Shared Potential Fields and their place in a multi-robot co-ordination taxonomy
Introduction
In the previous work, we introduced a novel form of multi-robot co-ordination architecture, which we termed the ‘Shared Potential Field’ (SPF) architecture [2], [3]. Two variations of the system were introduced, which differ in terms of their degree of belief in sensor readings: an optimistic variant of the SPF, which is more inclined to believe in the absence of obstacles, and a pessimistic variant, which is more inclined to believe in the presence of obstacles. From now on these are referred to as the ‘Optimistic SPF’ and the ‘Pessimistic SPF’, respectively. The Optimistic SPF and the Pessimistic SPF were compared against a non-sharing control in simulation, over a number of search problems varying in object density and the number of targets. Results showed that the SPF approaches significantly outperformed the non-sharing system. The fact that no difference was observed between the two SPF systems was a result of the lack of noise within the simulated environment.
In [4] the SPF approach was transferred onto a real robotic system and the single target search problem was repeated in a laboratory environment. Results showed that unlike in the simulation, only the Pessimistic SPF significantly outperformed the non-sharing control. This was attributed to the noisy nature of the real world, resulting in pessimism being the best practice. The SPF can be defined as a reactive robotic system. Therefore, it was decided to compare the SPF against a different type of robotic architecture. This paper is an extension to the previous work by Baxter et al. presented at CIRAS 2008 in which experiments comparing the SPF method against a hybrid system were discussed [5].
Hybrid systems were pioneered in the early work of Arkin [1], and are an attempt to merge the benefits of both deliberative and reactive systems. Deliberative systems plan all the actions they are going to take before performing them; as such they rely heavily on complete and accurate information about the environment. Reactive systems meanwhile do no perform and planning; each action taken is a consequence of sensory information. However, due to the reactionary nature of their actions reactive systems often find sub-optimal solutions to problems. In a hybrid system the high level goals of the system are achieved through a deliberative component, whilst the low level goals are achieved through a reactive component. For example, the deliberative component will plan the shortest path across a room taking into account static obstacles. Whilst traversing this path if an unexpected obstacle is discovered the reactive component will take over until the obstacle has been successfully passed and the original path rediscovered.
This paper is structured as follows: In Section 2 the SPF method will be described in detail. Two variants will be introduced a pessimistic and an optimistic approach in terms of belief in sensor values. The SPF method will then be compared to the traditional potential field method in terms of susceptibility to the known limitations of potential fields. The method’s place within Farinelli’s multi-robot taxonomy will also be discussed. Section 3 will describe the hybrid system that we will compare our SPF method against in this paper. The hybrid system consists of two modules, a deliberative path planner, and a reactive motor controller. In Section 4 the experimental setup will be explained in detail, including a description of the robots used and of the laboratory environment. Section 5 will present the results obtained, and will show that the SPF method significantly outperformed the hybrid system in almost all cases. Section 6 will conclude this paper, with a discussion of the results obtained and some proposals of possible future areas of research.
Section snippets
Shared Potential Field (SPF)
The outline of the processes involved in the SPF method is as follows: Individual robots construct potential fields from available sensor data (in the current system only ultra-sonic data is used), see Fig. 1A–B. Robots that are assigned to the same group then calculate local group intersections and share relevant potential field information, Fig. 1C. Each individual robot then creates a combined potential field using the shared information (Fig. 1D) and then makes the relevant action
The hybrid system
The hybrid system we implemented was comprised of two modules. A diagram of the complete hybrid system architecture is given in Fig. 9. The first module, a deliberative module, was the Wavefront propagation path planner, which given a map of the environment calculated the shortest path to randomly generated targets. Random targets were generated using a lagged Fibonacci pseudo-random number generator over a uniform distribution. The targets and positions and orientation were all generated
Experimental setup
The type of robot used in the experimentation was a Merlin Miabot Pro, see Fig. 12. Each Miabot was approximately 18 cm×8 cm×8 cm and was equipped with the following sensors/actuators:
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Differential drive: With an optical encoder resolution of 0.04 mm and a maximum reported speed of 3.5 m/s, this is limited to 1 m/s in the experimentation in order to allow accurate tracking by the overhead camera system. The Miabot is non-holonomic.
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Ultra-sonic array: With a range of approximately 3 cm–2 m and a
Results
Table 1 shows the average time taken, in seconds, for the hybrid system to complete the search task with a given number of Miabots. The best results for a given number of Miabots, in a given environment, are shown in bold. The hybrid system clearly performs best in the sparse environment (environment 3). However, this is still markedly worse than the two potential field sharing systems. Further detailed statistical analysis follows.
Discussion
In this paper we have presented the findings from comparing the SPF against a hybrid system, in a laboratory setting.
The results section clearly shows that the hybrid system performed best in the sparse environment (environment 3), this is due to two main reasons. Firstly, the sparser the environment, the more valid paths/goals the Wavefront algorithm could plan, which lead to a greater area of the environment being explored. Secondly, as there were less obstacles in the environment the ND
Joseph L. Baxter received a B.Sc. degree in e-commerce and digital business from the University of Nottingham, UK, in 2004. He is a researcher with the Automated Scheduling, Optimisation and Planning (ASAP) research group in the School of Computer Science at the University of Nottingham, UK. His primary research interest is in multi-robot systems.
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Joseph L. Baxter received a B.Sc. degree in e-commerce and digital business from the University of Nottingham, UK, in 2004. He is a researcher with the Automated Scheduling, Optimisation and Planning (ASAP) research group in the School of Computer Science at the University of Nottingham, UK. His primary research interest is in multi-robot systems.
Edmund K. Burke is Dean of the Faculty of Science at the University of Nottingham and he leads the Automated Scheduling, Optimisation and Planning (ASAP) Research Group in the School of Computer Science. He is a member of the EPSRC Strategic Advisory Team for Mathematics. He is a Fellow of the Operational Research Society and the British Computer Society and he is a member of the UK Computing Research Committee (UKCRC). Prof. Burke is the Editor-in-chief of the Journal of Scheduling, Area Editor (for Combinatorial Optimisation) of the Journal of Heuristics, Associate Editor of the INFORMS Journal on Computing, Associate Editor of the IEEE Transactions on Evolutionary Computation and a member of the Editorial Board of Memetic Computing. He is also the Research Director of EventMAP Ltd. and a Director of Aptia Solutions Ltd, both of which are spin out companies from the ASAP group. Prof. Burke has played a leading role in the organisation of several major international conferences in his research field in the last few years. He has edited/authored 14 books and has published over 180 refereed papers. He has been awarded 47 externally funded grants worth over £11M from a variety of sources including EPSRC, ESRC, BBSRC, EU, Research Council of Norway, East Midlands Development Agency, HEFCE, Teaching Company Directorate, Joint Information Systems Committee of the HEFCs and commercial organisations. This funding portfolio includes being the Principal Investigator on a recently awarded EPSRC Science and Innovation award of £2M, an EPSRC grant of £2.6M to investigate the automation of the heuristic design process and an EPSRC platform grant worth £423K.
Jonathan M. Garibaldi is an associate professor at the University of Nottingham, and is a member of the Intelligent Modelling and Analysis (IMA) research group. His main research interest is in the modelling of human decision making, primarily in the context of medical applications. His work to date has concentrated on utilising fuzzy logic to model the imprecision and uncertainty inherent in medical knowledge representation and decision making.
Mark Norman is the Managing Director of Merlin Systems Corporation Ltd. The Manufacturers of the Miabots and the global tracking system used in the experimentation dicussed in this paper.