Path Planning Strategies Inspired By Swarm Behaviour of Plant Root Apexes
Study Reference Number: 09-6401
Type of activity: Standard study (25 k€)
Background and motivation
Exploring unknown environments and identifying potentially interesting or hazardous areas is a challenging task for an autonomous agent. In the absence of a priori provided maps or landmarks guiding navigation, researchers are considering multi-agent systems trying to exploit the inherent parallelism of such systems. Many scientific research works following this direction draw inspiration from biological swarm models. In such models, self-organised exploration strategies emerge at the collective level as a result of simple rules followed by individual agents. To produce the global behaviour, individuals interact by using simple (often indirect or stigmergic) and local communication protocols. Social insects are a good biological example of organisms collectively exploring an unknown environment, and they have often served as a source of direct inspiration for research on self-organized cooperative robotic exploration and path formation in groups of robots using swarm intelligence techniques (e.g. Payton et al 2003, Svennebring and Koening 2004, Schmickl et al 2008, Nouyan et al 2008). The benefit of such distributed techniques lies in the fact that they produce robust and scalable systems, contrary to traditional approaches often based on centralised architectures and map-like representation of the environment.
Swarms are formed when individuals collocate to a higher order by using simple rules (in fish e.g.: align with next fish, keep speed and distance). Swarm formation is ubiquitous in nature and it is observed not only in highly developed vertebrate animals, but also in insects (ants: Hoelldobler and Wilson 2008, wasps: Gadagkar 2001). From an engineering point of view, it is beneficial to analyse the global patterns observed and subsequently to break them down into a set of simple rules governing individual agents, generating the complex global behaviour. Recently, Iain Couzin (Couzin et al. 2005, Couzin 2007) proposed a model for the flocking behaviour of fish schools by essentially identifying a minimal amount of information that allows biological complex behaviours at the collective level to be digitally reproduced. The a) repulsion, b) attraction, c) heading alignment laws do not have a proven biological origin, yet they are incredibly successful in generating (in digital simulations) behavioural patterns similar to the ones of real swarms. Thus, it makes sense to consider this set of basic behaviours as a starting point to design artificial multi-agent systems displaying flocking properties (e.g Izzo and Pettazzi 2007)
Swarms are often considered to be formed by groups of animals (birds, fish, insects, etc.). However, at a more abstract level, we can see other groups of autonomously deciding but jointly acting agents as a swarm, as long as the system is characterised by a lack of central coordination, limited and rather simple communication protocols and simplicity of the individual agents.
The physiological union of the tips of the roots of a plant (apexes) serves the greater task of supporting and nurturing the plant (among others). In fact, all directional growth decisions and a majority of environmental sensing are made in the apex. Growth patterns of roots are basically influenced by gravity, genetics, soil conditions, and distribution of nutrients (H2O, CO2, minerals, etc.). Since there is no anatomic evidence for a central sensing and decision unit and considering the rather low computational capacity of a plant cell (compared to neuronal systems of animals, for example), it appears meaningful to consider the apex as a simple autonomous unit taking decisions on own account (Baluška et al. 2004). There is some evidence of communication between apexes (Davies and Zhang 1991, Ali et al. 1999), but a higher, centralized brain has never been observed in plants. Yet, when looking at the root as a collective, growth patterns are not chaotic, but seem to follow a higher order, and emerge as a result of the individual decision-making of the apexes.
Considering a plant as a swarm of individuals is not a new concept, as it was firstly described in 1800 by Erasmus Darwin (Darwin 1800). At that time, plant-philosophers discussed the individual 'minds' of plant apexes (mostly those of the sprout) and their power to turn into an entire plant when cut off and put into soil as joining a greater organism and functioning similar to a swarm of individual animals. In later discussions this swarm concept was dismissed as a philosophical concept but still the absence of a central master mind and the distribution of decision loci led to the formulation of meta-population to characterize plants (White 1979).
Analyzing and subsequently simulating root growth has been in the focus of previous research (root analyses, e.g.: Berntson 1994, Coutts 1983, Doussan 1998, Ozier-Lafontaine et al. 1999, Lynch 1995, Pregitzer et al. 2002; growth and branching simulations e.g.: Pagès et al. 1989, Lynch et al. 1997, Hermann 2004). The major justification for these analyses derives from agricultural/physiological questions on root efficiency, soil exploitation, nutrient uptake per volume root, etc. The main means used are fractal methods, i.e., describing root architecture as a fractal. This work nicely models root architectures, also able to incorporate lack of nutrients, CO2, water etc. However, this technique involves recursive formulation and hierarchical levels and although the simulations of roots match quite well the observed growth patterns in real plants, it does not reflect the decision processes actually going on during root growth.
Trying to infer basic operational principles from plants, and in this case root swarms, for implementation on engineering the design of efficient exploration algorithms has the advantage that the exploration strategy’s blueprint is imprinted on the root and directly observable. Contrary to other biological systems for which thousands of experimental trials have to be observed in order to deduce patterns in the exploration strategies, in the case of roots these strategies are available and at our disposal right from the start. Even if the social insect metaphor is straightforward for implementation on engineering the design of efficient exploration algorithms, it suffers from an inherent disadvantage: the exploration of an unknown terrain (or volume) is done before the discovery of food sites, etc. and hence is very difficult to systematically observe.
The research team of the applying university is asked to submit a research proposal replying to the points outlined below.
1) Modelling root growth as a swarm of apexes
The main objective of the study is to identify the minimal amount of information that a root apex needs to know in order for the entire root to grow the fascinating and complex structures (e.g. bean- or dichotomous branching patterns) we know and that explore and exploit the soil. Information available from existing botanic research is to be used to locate these behaviours. Once identified, these behaviours will be coded into a plant root simulation algorithm, that is, an algorithm that generates a given root structure based on a set of rules (behaviours) at the level of the apex.
The growth decisions of each single apex are following an integration of a number of variables - fixed and dynamic ones. In order to model an apex's behaviour and the outcome of a group of apexes in a plant, the following assumptions are made:
- The group of apexes in one given plant is considered as a swarm, at a first stage not interfering with neighbouring plants. Each apex (tip of a root) is thus an autonomous agent. The apex decides its direction of growth according to a number of parameters it senses. So it is modelled as an agent that "senses" and "actuates", but also communicates with the other "agents". One possible way of interaction could be "stigmergic"; therefore, by modifying the environment, root apexes are influencing the behaviour of other apexes. Arguably, direct communication (specific root apex to root apex) is rather limited. The research group is asked to shed light on the communication strategies within the ‘root swarm’.
- The root part behind the apex displays the history of the 'swarm' of apexes decisions.
- Examples of root behaviours that may be taken into account are:
- Gravity (following, but also integrating results on micro-gravity research)
- Water (following)
- Nutrients (following)
- Touch (avoiding)
- CO2 availability (growth rate)
- Photosynthesis rate (growth rate)
- Other, neighbouring, roots of the same plant (avoiding, potentially using H2O gradient)
- Static force balance (counter-moment generating)
- In principle, the growth direction would use all the considered parameters transformed into vectors and summed up.
2) Assessment of the simulation algorithm
The simulation results are to be compared qualitatively to existing root growth simulation models and with detailed descriptive work from existing botanic literature. Secondly, the operational principles underlying the behaviour of the modelled apexes will be used as a basis to design the individual behaviour of autonomous agents involved in a collective exploration task. The performance of the resulting collective exploratory algorithm will be assessed and compared to existing state-of-the-art terrain exploration and dispersion robotic strategies. Finally, the resulting algorithm will also be tested on a simulated Mars surface-like environment.
Collaboration with the Advanced Concepts Team
This study is mainly addressed to research laboratories in the fields of plant biology, swarm intelligence research, artificial intelligence. The project will be conducted in close cooperation with the ACT-researchers. In addition to the frequent scientific discussions, ACT-researchers will provide input concerning space related issues, biological background and artificial intelligence expertise. Furthermore, the ACT researchers will, together with the university group, run computational experiments and steer the behaviour selection in outlining an exploration strategy suitable for autonomous agents (or, more generally a new search paradigm).
The underlying idea of this study originates from the scientific discussions held at the European Space Agency among the scientists of the Advanced Concepts Team and of Florence University (see e.g. Baluška 2004, team conducting the Ariadna study “Bio-inspiration from Plants' Roots” (available on-line at http://www.esa.int/gsp/ACT/publications/ act-bib-search.htm)
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