A review of the most common positioning systems is presented in this section with a specific focus on solutions for miniature robots used for swarm robotic applications.
2.1. Range and Bearing in Robotics
Positioning approaches mainly consist of two components: one is the signal classification and the other is a localisation algorithm. The localisation algorithm allows robots to employ an appropriate method to estimate their current positions relative to other robots in a group. It includes geometric positioning, proximity perception and vision analysis algorithms. In real-world applications, the prerequisite of autonomous motion requires the robots to acquire precise location information [9
]. Common positioning methods rely on various internal sensors, such as gyroscopes [10
], photoelectric encoders [11
] and multi-spectral instruments which can be fused to provide accurate estimates of the robots’ positions. Nevertheless, these conventional methods can be inaccurate because of defects related to these internal sensors [12
], and unknown uncertainties in, for example, the offset of the wheels and vibration of the robot’s mechanical structure. Such errors will accumulate and be amplified, potentially introducing significant errors in the position estimates of the robots. To resolve such problems, an external positioning reference without any accumulative error can serve as the independent third party to provide location information, which can then be exploited to correct the robots’ positions [13
]. The most common external localisation reference comes from the Global Positioning System (GPS) that requires a direct line-of-sight communication to the satellites. Hence its transmission signal may have poor coverage and intensity, particularly in indoor or subterranean environments [14
]. Therefore, indoor positioning technologies using alternative technologies that provide an external reference have been proposed to tackle the problem of accurately localising mobile robots. This include the use of technologies such as wireless local area network (WLAN), radio-frequency identification (RFID), ZigBee, Bluetooth, ultra-wideband (UWB), infrared (IR), computer vision (CV) and light detecting and ranging (LiDAR).
Due to the short response time and high accuracy, IR positioning systems are widely used to localise robots. In [15
], an innovative IR sensory system was proposed to position a mobile robot in an area, so-called an intelligent space
. By measuring the differential phase-shifts of a sinusoidally modulated infrared signal transmitted from a robot, the differential distance from the phase-shift data could be obtained. This information can then be analysed using hyperbolic trilateration to obtain an estimate of the position of the robot. With appropriate specification of the system parameters, the accuracy of the positioning of this technique has been shown to be in an acceptable range with an error of less than 10 cm. In [16
], the combination of IR sensors and a monocular camera was shown to provide a robust estimate of robot pose, with the technique able to fuse information from different sources. The primary innovation with this technique was that it was able to exploit the information from the camera to compensate for the relatively poor estimate of the robot’s position that was obtained from the IR scanners, and also resolve problems related to the relatively slow vision analysis systems through frequent updates from the IR sensors.
RFID is a mature and reliable technology that applies wireless communication to automatically identify objects. The implementation of RFID technology requires the use of an RFID reader equipped with one or more antennas and active or passive transceivers [17
]. In [18
], mobile robots carried an RFID reader at the bottom of the chassis, which was able to read RFID tags on the ground to enable it to provide an estimate of its position. The paper proposed a novel triangular pattern for arranging the RFID tags on the floor to reduce the estimation error that is obtained using a more conventional square pattern.
Ultra-wideband (UWB) is a wireless communication technology that emerged from time-domain electromagnetic technology. The UWB has been utilised for positioning of mobile robots in various applications. In [19
], an obstacle avoidance method for an autonomous unmanned boat was presented. The UWB positioning system was applied to monitor and transmit the real-time position of the unmanned boat simultaneously. The UWB distance estimation was also utilised in multi-robots formation control [20
]. In general, the positioning system based on the UWB is similar to radio frequency localisation system that consists of fixed anchors and mobile antennas. In addition, the associated software methods can be developed with various techniques, such as distance estimation with wave reflection, active measurements based on time of flight (ToF) [21
], time of arrival (ToA, TDoA) [22
], angle of arrival (AoA) and fingerprinting (RSSI mapping), and their combinations [23
]. An improved positioning performance for Pozyx
, a low-cost commercial positioning system, was proposed in [24
]. The method used a modified multilateration algorithm with adding a number of anchors as well as adjusting their positions. The results demonstrated an improvement in localisation precision by approximately 40%.
Ultrasonic waves can be used to determinate distance between a fixed station and the mobile targets. In ultrasonic positioning systems, the pivotal operation requires multiple ultrasonic sensors on-board to receive ultrasonic waves [25
]. A representative example associated with positioning of mobile robots using ultrasonic-based system is provided in [26
]. In this work an indoor ultrasonic positioning system with four beacon nodes was proposed. It was able to determine the position of an unknown node in real-time. The positioning principle exploits the time difference between the ultrasonic sensor and RF transmission. Hence, it calculates the distance from the time gap find the unknown node’s coordinates. There are several research works that combined ultrasonic systems with RF technology to estimate the positions of mobile robots [27
]. In [27
], the indoor positioning system referred to as
comprised receivers that were mounted on the robots and location beacons that were attached to the ceiling which continuously transmitted ultrasonic and RF signals. The limitation of this method is that it requires considerable manual configuration of the ultrasonic sensors to achieve coverage of large spaces, which would increase the positioning cost. The improved hybrid positioning method proposed in [28
] addressed this problem by significantly reduce the required configuration. The positioning system was similar to cricket, with the objects’ position being estimated using trilateral algorithms. The novelty with this approach was that it employs hop-by-hop localisation which requires the precise location of some nodes in advance; however, the others can be automatically located in real-time.
Visual localisation has recently become the mainstream positioning method for relatively large mobile robots operating in complex environments [29
]. In such systems binocular depth cameras act as sensing devices, providing information about the environment which can then be used to provide an indication of a robot’s position within it. In [30
], a multi-fisheye camera system was proposed that was able to provide 3D perception for self-driving cars. The localisation method involved in this work required the correspondence between 3D space map and 2D images obtained from a camera system to be determined. The algorithm used to determine the correspondence [31
] was based on Plücker coordinates which solves the pose estimation problem in two steps: (i) solve for the depth and (ii) solve for the rigid transformation with absolute orientation. Results obtained using GPS ground truth testing verified that the camera-based system could acquire good performance in the localisation and pose estimation. In related work, a modified mobile robot localisation approach was developed that was based on classification with a rejection option using computer vision [32
]. This approach employed topological map information, based on supervised learning, to optimise the performance of the localisation and navigation tasks in mobile robots. The methodology comprised two core components after capturing the images: (i) feature extraction and (ii) classification. With respect to feature extraction, it considered standard methods in digital image processing. For classification, it applied machine learning methods with a rejection option. Compared with the classic localisation systems using an omnidirectional camera, the proposed method can provide higher accuracy rate (99.94%) and smaller computational time in consolidated feature extractions and machine learning techniques. It also performed well in navigation test, which verified that it increased the navigation efficiency and reliability in mobile robotics.
LiDAR positioning technology exploits the LiDAR sensor, whose basic principle is similar to radar, yet it adopts the invisible light rather than radar waves to detect the distance. The LiDAR system serves as a typical localisation system by emitting a laser beam and receiving the reflected signal to calculate the distance to an object. The position and velocity of a target can be found by fusing the information obtained from multi-sensors, which is commonly applied in autonomous navigation of vehicles [33
]. In [34
], looking at different situations of mobile robots, different LiDAR localisation methods were proposed. The work [34
] developed a new algorithm to expand the crossover detection function by incorporating the crossover measurement from the robot’s perception and its relevant topological information with the pre-defined path network, and importing this information into the localisation system. The new method requires sufficient LiDAR data, and is mainly reliant on the search for the available free spaces that combine the obstacles occupied in setting grid with a Kalman filter used to data association and tracking. In [35
], an effective and robust system was designed for mapping and localisation of the micro unmanned aerial vehicles (UAVs) in an indoor environment. The estimation of a UAV’s 3D position is derived through efficiently fusing measurement data from the primary and secondary LiDAR. The innovative method assembles the point cloud obtained from LiDAR with the inertial data measured by a simple inertial measurement unit (IMU) to integrate the 3D data set. Specifically, localisation is performed by exploiting a scan matching approach based on a customised version of the iterative closest point (ICP) algorithm, while mapping is achieved by extracting robust line features from LIDAR measurements.
2.2. Range and Bearing for Miniature Robots
In the choice of the best technology when designing a localisation system, considering the distinctive traits for each approach, it is indispensable to balance the trade-off among environmental conditions, user demands and performance parameters. The localisation techniques described above utilised sophisticated hardware and complex algorithms which would require substantial computational processing and storage resources [36
]. All these aspects make it difficult to adapt the techniques to simple, micro-robotic platforms that can be scaled down in complexity and size [37
]. Considering the features of miniature multi-robot systems—low-cost, small, low-power, simple in structure—the existing positioning systems need to be selected and slightly modified to adjust for miniature swarm robots.
For a micro-swarm robotic system, its self-positioning implementation needs to interact with robot members, This interaction process includes two core modules, perception and communication. The perception function mainly relies on the sensor’s performance and precision. Actually, the communication system can support the robotic system in continuously updating and exchanging the information from the sensors between each individual agent [38
]. In the swarm robotic scenario, the implementation of perception also entirely relies on the inter-robot communication system, including the distance, bearing and velocity [39
]. An inter-robot communication system based on multiple IR sensors is a suitable choice for a multi-miniature robots system, as IR sensors system are characterised by the high precision, low aperture angle, affordable sensors and the low power requirements, which properly match the miniature robot’s requirements [40
]. In addition, IR radiation can not only be used to detect and perceive surroundings, but can also be specifically modulated to transport messages like binary phase shift keying and frequency shift keying. Except for peripheral unit, the robot’s main processor is also another pivotal component in calculating the bearing. The basic requirement for the main processor is to offer the constant change of individual behaviour in real-time, and have the capability to support the robot to participate in the swarm’s data exchange, to determine and share position information. Table 1
lists different miniature robotic platforms with similar multi-IR sensory systems but with different sensor configuration and hardware structure. There are inevitable errors in most of the positioning studies that are used in real-world applications.
There are various methods for calibrating errors in robotics, such as using artificial neural networks [53
]; and bio-inspired optimisation such as ant colony optimisation (ACO) [54
] and particle swarm optimisation (PSO) [55
]. For example, a positioning approach using a modified ACO algorithm was developed in [56
], enabling a multi-robot system to accurately approach an odour source. Apart from this, in [57
], PSO was utilised to determine multi-robot positions in a football match. The results demonstrated the feasibility of applying the PSO algorithm to finding robots’ positions. In robotics for surgical operations, a model-free based deep convolutional neural network was proposed [58
]. In another study [59
], a PSO based backpropagation neural network algorithm to solve an inverse kinematics problem of a medical puncture surgery robot was proposed, which could achieve precise positioning with an error of less than 0.1 mm.
The genetic algorithm (GA) is a heuristic global optimisation algorithm which takes inspiration from the biological principle of natural selection. It was widely used for optimising various problems in robotic systems. In tuning PID control gains for a robotic arm [60
], GA provided a better performance in parameter optimisation than conventional methods such as trails and error and empirical approaches. In another study [61
], GA was used to identify unknown parameters for a model of an existing 7-DOF hydraulic manipulator. In a study on mobile robots localisation, GA was utilised to solve a self-localisation problem in an indoor environment [62
]. GA has been used for various optimisation applications in robotic path planning [63
], as a fuzzy controller for obstacle avoidance [64
], for training a deep neural network [65
] and for engineering manufacturing [66
]. In a study on multi-robotics, a spatially structured genetic algorithm was proposed to improve the performance of positioning [67
]. In the previous work on swarm aggregation [68
], a GA was used for optimising weight parameters of the fuzzy system which estimates turning angles of the robots based on the captured sound amplitudes form four microphones. Therefore, the feasibility of using a GA optimisation in multivariable problems, e.g., in swarm robotics, has been demonstrated. GA also has the advantage that it does not get stuck at local optimum values, but searches the full population to find the global optimum. A disadvantage of using a GA is that it can be slower than alternative methods; however, as the optimisation was being done offline, speed was not a concern and the advantage outweighed this negative.
In summary, various localisation technologies, such as infrared, LIDAR, UWB, ultrasonics and RFID techniques, have been proposed and applied in real-world applications. For application in multi-robotic systems, the most suitable technology relies on a variety of factors, such as cost, size and required accuracy. For the low-cost, miniature swarm robotic system that is the focus of this work, a multiple infrared sensory system was believed to be the most suitable sensory system for the positioning. Compared to the previous studies, this work focuses on the provision of more precise bearing estimates for use with low-cost, simplistic robots.
There are many optimisation methods available to solve problems such as this, including particle swarm optimisation, differential evolution and genetic algorithms. In this work, we used a GA as an initial tool to determine the feasibility of the proposed approach. It is acknowledged that the most suitable optimisation method to use is problem dependent, and although GAs have been demonstrated to be robust and efficient, alternative approaches will be investigated in future research.