El Rol del estado en las viviendas

In chapter five ‘Reactive virtual forces’ will be put forward as a solution to exploration and mapping using a heterogeneous swarm, within a nuclear cave environment. This involves treating robots as particles under the influence of virtual analogues of the fundamental forces of nature. This method is akin to the use of virtual potential fields already present in the literature. Potential fields provide an easily implemented method of designing complex swarm behaviours. As will be shown in this section, there has been little work on potential fields for heterogeneous swarms or in their use for exploration. So far, this review has touched on various uses for virtual potential fields including pattern formation, spatial distribution, and path planning. In this section a history of potential fields research is given, this will show the current state of the art and highlight the novelty of the ‘reactive virtual forces’ implementation.

The first use of potential fields in robotics was by Khatib [124]. In this implementation ‘artificial potential fields’ were employed to allow manipulators to conduct obstacle avoidance. The artificial potential fields used were not grounded in physics, but instead involved attractive and repulsive forces dictated by functions designed by Khatib. This early work shows the utility of virtual potentials for obstacles avoidance, an important factor within the exploration of a nuclear cave.

The term ‘social potentials’ was coined in 1999, by Reif et al., so called because the forces between robots can be seen to represent their social relations [199]. In this work inverse square laws were utilised as potential fields, to guide social behaviour in a group of robots. The paper examines in simulation the use of these potentials for robot clustering, moving as a group, guarding/ escorting behaviour and for demining. The work focusses on a large homogeneous group of robots. This shows that virtual forces may be used for manipulating robot positions relative to one another. There is no focus on exploration of unknown environments, or the use of heterogeneous agents in this work.

maximise sensory data gathered. This problem was examined using potential fields in 2002 by Howard et al. [107]. The electrostatic force was used as a physical basis in simulations of a homogeneous swarm. This work shows that potential fields can be used to distribute robots in an environment to gather sensor data. Furthermore, it utilises the electrostatic force for distribution; in chapter five this same force will be utilised for obstacle avoidance.

‘Physicomimetics’ was introduced as a concept in 2004 by Spears et al. [223]. In this work pattern formation is motivated by physical forces, such as the Newtonian law for gravity. Hexag- onal and a square lattices were generated through the leveraging of the physical properties of mass and spin. This work was later extended to allow a hexagonal homogeneous swarm formation to move towards a light source. Again, this work exemplifies another of the forces used in the reactive virtual forces framework; the gravitational force. In addition, this work provides motivation for using real physical forces, grounded in mathematics, to control robotic swarms.

Zhou et al. combined the physical traits of crystal lattices, with virtual potential fields to create formations of robots [274]. ‘Attraction sites’ are generated around a robot, such as those found about a carbon atom when forming a lattice structure. These attachment sites become potential wells that other robots are attracted to. If the number and distribution of the attachment sites are altered, different patterns may be generated. This variation shows that a designer may slightly modify the interaction between forces and in doing so change the behaviour of a group of robots. It is this quality of virtual forces that makes them so versatile.

In 2007 Barnes et al. used a group of unmanned ground vehicles to maintain a pattern under the influence of potential fields [19]. In this work, it was postulated that potential fields could be extended to heterogeneous groups of robots. This poses an interesting discussion, as the rules used to dictate the homogeneous swarm would not need to be altered for use with the heterogeneous swarm. Having rules remain the same for both homogeneous and heterogeneous swarm eliminates the difficulty in specialising a controller for each unique agent within a swarm. Thus, this motivates the use of a virtual forces controller.

Further work exploring heterogeneity was compiled by McCook and Esposito [163]. This work simulates a convoy of military vehicles being harassed by an attacker. Heterogeneity is introduced by defining some robots as ‘defender units’ and others as ‘supply units’. Supply units feel a force that drives them away from the attacker, whereas defenders feel an attractive force to stop the supply units being harassed. Robots in this case have predetermined roles and hence they do not have the same controller. Despite this, this work shows an interesting use of heterogeneous agents working together towards a goal under the influence of virtual forces.

Work by Wiegand et al. examines how heterogeneous agents may be defined when utilising virtual forces [251]. It is stated that for heterogeneity to be included each particle being used must have its mass and coefficient of friction defined. Once these parameters are defined, an engineer must express any special relationships between agents. In doing so the appropriate behaviour with the potential fields is created. This is similar to the idea of utilising different virtual physical

properties to leverage heterogeneity within the ‘reactive virtual forces’ framework, however in this case there is no need to define special relationships.

In 2016 counter rotating artificial potential fields were utilised to fully inspect obstacles with a pair of robots by McIntyre et al. [164]. Waypoints are used to instigate path planning, whilst attracting forces are used for goals and repulsing forces for obstacles. Potential forces are also used to maintain the separation between robots. As the distance between the robots is their only constraint, they behave as a fluid. When approaching an obstacle, the midpoint between the robots is determined, and the robots are assigned goals on different sides of the obstacle. This ensures that both sides of the obstacle are scanned. The work is tested in simulation, on a pair of homogeneous robots. The use of attractive and repulsive forces for mapping an object is similar to the ‘reactive virtual forces’ framework. However, the ‘reactive virtual forces’ framework uses physical forces for exploration of unknown environments, whereas the work put forward by McIntyre et al. uses predetermined waypoints in a known environment.

Finally, in 2018 Bridgwater et al. utilised ‘reactive virtual forces’ for the exploration and mapping of an unknown environment. This work examined the used of virtual forces, grounded in physics on both heterogeneous and homogeneous swarms. A geometric map was created using an occupancy grid. It was found that the heterogeneous swarm covered the environment more efficiently. Later in this thesis, the ‘reactive virtual forces’ framework will be shown to be an efficient solution to the exploration and mapping problem with a heterogeneous swarm in an unknown nuclear cave environment.

Overall, it is clear there has been prior investigation into the use of potential fields for the distribution of robots in an environment. Despite this, there has been little work examining po- tential fields for exploration. In addition, the use of heterogeneous swarms is still underdeveloped. To the best of the authors knowledge, there have been no studies using a heterogeneous swarm, under the influence of virtual reactive forces, for exploration and mapping. Thus, utilising the gravitational force, electrostatic force, and strong nuclear force in the same exploration control architecture appears to be novel, and their utility will be outlined in subsequent chapters.