Cost-Effective Localization of Mobile Robots Using Ultrasound Beacons and Differential Time-of-Flight Measurement

Abstract

This paper presents an innovative and cost-effective solution for the absolute localization of mobile robots using ultrasound beacons. The proposed system addresses the challenge of precise positioning within a controlled environment by employing Differential Time-of-Flight (ToF) measurements to determine the relative distances between the robot and optimally placed beacons. Unlike other ToF methods that require synchronization pulses, the proposed approach eliminates this requirement, significantly simplifying the setup and reducing system complexity. Furthermore, the system achieves a higher sampling rate than conventional synchronization-based systems, enhancing real-time performance. Detailed analysis and simulation demonstrate the system’s ability to provide accurate and reliable localization. The results highlight the potential for broad application in various robotic environments, offering a robust solution for absolute positioning without complex synchronization strategies. This work underscores the advantages of using ToF measurements with ultrasound beacons and contributes to the ongoing development of efficient and cost-effective robotic localization systems.

1. Introduction

Accurately determining the position of a mobile robot is crucial to its effective operation. As such, robot localization has been the subject of extensive research since the inception of robotics. Active beacon navigation is a reliable positioning solution that is often implemented in navigation systems for ships, airplanes, and commercial mobile robots. Active beacons with known fixed positions serve as absolute reference points, ensuring highly accurate positioning information is obtained. As a result, this approach offers high positioning reliability.

Active beacon technologies are generally based on Time of Flight (ToF) and Angle of Arrival (AoA). ToF consists of precisely measuring the time that a signal travels between an emitter and a receiver. Using the speed of the signal through the medium, the total distance travelled by the signal can be calculated. This distance, combined with the known position of the emitter, can be used to determine the position of the receiver using trilateration or multilateration techniques. This method is used in [1,2], employing regular ToF and round-trip ToF to calculate the position of the client, obtaining an accuracy of several centimeters. In [3], a ToA method is proposed that combines two different types of beacons that achieve a reduction in the overall frequency that the client needs to sense, allowing the use of much simpler sensors. AoA, on the other hand, uses the angle of the incoming signal relative to the receiver’s orientation to estimate the direction of the emitter. By measuring the angle of arrival from multiple emitters with known positions, the receiver’s position can be estimated using triangulation techniques.This method is used in [4] to obtain the position of each of the individuals of a swarm of unmanned aerial vehicles. In [5], an alternative method is proposed that utilizes the Angle of Arrival (AoA), which involves an initial estimation of the client’s position to adjust the beam forming process, thereby achieving more accurate results.

Additionally, other solutions propose merging previous techniques to improve localization precision. In [6], a hybrid method is presented that combines the ToF and AoA, designed to be used in environments with a dense amount of obstacles that hinder the performance of simpler methods. In [7,8], a method is suggested that combines the ToF and AoA with an angle of departure (AoD)-based method.

Although geometry methods, like trilateration or multilateration techniques, are still more widely employed [9], deep learning algorithms are gaining increasing popularity for this purpose. In [10], a method is proposed that employs ToF with a fully connected deep neural network that estimates the position. On the other hand, an AoA-based technique using a shallow neural network is presented in [11].

Active beacons offer the advantage that the data required to estimate the robot’s position do not need as much processing compared to other techniques, so low-power solutions are easier to implement in beacon-based systems. In addition, the beacons are fixed and the positions of the beacons relative to the installation are known. This enables every calculated position to be directly related to the installation itself, providing absolute positioning without the necessity for inference.

As the prevalence of the Internet of Things (IoT) and robotics continues to rise, the demand for accurate and reliable positioning information at a low cost becomes more important across various applications, including smart cities, industrial settings, public spaces, healthcare, and domestic applications. This has sparked an increasing interest within the research community in the development of lightweight, low-power positioning solutions. In [12,13], different approaches to the localization of nodes in wireless sensor networks are presented using triangulation to estimate the position of a node. Another current development in the field of indoor positioning is the development of Ultra-Wide-Band Technology (UWB). In [14], an approach to localization using trilateration is proposed using a UWB radar with an antenna array that supports trilateration for indoor short-range positioning. Other systems integrate other technologies, such as Bluetooth [15], Wi-Fi [10,16], or radio frequency identification (RFID) [17], although these may require specialized sensors or a thorough mapping of the environment to understand the spatial distribution of signal characteristics [3].

In this work, a solution that uses ToF measurements is presented to determine the relative distances between a robot and optimally placed ultrasound beacons, facilitating accurate absolute positioning within a predefined map. By eliminating the need for synchronization pulses, the system setup is significantly simplified, which reduces the overall complexity. Furthermore, the proposed approach improves real-time performance by achieving a higher sampling rate compared to conventional synchronization-based systems.

The remainder of this paper is structured as follows. In Section 2, a localization solution is presented, detailing the principles and implementation of the proposed ultrasound-based system. In Section 3, the implementation details are provided, including the hardware setup and the measurement results. Section 4 presents the comprehensive simulation results and analysis that demonstrate the effectiveness of the proposed method. In Section 5, a discussion of the results obtained and their implications in the field of mobile robot localization is provided. Finally, Section 6 concludes the paper, summarizing the key findings.

2. Localization Solution

This section introduces a novel and cost-effective localization solution that uses ultrasound technology to achieve precise positioning without complex synchronization mechanisms. The proposed system utilizes ultrasound beacons and receivers, coupled with an innovative time difference measurement approach, to determine a robot’s position within a predefined area. The following subsections will detail the background of ultrasound technology in localization, the core principles of the proposed system, its base operation, the analysis of the localization strategy, and the mathematical principles underlying the approach.

Ultrasound is a commonly used technology for indoor positioning and beacon systems, which is notable due to its favourable cost/performance ratio, wide availability, and robustness in challenging environments. Various approaches to ultrasonic localization exist, demonstrating the technology’s versatility and reliability in numerous industrial and commercial applications. For example, in [18], a relative positioning system is demonstrated using three ultrasonic sensors to obtain Time-of-Flight (ToF) data and using the time differences between the signals to calculate the robot coordinates. Another application in which ultrasound is widely used is obstacle detection and avoidance. In [19], a small autonomous mobile robot is presented equipped with a microcontroller and four ultrasonic sensors to avoid real-time obstacles, using a linear recursive Kalman filter to improve the response of the system and ensure smoother movement. These examples illustrate the range of applications for ultrasound technology, from presence detection to parking systems.

2.1. System Design, Core Innovations, and Benefits

Unlike traditional localization methods that rely on trilateration and require precise synchronization signals (such as infrared light), the system presented in this work operates on a fundamentally different principle. By eliminating the need for absolute ToF measurements and synchronization mechanisms, the system’s design is significantly simplified while simultaneously enhancing accuracy and reliability. This approach differs from conventional beacon systems demonstrated in [20,21], which typically use ultrasound for ToF measurements in combination with synchronization signals.

The core innovation of this approach lies in its ability to determine position using only the time differences between received ultrasound signals. This method eliminates the need for synchronization between beacons and the robot. As a result, the solution offers substantial advantages in terms of reduced system complexity, lower implementation costs, and improved robustness against timing errors.

The proposed system is specifically tailored for real-time applications in dynamic indoor environments, such as hospitals, museums, and other public spaces with foot traffic. Thanks to ultrasound technology, the system maintains robustness in changing environments and supports multiple robots simultaneously, ensuring consistent performance where it is essential. Moreover, the installation cost is economical, as multiple robots can share the same ultrasound pulses.

A standout feature of our system is its relatively low computational footprint, especially compared to SLAM or vision-based localization methods. The simplicity of our approach could allow for real-time processing on a high-performance microcontroller, avoiding the need for more powerful and energy-intensive processors running a full OS. This not only reduces overall system costs but also significantly lowers power consumption.

The system comprises n multiple beacons and n receivers, optimally placed to cover the operational area. The network of ultrasound beacons emit signals at precise intervals and in a specific order, while receivers mounted on the mobile robot detect and process these signals for position calculation.

The system’s ability to function without requiring precise timing synchronization allows for improved flexibility across diverse indoor settings. It can adjust more readily to different spatial configurations and is less susceptible to environmental factors that might disrupt precise timing signals. Furthermore, the simplification of the hardware requirements makes the system more cost-effective to implement and maintain, without sacrificing accuracy.

2.2. System Overview

Figure 1 illustrates the overall setup of our ultrasound-based localization system. Ultrasound beacons are mounted on the ceiling to provide consistent coverage and minimize obstructions. The mobile robot, equipped with ultrasound receivers, moves within the area covered by the beacons. This configuration allows for accurate positioning of robots with varying heights, as the system can account for the vertical offset between the beacons and the robot-mounted receivers.

2.3. Base Operation

The localization system employs a sequential ultrasound emission strategy in combination with a time difference measurement approach. This method circumvents the need for beacon–receiver synchronization typical in ToF systems. The operational sequence and signal processing technique are as follows:

Signal Emission: The system operates by firing the beacons in pairs according to a pre-determined sequence. Each pair of beacons emits an ultrasound signal simultaneously. This paired emission strategy allows for relative time measurements, reducing the complexity and potential errors associated with absolute time synchronization. By using pairs of beacons, the system can create distinct time differences that are crucial for the localization process.

Time Difference Measurement: As the signals travel from the beacons to the receivers, the system measures the time differences ($\Delta t$) between the arrivals of these signals at each receiver. These time differences are then used to calculate the relative distances between the beacons and the robot, based on the known speed of sound in the medium. By using time differences rather than absolute times, the need for precise clock synchronization between beacons and receivers is eliminated.

Position Calculation: By analyzing the time differences from multiple pairs of beacons, the system can triangulate the precise position of the robot. The calculation utilizes hyperbolic multilateration techniques, where each time difference measurement defines a hyperbolic curve on which the robot must lie. The intersection of these curves, derived from multiple beacon pairs, pinpoints the robot’s position with high accuracy. This approach, based on the known positions of the beacons and the measured time differences, allows for high-accuracy localization without the need for complex synchronization mechanisms.

2.4. Working Principle

The core principle of this localization system revolves around measuring the time differences ($\Delta t$) between the arrivals of signals from pairs of beacons at the robot’s receivers. These time differences can be interpreted as hyperbolic loci in space, known as isochrones (from Greek “iso-” meaning “equal” and “chronos” meaning “time”), which represent all points where the time difference between signals from two beacons remains constant.

All possible solutions for a given time difference lie on a hyperbolic function in space. The isochrones are a visualization of this hyperbolic space, represented as color gradients in the figures. By analyzing the intersections of these isochrones from multiple pairs of beacons, the system can determine the robot’s precise location with high accuracy.

To better illustrate this concept, Figure 2 and Figure 3 provide visual representations of the hyperbolic function through color gradients. Each color in the gradient corresponds to a specific time difference value, effectively representing the function across the operational area. These visualizations offer valuable insight into the geometric relationships that underpin the system’s functionality and demonstrate how time differences translate into spatial locations.

When a pair of beacons emit ultrasound signals simultaneously, the robot’s receivers detect the arrival times of these signals. The system computes the time difference ($\Delta t$) between the signal arrivals, placing the robot on an isochrone that represents all possible locations where this time difference could be observed. The intersection of isochrones from multiple beacon pairs provides the robot’s precise location.

Figure 3 shows the complete isochrone plot for all beacon pairs. Each color represents isochrones for a different beacon pair, illustrating how time differences vary across the operational area. The dense network of isochrones demonstrates the rich information available from just three beacons, enabling precise localization.

Figure 4 focuses on the specific isochrones that pass through the robot’s position. This visualization clearly shows how the intersection of these isochrones from different beacon pairs determines the robot’s exact location. Each colored line represents the isochrone from a beacon pair that corresponds to the time difference measured by the robot.

These visualizations highlight the effectiveness of the time difference approach. They demonstrate how this method achieves accurate localization by leveraging the geometric relationships between the beacons and the robot.

2.5. Mathematical Principles of Hyperbolic Multilateration

The core of the localization method developed in this work is based on the analysis of isochrone curves generated by time differences ($\Delta t$) between signals from pairs of beacons. These isochrones are hyperbolic curves that represent all points in space where the difference in the distances to two beacons is constant.

While this mathematical model forms the foundation of our localization system, the practical implementation involves considerations beyond the scope of this analysis, particularly regarding optimal beacon placement.

For a pair of beacons located at $(x_1,y_1)$ and $(x_2,y_2)$, the equation for the hyperbolic isochrone curve can be expressed as follows:

$$\sqrt{{(x-x_1)}^2+{(y-y_1)}^2}-\sqrt{{(x-x_2)}^2+{(y-y_2)}^2}=\Delta t·v$$

(1)

where

• $(x,y)$ represents any point on the hyperbola;
• $\Delta t$ is the measured time difference between signal arrivals from the two beacons;
• v is the speed of sound in the medium (approximately 343 m/s in air at room temperature).

To determine the robot’s position, the intersection of isochrone curves from different pairs of beacons should be found. Consider a system with three beacons located at $(x_1,y_1)$, $(x_2,y_2)$, and $(x_3,y_3)$. Two hyperbolic equations can be formed:

$$\left\{\begin{array}{c}\sqrt{{(x-x_1)}^2+{(y-y_1)}^2}-\sqrt{{(x-x_2)}^2+{(y-y_2)}^2}=\Delta t_{12}·v\hfill \\ \sqrt{{(x-x_2)}^2+{(y-y_2)}^2}-\sqrt{{(x-x_3)}^2+{(y-y_3)}^2}=\Delta t_{23}·v\hfill \end{array}\right.$$

(2)

where $\Delta t_{12}$ and $\Delta t_{23}$ are the measured time differences between signals from beacons 1 and 2, and beacons 2 and 3, respectively.

Solving these nonlinear equations simultaneously provides the coordinates $(x,y)$ of the robot. This solution represents the unique point where all the measured time differences are satisfied, thus pinpointing the robot’s position.

2.6. Adapting the Model for Ceiling-Mounted Beacons

To ensure the localization system’s practicality and wide applicability, ceiling-mounted ultrasound beacons were chosen to support ground-based robots of varying heights. This vertical separation between beacons and receivers introduces a modification to the modeling that requires the addition of a plane offset to the mathematical model. This adaptation is necessary for the system’s real-world functionality, enabling accurate localization in three-dimensional space while maintaining the system’s core principles.

Mathematical Adaptation

To incorporate this ceiling-to-ground configuration and variable robot heights, the equation must be modified as follows:

$$\sqrt{{(x-x_i)}^2+{(y-y_i)}^2+{(H-h_r-z_i)}^2}-\sqrt{{(x-x_j)}^2+{(y-y_j)}^2+{(H-h_r-z_j)}^2}=\Delta t_{ij}·v$$

(3)

where

• $(x,y,0)$ represents the robot’s position on the ground plane;
• $(x_i,y_i,z_i)$ and $(x_j,y_j,z_j)$ are the coordinates of two ceiling-mounted beacons;
• H is the ceiling height;
• $h_r$ is the height of the specific robot;
• $\Delta t_{ij}$ is the measured time difference between signal arrivals from beacons i and j;
• v is the speed of sound in the medium.

This equation ensures that the calculated position accurately reflects the robot’s true location on the ground, accounting for its specific height and the ceiling-mounted beacon configuration.

2.7. Considerations on Beacon Placement

The optimal placement of beacons in a given environment is a complex problem that warrants its own dedicated study. It depends on various factors specific to each implementation scenario, including room geometry, potential obstructions, expected robot paths, and desired coverage area. While a comprehensive analysis of optimal beacon placement is beyond the scope of this paper, it is important to note that our system’s flexibility allows for beacon positions to be optimized during the installation phase. This adaptability enables the system to be fine-tuned to best suit the particular requirements and constraints of each environment. Factors that might influence beacon placement include the following:

• Maximizing coverage area;
• Minimizing geometric dilution of precision;
• Avoiding areas of potential signal interference;
• Accommodating architectural features or obstacles.

The process of determining optimal beacon placement could involve techniques such as computer simulations, on-site testing, or even machine learning algorithms. However, such optimization methods represent a separate field of study and are not explored in detail in this work. Our focus remains on the fundamental principles and advantages of the proposed localization system, with the understanding that practical implementations would involve additional considerations for beacon placement.

3. Implementation Details

The performance and efficacy of the proposed ultrasound-based localization system were evaluated through a combination of hardware implementation, practical measurements, and simulation. The results demonstrate the system’s capability to accurately measure time differences between ultrasound signals, which is crucial for precise localization.

3.1. Hardware

A test system is developed to validate the idea principle and take measurements to evaluate possible performance and limitations.

The amplifier board, shown in Figure 5, is designed with a high-impedance operational amplifier set to offset the signal and provide gain, allowing both sides of the oscillation to be viewed within the 0 V to 3.3 V range, making it compatible with a microcontroller ADC. The gain can be fine-tuned using an on-board electronic potentiometer, allowing for sensitivity control during operation. This sensor board measures 3 cm by 3 cm.

The breakout board, shown in Figure 6, is used solely for testing purposes. It facilitates the connections necessary to sample the data during the experiments. This board measures 5 cm by 4 cm.

The emitters, depicted in Figure 7, are based on an STM Nucleo-32 board and generate pulses to drive the ultrasound emitter. An ultrasound driver is implemented using an H-bridge configuration, which allows for efficient switching of the voltage polarity to the ultrasound transducer, thereby maximizing the output power. The width and number of pulses can be adjusted via software. The boards are connected using flat cables to form the emitter network. The emitter device measures 10 cm long by 7 cm tall by 6 cm wide.

The hardware was developed with the purpose of demonstrating the viability and capability of capturing precise time differences in ultrasound signal arrivals with a very low-cost approach. It is important to note that these dimensions represent the current development and testing hardware. In a final implementation, the hardware would be significantly miniaturized. The current larger sizes are due to the use of development boards, connectors, and other components that facilitate testing and modification. A production version would be optimized for size and efficiency, resulting in much more compact hardware suitable for integration into various robotic platforms.

3.2. Test Design

The experimental design for this study was chosen to demonstrate the fundamental viability of our proposed ultrasound-based localization system. Our experiments focused on three key aspects:

• Static accuracy: Single-point and two-point measurements were conducted to establish the system’s baseline accuracy and its ability to distinguish between different positions.
• Dynamic tracking: A circular motion experiment was performed to evaluate the system’s performance in tracking a moving target.
• Time difference precision: Measurements with varying distances between emitters were taken to evaluate the system’s general precision and sensitivity.

While these tests are limited in scope, they serve as a proof of concept, providing concrete evidence of the system’s functionality and potential.

3.3. Measurement

To test the capture system, two sets of measurements were taken with the emitters positioned 0.5 m and 1 m apart from each other, with the closest sensor being 1 m from the source using the developed sensor. These captures demonstrate that the system is capable of precisely detecting small differences in time. However, it should be noted that when the time differences are very small, the overlapping of waves can occur, making it challenging to distinguish between them.

Figure 8 presents the oscilloscope capture with emitters positioned 1000 mm and 1500 mm from the receiver. The system’s precision is demonstrated by the clearly distinct arrival times of the signals and their subsequent attenuation.

To further evaluate the system’s repeatability, Figure 9 depicts the arrival and attenuation of the signals with one emitter 1000 mm and the other 2000 mm from the receiver, averaged over 100 samples. This averaging demonstrates minimal jitter, underscoring the high repeatability of the system.

The gain of the amplifier was set at a level adequate for direct reception, which minimizes the impact of echoes. This configuration ensures that echoes are very small compared to the direct signal, enhancing the system’s accuracy in detecting the primary signals.

These measurements demonstrate the effectiveness of the developed sensor in precisely capturing small time differences between ultrasound signals, despite the challenge of wave overlap at very short time intervals. The high directivity of the sensor effectively mitigates the problem of small intervals. Placing an array of three or four sensors per robot resolves this issue and increases accuracy. The high precision of the amplifier and the system’s repeatability are evident, confirming its capability for accurate and reliable time difference measurements.

4. Simulation Results and Analysis

In this section, we present the results of our simulation, focusing on the relative error and identification of critical areas in a sample system with real sampling times. Our initial testing revealed that the timing error was extremely low, so this error source was discarded from the analysis. To validate and evaluate the performance of the system, we performed a simulation comparing the localization accuracy across various scenarios. We introduced normalized errors in the sample times, speed of sound, and measurement accuracy based on data collected during our testing. This approach allowed us to more accurately model real-world conditions and assess the system’s robustness in the face of typical variations and uncertainties.

4.1. Static Localization Performance

Figure 10 provides a comprehensive overview of our localization system’s performance across the entire test area. Key observations are as follows.

The linear arrangement of beacons along the x-axis significantly influences the system’s performance, creating a unique error pattern. Estimated positions (red dots) cluster around actual positions (thin red crosses), visually indicating the system’s precision. Error circles (blue dashed for maximum, green dotted for average) vary in size across the test area, suggesting non-uniform accuracy. Accuracy appears to be higher near the center of the beacon arrangement and decreases towards the edges of the covered area, particularly in the y-direction. There is a slight elongation of error circles in the y-direction, particularly for points further from the x-axis, likely due to the linear beacon arrangement.

4.2. Analysis of a Central Point

Figure 11 offers a zoomed-in view of a single test point at the center of our grid (1.0 m, 1.0 m), allowing for a detailed examination. The distribution of estimates (red dots) forms a line around the actual position, indicating balanced errors in the x- and y-directions at this central location. The tight clustering of estimates suggests high precision, with most estimates falling within a small area. The proximity of the estimated cluster to the actual position (red cross) demonstrates high accuracy with no significant systematic bias. The relatively small size of the error circles, particularly the average error circle (green dotted), indicates good overall accuracy at this central point. This central point’s equidistant position from all beacons likely contributes to its high accuracy, showcasing the optimal performance of the system under ideal conditions.

4.3. Error Distribution Analysis

Figure 12 presents the comprehensive error distribution across all test points and estimates. The histogram reveals a right-skewed distribution, typical for error measurements in localization systems. The mean error (red dashed line) is slightly larger than the median error (green dotted line), consistent with the right-skewed nature of the distribution. This suggests that while most errors are small, occasional larger errors pull the mean higher. Most errors are concentrated in the left part of the distribution, indicating that the majority of estimates have relatively small errors, which is a positive indicator of the system’s overall accuracy. The long tail to the right shows that larger errors do occur, albeit less frequently. These could represent estimates at the edges of our test area, where the system’s performance is expected to degrade. The peak of the distribution occurs at a low error value, further confirming the system’s overall accuracy for most measurements.

4.4. Dynamic Localization Performance

Figure 13 illustrates the system’s performance in tracking a robot moving in a circular path. The actual path (blue line) forms a perfect circle, centered at (1, 1) with a radius of 0.5 m. Estimated positions (colored dots) generally follow the circular path, demonstrating the system’s ability to track dynamic movement. The color gradient of the estimated positions provides insight into the error distribution during motion. Lighter colors (lower errors) seem to dominate, indicating generally good tracking performance. Some areas of the circle show darker colored estimates, suggesting higher errors. These could be points where the robot’s motion aligns unfavorably with the beacon arrangement. The beacons (blue dots at the corners) provide context for understanding how their positioning affects the tracking accuracy at different points along the path.

Figure 14 complements the circular motion analysis by showing how the localization error varies with the position of the robot. The error plot shows a periodic pattern, corresponding to the robot’s revolutions around the circular path. The shape of the measured circle is due to the robot changing position slightly between measurements.

5. Discussion

This section discusses the implementation, advantages, limitations, and implications of the proposed ultrasound-based localization system for mobile robots. It also compares this approach to existing technologies.

5.1. Implementation Overview

The localization system utilizes ceiling-mounted ultrasound beacons and accommodates robots of varying heights:

• Beacons are mounted on the ceiling to provide consistent coverage and minimize obstructions.
• The system is designed to work with robots of different heights, enhancing its versatility.
• The plane offset between beacons and robots varies based on robot and ceiling height.

5.2. Key Advantages

The proposed system offers several advantages:

• Cost-effectiveness: Ultrasound components are inexpensive compared to other localization technologies, making the system more affordable for large-scale deployments.
• Environmental robustness: The system performs well in various lighting conditions, unlike optical or laser-based methods.
• Differential measurement: By focusing on time differences rather than absolute times, this approach mitigates variations due to environmental factors.
• Scalability: The system can be easily expanded by adding more beacons, allowing for coverage of larger areas or improved accuracy.

5.3. Limitations and Challenges

While our system offers numerous benefits, it is important to acknowledge its limitations and potential challenges:

• Range limitations: Ultrasound signals attenuate relatively quickly in air, potentially requiring a higher density of beacons for larger areas. However, for the applications we envision—installations with foot traffic and dynamic environments—the current range of 6 to 10 m should cover all cases.
• Acoustic interference: Environments with significant ambient noise or other ultrasonic sources may experience interference. However, the ultrasound band is relatively quiet, and the narrow frequency of our emitted signal allows for easy filtering, reducing potential ambient interference.
• Update rate: The system’s update rate may be lower compared to some other technologies. For the target application with robots that move at walking pace this is less of a concern.
• Obstacles: Solid obstacles between beacons and receivers could potentially block signals. However, ultrasound can pass around obstacles with some power loss, and our system has sufficient gain to detect very soft signals. Additionally, placing the receiver high on the robot will mitigate most potential signal blockages.

It is worth noting that these limitations are less significant in our target application of indoor environments with walking-speed robots. In such settings, the update rate is sufficient, range limitations are manageable, and acoustic interference can often be minimized through environmental design. The installation of a solution is also part of the system, and any coverage limitations should be addressed in this phase.

5.4. Comparison with Other Positioning Technologies

To better understand the strengths and limitations of the proposed ultrasound-based localization system, it is compared with other common positioning technologies: vision-based systems, LiDAR, SLAM, and traditional odometry.

Table 1. Comparison of localization technologies.

Technology	Accuracy	Scale	System Cost	Sensor Cost	Adaptability
US Beacon	Medium	Room-level	Low	Low	High
Vision SLAM	Medium	Room-level	Medium	Medium	Low–Medium
LiDAR SLAM	High	Medium-scale	High	High	Low–Medium
Odometry	Low	Medium-scale	Low	Low	High

provides a comprehensive comparison of these technologies across key performance metrics, including localization accuracy, scale, system cost, sensor cost, and adaptability.

Vision-based localization systems have gained popularity due to their ability to provide rich environmental data. However, these systems often struggle in low-light conditions or environments with limited visual features. In contrast, the ultrasound system operates independently of the lighting conditions, making it more versatile in various indoor settings. Furthermore, the ultrasound system generally requires less computational power compared to complex image processing algorithms, offering a more cost-effective solution. This lower processing requirement is a significant advantage for applications where power consumption is a concern.

LiDAR (Light Detection and Ranging) is known for its high accuracy, fast update rates, and excellent range and resolution, which makes it well suited for outdoor or large-scale indoor applications. Although LiDAR provides superior performance in these aspects, the ultrasound system is generally more cost-effective, particularly for smaller-scale applications, and offers absolute positioning in real time without the need for additional algorithms. The ultrasound system typically consumes less power than LiDAR. However, LiDAR’s superior range and resolution make it more suitable for applications requiring detailed environmental mapping or long-range sensing. Simultaneous Localization and Mapping (SLAM) has become increasingly popular, especially with the availability of cost-effective sensors. While SLAM offers flexibility in unknown environments, it may be less reliable in dynamic settings compared to the proposed ultrasound system. The beacon-based system generally has lower computational needs compared to most SLAM implementations, allowing for simpler, more power-efficient hardware. Furthermore, the proposed system provides absolute positioning within the beacon network, while SLAM typically provides relative positioning that may drift over time without loop closure. The ultrasound-based approach can be more robust in dynamic environments where the physical space is changing, which can challenge SLAM algorithms.

Traditional odometry, often using wheel encoders or Inertial Measurement Units (IMUs), offers a cost-competitive alternative for robot localization. Like the ultrasound beacon-based system, odometry solutions can be implemented with relatively inexpensive hardware and have minimal computational requirements. However, odometry suffers from cumulative errors over time, leading to a drift in position estimates. This is particularly problematic for long-term operation or after sharp turns. In contrast, the ultrasound-based system provides absolute positioning that does not degrade with time. While odometry can offer very high update rates, making it suitable for real-time control of fast-moving robots, it often needs to be combined with other localization methods for reliable long-term operation.

Recent advances in SLAM and other advanced positioning strategies have made significant progress, particularly with the increasing availability of cost-effective LiDAR and camera solutions. However, these technologies still face challenges in dynamic environments and in optimizing cost and power consumption for certain applications. In contrast, the proposed ultrasound-based system offers a cost-effective alternative, as the main investment is made in the installation of the beacons, while the robots only require low-cost receivers. This is particularly advantageous for scenarios involving a fleet of robots, where equipping each robot with expensive sensors can be cost-prohibitive.

Despite its limitations in sampling rate and range compared to some other technologies, the ultrasound-based system provides a balanced solution that is especially suitable for controlled indoor environments. In these settings, factors such as cost-effectiveness, robustness, and simplicity often take precedence over high-speed tracking or large-scale mapping capabilities. The proposed system’s ability to provide accurate, absolute positioning with minimal computational overhead and power consumption makes it an attractive choice for a wide range of indoor applications.

Ultimately, the choice between these technologies depends on the specific requirements of the application. Factors to consider include the type of environment (e.g., indoor, outdoor, and dynamic), accuracy requirements, update rate needs, available computational resources, power constraints, and budget. The ultrasound-based isochrone method presented in this paper offers a unique combination of benefits that make it particularly well suited for indoor applications demanding accurate and efficient localization.

By leveraging the advantages of ultrasound technology, such as its robustness to lighting conditions and low computational requirements, the proposed system fills a crucial gap in the spectrum of localization solutions. It provides a cost-effective and reliable alternative for applications where the operating environment is well defined, and the primary focus is on achieving precise positioning without the need for complex, resource-intensive algorithms or expensive sensor suites.

5.5. Real-World Applications

The ultrasound-based localization system offers significant advantages in public spaces with high pedestrian traffic. Unlike SLAM or LiDAR systems, it maintains accuracy in dynamic environments, relatively unaffected by moving individuals or varying crowd densities. This robustness, combined with its non-reliance on visual data, makes it effective in areas such as retail stores, hospitals, and museums, where consistent performance with people traffic is essential for robotic operation.

The system is especially well suited for medical supply robots in hospital corridors, positioning interactive guide robots in museums, and other public spaces that offer a controlled environment where an installation can be made. In traditional robotics applications such as warehouse and factory automation, it can serve as a complementary system or cost-effective solution for precise absolute positioning of inventory management robots or automated guided vehicles (AGVs). Its capacity to provide accurate localization in the presence of moving objects or personnel makes it valuable in environments where human workers and automated systems coexist, offering a reliable alternative or backup to existing positioning methods.

6. Conclusions

In conclusion, the ultrasound-based localization system offers a unique combination of cost-effectiveness, environmental robustness, and scalability, which makes it particularly well suited for indoor robotics applications. Although it has limitations in terms of range and update rate, these are often outweighed by its advantages in many practical scenarios. As robot deployment in indoor environments continues to grow, this approach provides a valuable addition to the toolkit of localization technologies, especially for applications that prioritize affordability and simplicity without compromising accuracy.

This work contributes to the field of robot localization by demonstrating the viability of a low-cost, computationally efficient approach to absolute positioning in indoor environments. This challenges the notion that high-precision indoor localization necessarily requires expensive sensors or complex algorithms. Furthermore, the use of differential measurements provides a novel approach to mitigating environmental variations in ultrasound-based systems.