajectory Fig 18 The real trajectory taken by the NOMAD 200 mobile robot in an environment with front obstacles Conclusions NNs, because of their adaptive and learning abilities, are often used in mobile robot navigation But the use of a monolithic NN has disadvantages that can be circumvented by the application of a modular strategy MNNs are major candidates for mobile robot navigation in unknown dynamic environments The overload of sensorial information available for analysis can be dealt with by using the divide and conquer principle underlying MNNs This work has proposed a new modular architecture to navigate mobile robots in unknown environments This architecture presented a performance improvement when compared with a monolithic NN, because crosstalk problems were prevented and smaller architectures were achieved, yielding better final generalisation ability Taking advantage of the modular structure defined, new modules were added to the base architecture, as a way to improve its performance in specific situations Moreover, each moduleÕs internal structure has been constructively determined, using a dynamic node creation Method This algorithm allows an appropriatelysized topology to be designed for each neural module and permits weight definition using a modified BP algorithm The results obtained for the NOMAD 200 mobile robot with this modular constructive architecture show its effectiveness and robustness, showing that MNNs can be used to navigate a mobile robot around obstacles, without knowledge of the environment 211 Future work will include the study of online learning as a way to improve the system performance If it is found that the robot has made a mistake, it could be possible to identify the module responsible and eventually re-train or re-construct it Another line of future work is the research into potential improvements introduced by adding static environmental information, such as artificial landmarks Acknowledgements This work was partially supported by the Por´ tuguese Ministerio da Ciencia e Tecnologia and the European ˆ Union through the R&D Unit 326/94 (CISUC) References Jacobs R, Jordan M (1993) Learning piecewise control strategies in a modular neural network architecture IEEE Trans Sys Man Cybern 23(2):337–345 Haykin S (1999) Neural networks—a comprehensive foundation Prentice Hall, New York Sharkey A (ed) (1999) Combining artificial neural networks Springer, Berlin Heidelberg New York Ronco E, Gawthrop P (1995) Modular neural networks: a state of the art Technical report: CSC-95026, Centre for System and Control, University of Glasgow, Glasgow, UK Parekh R, Yang J and Honavar V (1995) Constructive neural network learning algorithms for multi-category pattern classification Technical Report TR95–15, Artificial Intelligence Research Group, Department of Computer Science, Iowa State University, Ames, IA Krose B and van Dam J (1997) Neural vehicles In: van der Smagt P, Omidvar O (eds) Neural systems for robotics, Academic Press, New York Baum E, Haussler D (1989) What size net gives valid generalisation? Neur Comput 1:151–160 Auda G, Kamel M (1999) Modular neural networks: a survey Int J Neur Sys 9(2):129–151 Nehmzow U (1992) Experiments in competence acquisition for autonomous mobile robots Dissertation, University of Edinburgh 10 Sarkey N, Heemskerk J (1996), The neural mind and the robot In: Browne A (ed) Current perspectives in neural computing, IOS Press, Amsterdam, The Netherlands 11 Kwok T, Yeung D (1997) Constructive algorithms for structure learning in feed forward neural networks for regression problems IEEE Trans Neur Ntwks 8(3):630–645 12 Mataric M (1992) Integhration of Representation Into GoalDriven Behavior-Based Robots Proceedings of the IEEE Transactions on Robotics and Automation 8(3) 13 Mayoraz E, Aviolat F (1996) Constructive Training Methods for Feed Forward Neurol Networks with Binary Weights Int J Neur Sys 7(2) 14 Mozer M, Smolensky P (1988) Skeletonization: a technique for trimming the fat from a network via relevance assessment Adv Neur Info Proc Sys 1:107–115 15 Pomerleau D (1991) Rapidly adapting artificial neural networks for autonomous navigation Neu Inf Proc 3:429–435 16 Dracopoulos D (1998) Robot Path Planning for Maze Navigation Proceedings of the 1988 IEEE World Conference on Computational Intelligence, pp 2081–2085 17 Schmidt A, Bandar Z (1997) A Modular Neural Network Architecture with Additional Generalisation Abilities for Large Input Vectors Proceedings of the 3rd International Conference on Artificial Neural Networks and Genetic Algorithms (ICANNGA 97), Springer, Berlin Heidelberg New York, pp 40–43 18 Jacobs R, Jordan M (1991) A competitive modular connectionist architecture In: Lippmann et al (eds) Neural Information Processing Systems 3, vol ´ 19 Silva C, Cristomo M, Ribeiro B (2000) Monoda: A Neural Modular Architecture for Obstacle Avoidance Without Knowledge of the Environment Proceedings of the 2000 International Joint Conference on Neural Networks 20 Ash T (1989) Dynamic node creation in backpropagation networks Connect Sci 1(4):365–375 ´ 21 Silva C, Cristomo M, Ribeiro B (2000) A Modular Learning Architecture for Navigating NOMAD Mobile Robot 8th International Conference on Information Processing and Management of Uncertainty in Knowledge Based Systems ... approach, as a way of computing the information to obtain a better neural learning system A modular approach can also be justified on a biological basis In the human brain specific areas have been identified,... tasks that not per se solve any particular problem However, in combination, those specific areas accomplish greater tasks, not foreseeable if the particular areas are examined separately An example... the use of a monolithic NN has disadvantages that can be circumvented by the application of a modular strategy MNNs are major candidates for mobile robot navigation in unknown dynamic environments