Introduction
Introduction to networked robot systems
Launched in 1994, the first networked robot system (NRS) garnered over 2.5 million accesses within seven months, allowing users to operate a manipulator to excavate artifacts in a nuclear-contaminated area to find evidence of ancient water flows Over the next seven years, more than forty similar systems were developed, enabling remote experiences such as visiting museums, gardening, underwater navigation, ballooning, and handling protein crystals This growing trend led to the establishment of the term "Networked Robots" by the IEEE Society of Robotics and Automation in 2004.
A networked robot is a robotic system that connects to communication networks like the Internet or Local Area Network (LAN) This connection can be established through wired or wireless methods and utilizes various protocols, including TCP, UDP, or 802.11.
The definition of networked robot systems (NRSs) has been expanded to encompass two key subclasses: autonomous systems and teleoperated (manual) systems, addressing a wider range of challenges and applications.
Autonomous Networked Robotic Systems (NRSs) utilize a controller to generate signals that operate the robot, which includes actuators and sensors This system enables communication between the robot and the controller through a network, effectively extending the robot's operating range Additionally, the network facilitates long-distance communication among multiple robots, allowing them to coordinate their activities efficiently.
Teleoperated NRSs involve human operators who send commands to robots, which then execute these commands and provide feedback through a network Input devices and user graphic interfaces facilitate this process, serving as passive controllers that convert the operators' commands into control signals.
NRSs (Networked Robotic Systems) require the integration of various fields, including robotics, sensor systems, ubiquitous computing, artificial intelligence, and network communications These systems extend beyond traditional robotic challenges like localization and motion control, addressing complex distributed systems that operate over diverse communication networks Key challenges include ensuring system reliability and performance amidst issues such as time-varying transmission delays, message loss, out-of-order delivery, and fluctuating transmission bandwidth As a result, numerous innovative applications are emerging, spanning areas from automation to exploration.
Applications of networked robot systems
Applications of NRSs can be classified into five groups including industrial robots, educational robots, medical robots, service robots, and other various robots
Networked robots are increasingly utilized in industrial applications, such as a teleoperated robot system developed for coal mining, which features dual cameras, laser scanners, and various sensors to gather environmental data This information is transmitted over a network to a human operator, who remotely controls the robot to perform tasks like shoveling and breaking Key benefits of this system include the protection of human workers from hazardous environments and the robot's ability to endure strenuous tasks However, challenges remain, particularly in sensor fusion and localization.
Figure 1.1: The coal mining networked robot system[36]: (a) The robot with actua- tors and sensors; (b) The operator with input devices and user graphic interfaces
Networked robots facilitate the creation of telelaboratories, allowing students to remotely operate real manipulators through the Internet This innovative approach provides access to essential tools, such as teach pendants and control computers, enhancing practical learning experiences Key benefits of telelaboratories include the ability to share costly equipment among educational institutions, streamlined evaluation processes, and increased flexibility in hands-on practice.
Figure 1.2: A telerobotic laboratory platform[82]: (a) The telelaboratory with ro- botic devices; (b) The web-based interface to interact with the telelaboratory
Medical networked robots enable remote diagnosis and treatment by skilled doctors For instance, Masuda created a telerobot for echography, allowing remote operators to control the robot's movement and adjust the ultrasonic probe's angle using two joysticks The robot captures and compresses ultrasonic images, transmitting them via the Internet for examination Additionally, a tele-surgical system features two slave manipulators at the patient's location, controlled by joysticks at the operator's site, with tactile and force feedback sensors facilitating interaction between the operator and patient.
Figure 1.3: The telesurgical system [14]: (a) Setup of slave manipulators around the operating table; (b) An experiment with the surgeon and patient
Networked robots are increasingly providing services in various environments, including homes, offices, and public spaces Research by Sanfeliu et al has introduced innovative methods for enhancing cooperation between networked robots and humans These robots perform essential tasks such as guidance, assistance, transportation, and surveillance in urban settings Their architecture incorporates collaborative urban robots, intelligent sensors like video cameras and acoustic devices, as well as smart communication tools such as PDAs and mobile phones.
Figure 1.4: Service networked robots in urban areas [62]: (a) A service robot; (b)
The robot interacts with human to supply information; (c) Robots cooperate in a guidance task
Networked robots are versatile and can be utilized in various applications, such as remote surveillance, where a robot equipped with five sensory subsystems detects fire, intruders, and obstacles while monitoring the environment Another example is the GARBI robot, designed for observation and manipulation in shallow water, featuring a 3D vision system for remote control Additionally, a prototype rover was created for testing Mars technology, showcasing the adaptability of networked robots Other innovative uses include pet robots, tour-guide robots, and intelligent wheelchairs.
Recent advancements in Networked Robotic Systems (NRSs) in Vietnam include the development of a telemanipulator system by Cong Thanh, which features a master-slave manipulator setup that communicates over a local area network This system allows human operators to control the master manipulator, while the slave mimics its movements based on received signals Additionally, a telehealthcare system has been established, utilizing cameras in patients' homes to monitor and transmit visual data to a central processing unit, alerting doctors in case of detected abnormal behaviors Furthermore, a NRS designed for locating high radioactivity areas in disaster zones employs a partial swarm optimization algorithm to facilitate cooperation among robots for effective task execution.
The preliminary results demonstrate the applicability of Networked Robotic Systems (NRSs) in Vietnam, highlighting their potential use in emerging sectors such as traffic control, ubiquitous healthcare, and underwater exploration.
Related works
As the field of robotics continues to evolve, numerous projects have emerged addressing the challenges associated with networked robots This section provides an overview of research focused on localization, stabilization control, and navigation, which are key topics discussed in this thesis.
1.3.1 Study of NRSs on localization
Localization is essential for the effective operation of robotic systems, as it enables robots to understand their position within an environment to successfully perform tasks In the context of NRSs, localization can be achieved through two primary methods: advanced interface techniques and optimal filters.
A Localization using advance interface techniques
Advanced interface techniques enhance robot localization by reconstructing the operating environment A virtual environment, proportional to the real working space, is created on-site, allowing commands to be processed and the robot's future position to be predicted, thus accommodating time delays and providing a realistic user experience Additionally, model-based virtual reality techniques have been employed to develop a complete 3D polygonal model of the environment, enabling operators to control the robot through this model An innovative approach known as the ecological interface paradigm further enriches the 3D virtual environment by integrating real video information, offering a more immersive interaction experience.
Hou and Su enhanced robot navigation by installing four external cameras that create adjacent visual grids, eliminating dead zones A recognition algorithm identifies the robot's relative position along with targets, landmarks, and obstacles Additionally, local pose estimation is achieved using odometry, sonar, and compass sensors, with this data transmitted to a remote site, although it does not account for changes during communication Furthermore, a map-based localization method allows for determining the robot's absolute position by comparing a local reference map with one constructed using GPS mapping techniques at the remote site.
Advanced interface techniques often overlook critical communication network issues such as network delay, message loss, and out-of-order delivery The data transmission between the remote controller and the actuator is frequently assumed to be reliable and is seldom addressed From an estimation theory perspective, substantial delays and losses can lead to inaccuracies in state estimation and control, which can significantly degrade overall system performance.
The optimal filtering method enhances the state-space representation of the Networked Robotic System (NRS) by integrating network parameters, utilizing estimation theory for precise robot localization Sinopoli et al introduced an augmented Kalman filter in their study, designed for state estimation amid intermittent observations In this model, the arrival of observations is represented as a binary random variable, λ_t, with its variance defined by the output noise variance when λ_t equals 1, and as σ²I when it does not, where σ is a real constant and I represents the identity matrix.
Kalman filter is then reformulated using a “dummy” observation (if a real observa- tion does not arrive) and takes the limit as σ → ∞ This approach was expanded in
This study addresses the challenges of random delays and packet loss by defining the arrival of observations as a binary random variable It introduces an infinite buffer to store and rearrange delayed measurements, allowing for estimation from the earliest to the most recent data at each step However, the iterative nature of this filter makes it computationally intensive Alternatively, employing a finite buffer can simplify the process, but it necessitates that the time delay remains within certain limits.
Moayedi et al recently developed an adaptive Kalman filter tailored for networked control systems, addressing mixed uncertainties such as random delays, packet dropouts, and missing measurements by utilizing a set of matrices in the system model The filter gain is determined through a series of recursive discrete-time Riccati equations Similarly, Ma and Sun proposed an optimal filter that manages random sensor delays, packet dropouts, and uncertain observations by introducing three Bernoulli distributed random variables to create a unified model of mixed uncertainties This approach also involves solving a Riccati equation and a Lyapunov equation to derive the estimator While both filters effectively tackle network-induced issues, they fall short in optimizing for out-of-order delivery scenarios.
In addition, those filters are designed for linear systems Further modifications are required to extend them to nonlinear systems such as NRSs
1.3.2 Study of NRSs on stabilization control
Stability is a crucial criterion for networked robotic systems (NRSs), similar to traditional robotic systems Various studies have addressed this issue, including Wargui et al., who developed a stable controller for NRSs with nonholonomic constraints by initially deriving control laws for delay-free scenarios and later adapting them to accommodate time delays through a multistep predictive estimator Additionally, a study estimated the maximum allowable time delay at the control input without compromising system stability and introduced a single-layer neural network for stable control of the networked robot Luck implemented a time buffer exceeding the worst-case delay to achieve time invariance, applying classical control theory Furthermore, Xi and Tarn proposed an event-based control scheme to mitigate the effects of time delays on system performance.
In addition to the primary methods discussed, several innovative approaches have emerged One study utilized the minimum jerk motion model to forecast user input, enabling effective stabilization of remote robots Another research effort focused on transmitting multiple commands within a single packet, accounting for all potential delays to maintain the relevance of control signals.
The aforementioned approaches primarily address time delay issues; however, network communications are also impacted by additional challenges, including message loss, out-of-order delivery, and restricted transmission bandwidth These complications can significantly affect control mechanisms, potentially leading to overall system instability.
1.3.3 Study of NRSs on navigation
Robot navigation includes different interrelated activities such as perception, locali- zation, cognition, and motion control In NRSs, studies on navigation include two methods: direct and behavior-based navigations
In direct navigation, teleoperators utilize primitive force or velocity commands for remote control, enhanced by haptic interfaces that provide force feedback A two-way full bridge strain gauge sensor is positioned at the robot's front center to measure the force exerted when the teleoperator pushes an object This data is transmitted via the Internet to the teleoperator's haptic joystick, which generates corresponding forces felt by the operator Another study introduced a haptic device that emphasized communication, proposing a compensative parameter to adjust the feedback transfer function for time delays, ensuring accurate force feedback during operation The advantage of force feedback lies in its ability to give operators a sense of interaction; however, further development of control architectures is necessary to optimize the overall system functionality.
A direct control architecture for Internet-based personal robots, which is insensitive to time delays, has been proposed This architecture includes key components such as a command filter to recover lost control commands, a path generator, and a path-following controller to minimize the time gap between real and virtual robots Additionally, a posture estimator is utilized to address discrepancies between different environments Furthermore, Wang and Liu introduced the telecommanding concept, where each command is tailored for a specific task and defined with multiple events, enabling the robot to respond intentionally to expected events while also reacting to unexpected ones.
The proposed approaches offer flexible control options; however, directly transmitting control signals to the actuator over the network can lead to issues such as delays or signal loss, resulting in unexpected actuator performance Furthermore, direct navigation necessitates that the operator possesses experience in managing unforeseen circumstances arising from network challenges.
Behavior-based navigation has emerged as an alternative to direct navigation, focusing on identifying various responses to sensory inputs A multi-level fusion architecture for intelligent navigation has been proposed, featuring eight modules that facilitate four key behaviors: trajectory planning, trajectory tracking, obstacle avoidance, and supervision, coordinated by an arbiter that analyzes sensory information to determine the appropriate behavior Additionally, a multibehavior-based mobile robot has been developed for remote supervision via the Internet, employing a system where local intelligence is categorized into motion planner, motion executor, and motion assistant, each functioning as an agent This multi-agent control approach integrates individual agents into a centralized architecture, leveraging principles of sensor fusion and distributed intelligence However, a notable drawback is the absence of mechanisms to address issues arising from communication network challenges.
The goal of the research
This research focuses on the supervision and control of Networked Robotic Systems (NRSs), aiming to develop innovative algorithms for localization, stabilization control, and navigation—key challenges in the field Given the complexity and variability of networks based on their architecture and intended applications, the study utilizes the Internet as the communication medium, specifically addressing factors such as time delay, message loss, and out-of-order delivery.
The localization algorithm will be developed using an optimal filter approach, incorporating a unified state-space representation to address network-induced issues By applying estimation theory, a novel filter will be formulated for the localization of Networked Robot Systems (NRS).
The development of the stable controller will utilize Lyapunov stability theory alongside optimal filtering techniques By applying Lyapunov stability theory, we can derive control laws designed to stabilize non-networked robotic systems These control laws will subsequently be adapted for networked robotic systems through the implementation of optimal filters.
The navigation system will utilize a behavior-based approach that integrates localization results with stable control into a cohesive architecture This architecture simplifies complex navigation tasks by breaking them down into distinct behaviors Coordination among these behaviors is managed through fuzzy logic, ensuring effective operation For optimal navigation performance, localization accuracy must meet a positional precision of 30 cm and an orientation accuracy of 10 degrees.
The organization of this thesis
The thesis is structured into six chapters, as illustrated in figure 1.5 Chapter 1 provides a concise overview of the NRS, exploring its applications and reviewing relevant literature It concludes with the research objectives and an outline of the thesis structure.
Chapter 2 describes the system model A state-space representation of the NRS is introduced with the existence of network parameters Details of each parameter are then analyzed Finally, the kinematic model, hardware configuration, and data communications of the NRS are presented
Chapter 3 addresses the issue of localization by first examining various related methods, highlighting their strengths and weaknesses It subsequently introduces our algorithm, detailing its theoretical foundations along with the results from simulations and experiments.
Chapter 4 Motion control using Lyapunov theory and predictive filter
Chapter 5 Navigation using behavior- based model
Chapter 3 Localization using optimal filter
Figure 1.5: Schematic structure of the thesis
Chapter 4 describes the design of the stable controller It starts with the deriva- tion of the control laws that stabilize the non-networked robot system It then ex- plains the expansion of those control laws to the NRS The chapter ends with simu- lation and experiment results
Chapter 5 synthesizes the findings from prior chapters to establish a navigation model, beginning with an overview of various navigation strategies, followed by an in-depth exploration of our behavior-based navigation approach, including detailed descriptions of each behavior and the corresponding experimental results.
The thesis ends with chapter 6 which lists summary of the research, declaration of main contributions, and recommendation for future work.
System Model
State-space representation of the NRS
Consider a general robotic system with fundamental components including the con- troller, actuator, process, and sensor Its state-space representation in discrete-time domain is given by:
In the given mathematical model, the time index \( k \) is defined within the set of natural numbers, while the state vector \( x_k \) belongs to \( \mathbb{R}^n \), and the input vector \( u_k \) is part of \( \mathbb{R}^q \) The output \( z_k \) is represented in \( \mathbb{R}^m \), with \( f \) and \( h \) serving as the state and output functions, respectively Additionally, the process noise \( w_k \) and measurement noise \( v_k \) are considered independent, zero-mean, white-noise processes characterized by normal distributions: \( w_k \sim N(0, Q_k) \) and \( v_k \sim N(0, R_k) \) This independence and the assumption of normality are commonly accepted practices in the field, supported by the central limit theorem.
Our study focuses on a differential-drive mobile robot featuring two driving wheels and two passive wheels The driving wheels control the robot's position and orientation, while the passive wheels, located at the front and rear, ensure stability without affecting the robot's kinematics The robot's pose is defined by the coordinates of the wheels' axis center (x, y) and the chassis orientation θ relative to the X axis Figure 2.1 illustrates the coordinate systems and notations used, including the global coordinate system (XG, YG).
The local coordinate system YR is linked to the robot's center, where R represents the radius of the driving wheels and L indicates the distance between the wheels The robot is assumed to be a rigid body that moves on a plane with non-slipping and pure rolling motion.
Figure 2.1: The robot’s pose and parameters
The kinematic model of the robot is then given by [30]:
(2.3) where ω L and ω R are the angular velocities of the left and right wheels at its center of rotation, respectively Let
L ω ω ω = − (2.5) be the tangential and angular velocities of the robot, equation (2.3) is rewritten as: cos sin c c c x v y v θ θ θ ω
As the system operates over digital communications network, equation (2.6) need be discretized Let T s be the sampling period, the discrete time model is ob- tained from Taylor's expansion at k as:
T T dx dx dx x x T dt dt n dt
Taking n=1, the discrete time Euler approximation of the robot is given by:
The validity of this approximation relies on the sampling period being adequately small Specifically, the selection of the sampling period is determined by the approximation error outlined in Taylor's theorem, which includes the Remainder Term.
In our system, the sampling period is set at 100 ms, leading to a maximum approximation error of 0.5 cm This level of accuracy comfortably meets the system's requirement of 30 cm, which corresponds to the radius of the robot chassis.
From the kinematic equation (2.8), vectors in the state equation (2.1) are defined for our system as follows:
• The state vector x includes the position and orientation (pose) of the robot:
The input vector \( u \) represents the angular velocities assigned by the controller to the left and right driving wheels, expressed as \( u = [ \omega \, \omega_L \, \omega_R ]^T \) These angular velocities are directly related to the robot's translational and angular velocities, as defined by equations (2.4) and (2.5) For ease of notation, we often use \( [ v_c \, \omega_c ]^T \) in place of \( [ \omega \, \omega_L \, \omega_R ]^T \).
• The state function f is represented by equation (2.8) It relates the state vector
The process noise \( w \) is modeled as the noise affecting the input, which is suitable as long as systematic errors are corrected through calibration The real angular velocities of the driving wheels, denoted as \( \omega_L \) and \( \omega_R \), include this noise Consequently, the process noise \( w_k \) is defined as \( n n^T k = \begin{bmatrix} \omega_L \\ \omega_R \end{bmatrix} w \).
Our system utilizes sensors to accurately measure the robot's position and orientation, with optical encoders on the driving motors capturing the position (x, y) and a compass sensor determining the orientation (θ) For a comprehensive understanding of the sensor implementation, please refer to section 2.3.1 Consequently, the vectors in the output equation (2.2) are defined based on these measurements.
• The output vector z includes the position and orientation of the robot:
• The output equation (2.2) can be simply rewritten as: z x v = + (2.13)
Measurement noise from sensors, along with process noise, is characterized as independent, zero-mean, and white-noise processes that follow a normal probability distribution The calculation of their covariances is discussed in section 3.4.
The decentralized robot system operates based on various network parameters, making its functionality reliant on complex communications networks These networks can vary significantly in architecture and implementation, influenced by the medium employed and the specific applications they are designed to support.
Figure 2.2: Model of the NRS
This study presents a network model that serves as an intermediary between the process and controller, facilitating the transmission of input signals and observation measurements while accounting for potential delays, losses, and out-of-order deliveries The delays are treated as random variables that can be measured at each sampling instance, with out-of-order packets being interpreted as instances of prolonged delays Packet arrival is characterized by a binary random variable, λ k, as defined in previous research [64].
1, if a packet arrivesduring time 1to
In a networked control system, the delays between components are crucial for performance, with n representing the delay from the controller to the actuator and m denoting the delay from the sensor to the controller Two binary random variables, k ca and λ k sc, indicate the arrival of inputs and measurements, respectively The controller, a software program on a remote computer, generates setting velocities u=[ω ω L R] T in three ways: predetermined values for localization, real-time computations for stabilization control, and user inputs via joystick for navigation These velocity values are transmitted to the actuator, while the system's output z=[x yθ] T is measured by sensors, which are affected by measurement noise The sensor data is also sent to the controller in packets that include timestamps and sequence numbers to assess delay, loss, and order Understanding the timing of these signals is essential for effective system operation.
(Delay, Loss, Out of Order)
Figure 2.3: Timing of signals in the NRS
At time k, the controller transmits a control input u to the actuator, but due to network delays or out-of-order transmission, the signal is received at time k+n After one sampling period, at time k+n+1, the system state changes, and the sensor captures this change with a measurement z This measurement is then sent over the network and reaches the controller at time k+n+m+1, where it is used as feedback to initiate a new control cycle Throughout this process, there is always a risk of losing either the control input or the measurement.
The robot's state at time k is influenced by the control input from time k-n-1, while the measurement received at time k corresponds to an earlier time k-m Consequently, the system described by equations (2.1) and (2.2) is time-varying and can be reformulated accordingly.
Equation (2.15) outlines the robot's state influenced by the network, serving as the foundational model for the NRS in this study Subsequent sections will delve into the specifics of the model's components, including the communications network and the robot itself.
The communications network
Industrial communications networks emerged in the 1970s within the automotive industry to reduce cabling costs, simplify system setup, and promote modular design Over the years, various networks have been developed to meet diverse application needs, utilizing different communication protocols and topologies For industrial and transportation applications, fieldbuses such as FIP and PROFIBUS, along with automotive buses like CAN, are commonly used In contrast, general-purpose networks, including IEEE LANs and ATM-LAN, as well as the Internet, are more suitable for service and educational applications This article provides an overview of popular networks and their key characteristics.
Four types of network including the Foundation Fieldbus, CAN, Ethernet, and Inter- net will be briefly presented They are commonly used in NRSs
The Foundation Fieldbus, developed by the Fieldbus Foundation in 1994, was designed to replace the traditional 4-20 mA standard and is now extensively used in heavy process industries, including oil refineries, chemical plants, paper mills, and power generation facilities It features two communication protocols: H1, which operates at 31.25 Kbit/s for connecting field devices like sensors and actuators, and HSE (High-Speed Ethernet), which utilizes 10 or 100 Mbps Ethernet for a high-speed network backbone A typical Foundation Fieldbus network combines HSE connections between computers and slower H1 links among devices, allowing for a hierarchical topology through the use of bridges Access control is managed by link masters, with the Link Active Scheduler (LAS) overseeing the bus, issuing commands for data broadcasting, publishing time information, and permitting unscheduled messages such as alarms and events.
Development of CAN started originally in 1983 by the German company Bosch
The Controller Area Network (CAN) was originally developed for the automotive industry but has since been adopted in sectors such as aerospace, industrial automation, and medical equipment Defined by ISO standards 11898 and 11519-1, CAN supports a bit rate of 1 Mbit/s for network lengths up to 40 meters and 500 Kbit/s for longer distances In a CAN network, devices like sensors and actuators connect through nodes, each comprising a transceiver for signal transmission, a CAN controller for message conversion, and a host processor for message processing There is no limit to the number of nodes, which can send and receive messages, albeit not simultaneously When the bus is free, any node can initiate transmission, but if multiple nodes transmit simultaneously, the message with the highest priority is granted access CAN supports 229 different priority levels, with numerically smaller ID values indicating higher priority for message transmission.
Ethernet, standardized as IEEE 802.3 in 1985, has continuously evolved to address emerging demands, solidifying its status as a leading local area network (LAN) technology Capable of transmitting data at speeds ranging from 10 Mbit/s to 100 Gbit/s, the most prevalent speeds in use today are 10 Mbit/s and 100 Mbit/s.
Ethernet supports data transfer speeds of up to 1000 Mbit/s, with segments typically limited to 100 meters in length Multiple segments can be interconnected using hubs or switches, allowing for an extensive number of stations, each identified by a unique Ethernet address composed of six colon-separated numbers The first three bytes represent a vendor ID, while the last three are designated by the vendor Ethernet utilizes the CSMA/CD (Carrier Sense Multiple Access with Collision Detection) protocol, enabling stations to recognize idle and busy links, and to detect frame collisions When a collision occurs, the involved stations back off and attempt retransmission after a random delay Ethernet frames range from 64 to approximately 1500 bytes, starting with a 64-bit preamble for synchronization, followed by a header with source and destination MAC addresses, a payload section containing data between 46 and 1500 bytes, and concluding with a 32-bit cyclic redundancy check.
Starting from ARPANET, the Internet was brought online in 1969 which initially connected four major computers at universities in the southwestern United State
The Internet has evolved into a global data communications system that connects millions of private, public, academic, and business networks through an international telecommunications backbone utilizing various electronic and optical technologies As a decentralized network of networks, the Internet exhibits a wide range of data transfer rates and connection characteristics Additionally, there is no centralized governance overseeing its technological implementation or policies regarding access and usage, with each device, including computers and mobile phones, identified by a unique number.
An IP address is a unique identifier for devices on a network, consisting of 6 bytes for IPv6 and 4 bytes divided into five classes (A, B, C, D, and E) for IPv4 The Internet Protocol Suite, commonly known as TCP/IP, facilitates data transmission between hosts through a layered architecture that includes application, transport, Internet, and link layers As user data moves down the protocol stack, each layer adds encapsulation at the sending host, which is then reversed at the receiving host to ensure proper data delivery.
Networks, despite their varying designs and complexities, exhibit common characteristics when utilized for Networked Real-time Systems (NRSs) This study focuses on key issues such as network delay, message loss, and out-of-order delivery By addressing these challenges, control algorithms can be optimized for both specific network types and general communication networks, enhancing overall effectiveness.
Transmitting a message across a network involves varying transfer times influenced by the network's conditions and scheduling policies While some systems may exhibit nearly constant transfer times, many experience fluctuations based on factors such as network load, the priorities of concurrent communications, and electrical disturbances.
Network delay can be effectively measured by comparing the timestamp of a sent message with its receiving time, necessitating synchronized internal clocks between the sender and receiver This synchronization process typically involves estimating the time difference between the clocks of two nodes through the exchange of clock-request messages In this study, we detail the method used for clock synchronization.
Node S aims to estimate its clock difference with node R, where t S represents the local time at node S, t R denotes the local time at node R, and t * signifies the absolute time The local clocks at both S and R exhibit skews relative to the absolute time.
= + (2.16) where δ S and δ R are the clock mismatches The clock offset, δ, is defined as:
From equations (2.16) and (2.17) it follows that:
To estimate the clock offset δ, the process begins with a synchronous request from node S to node R at time t S a Upon receiving this message, node R immediately replies with its local clock value t b R This response reaches node S at time t S c, as illustrated in Figure 2.4.
Let ∆t SR and ∆t RS be the transfer times from S to R and from R to S, respectively The transfer times are given by:
Assuming that E t(∆ − ∆ SR t RS ) 0= , where E denotes the expectation operator, we get:
By repeating the clock synchronization experiment we can find an accurate estimate of δ The network delay is then determined by equation (2.19)
In packet switching networks, messages often arrive out of order due to the way they are transmitted in datagram packets The delivery sequence can be affected by various factors, including link states and router configurations, leading to packets taking different routes and arriving at their destination in a disordered manner.
Out-of-order messages can be identified by assigning sequence numbers to sent messages For example, if messages arrive in the order of 1, 3, 4, 2, and 5, message 2 is considered out of order This situation can also be viewed as a significant delay; in this case, message 2 is delayed by two sampling periods compared to the others Formally, an out-of-order message with sequence number i that arrives at time k (where i < k) represents a delayed message with a specific time delay.
The equation ∆ = ∆ + − (2.21) defines the transfer time ∆t k at time k, where j represents the sequence number of the last received chronological message, and T s denotes the sampling period A delayed message occurs when the highest sequence number received at the arrival time is k, while an out-of-order message is identified when subsequent messages, such as k+1 and k+2, are present at the receiver at that time Understanding the distinction between delayed and out-of-order messages is crucial for effective data transmission and processing.
The Robot
Robots utilized in Non-Robotic Systems (NRSs) can vary from manipulators to humanoid robots, depending on specific research objectives and applications This study involved the development of a real NRS, designed as a platform for experimentation and analysis An overview of the system is illustrated in Figure 2.5, with detailed descriptions of its hardware configuration and data communication processes provided in the following sections.
Figure 2.5: Overview of the developed NRS
The hardware configuration consists of two parts: actuators and sensors, and user- interaction devices Details are described as follows
Figure 2.6: Hardware configuration of the robot
Measuring 60 cm x 60 cm x 110 cm, the robot is equipped with essential components for effective sensing and navigation Key features include drive motors for motion control, sonar sensors for obstacle avoidance, and compass and GPS sensors for accurate heading and global positioning Additionally, it utilizes a laser range finder (LRF) and a vision system to enhance its mapping and navigation capabilities.
The drive system features high-speed, high-torque reversible DC motors equipped with quadrature optical shaft encoders that deliver 500 ticks per revolution for accurate positioning and speed measurement Control of the motors is managed by the Motion Mind PID controller, a microprocessor-based electronic circuit with embedded firmware that utilizes a PID algorithm for precise motor control.
Motion mind 3 Laser range finder
The heading module features a CMPS03 compass sensor that utilizes the Hall effect to accurately determine the robot's orientation with a resolution of 0.1° It operates on two axes, x and y, which measure the strength of the magnetic field components aligned with each axis The module communicates axis measurements to the connected microcontroller via synchronous serial communication.
North y-axis x-axis angle θ angle θ=arctan(-y/x)
Figure 2.7: Operation of the compass sensor
The GPS technology is primarily utilized for outdoor positioning, employing the HOLOX GPS UB-93 module Additionally, our system can leverage Assisted GPS (A-GPS) to enhance location accuracy by utilizing satellite information from the network, particularly in areas with weak signal conditions.
The system provides eight SFR-05 ultrasonic sensors split into four arrays, two on each, arranged at four sides of the robot [21] The measuring range is from 0.04 m to 4 m
The robot features a detachable visual system that can be equipped with either a Sony EVI-D100 pan-tilt-zoom (PTZ) color camera or a Hyper-Omni Vision SOIOS 55 omni-directional digital camera The CCD camera provides a clear view of the surrounding environment with a horizontal range of -100° to +100° and a vertical range of -25° to +25° In contrast, the omni-directional camera utilizes a hyperbolical mirror positioned above a standard camera, enabling it to capture a comprehensive 360-degree view around the robot.
Figure 2.8: Operation of the omni-directional camera
The robot features a 2D SICK-LMS 221 laser range finder (LRF) on its front, capable of measuring distances from 0.04m to 80m using the time-of-flight measurement principle This technology works by emitting a laser pulse that reflects off an object, with the time taken for the pulse to return used to calculate the distance An integrated rotating mirror allows the laser pulses to sweep across a radial area, effectively defining a 2D field in front of the sensor.
Figure 2.9: Operation of the laser range finder [68]: (a) Direction of scanning angle; (b) The scanned image
Actuators and sensors communicate through various channels, including low-rate options like RS-485 and RS-232, as well as high-rate connections utilizing USB ports The RS-485 devices are controlled by a 60MHz Microchip dsPIC30F4011 microcontroller, which operates independently.
The communication scheme between sensors, actuators, and controller boards utilizes an RS-485 bus for efficient data transfer among controllers Devices employing RS-232 connections are linked through USB-to-COM modules Control commands and brief messages are transmitted over low-rate channels, while images captured by cameras are directed to a high-rate USB port for enhanced performance in the system.
Motor for vertical rotation of LRF
Motor for driven wheel encoders are used to measure indirectly the robot position (x, y) whereas the compass sensor is employed to directly measure the robot orientation θ with absolute value
Control devices are situated at the user's location, comprising an ASUS notebook with a 1.5GHz M-Centrino processor, 500MB RAM, and Windows XP, alongside a joystick A specialized control software enables users to receive feedback from the remote site and navigate the robot effectively To enhance user experience, a 3D Logitech Extreme joystick, featuring 10-bit resolution for both horizontal and vertical axes and 12 functional buttons, is incorporated This joystick translates user inputs into a series of control parameters, which are then processed by the control software.
Figure 2.11: Graphic user interface of the control software written in Microsoft
The robot can connect to the Internet using two configurations: one via an 802.11 wireless access point and the other through a 3G mobile network Both setups employ a multi-protocol model to manage data communications, optimizing overall performance by utilizing different protocols tailored to the specific types of data exchanged The selection of these protocols is informed by a thorough analysis of their compatibility with the data exchanged in a Networked Robotic System (NRS).
The Internet protocol suite is organized into four key layers: data link, network, transport, and application Each layer comprises multiple communication protocols that serve specific functions Research on networked real-time systems (NRSs) has predominantly concentrated on transport protocols Among the various transport protocols, including TICP, ALCAP, and STCP, the transmission control protocol (TCP), user datagram protocol (UDP), and real-time transport protocol (RTP) are the most widely utilized and recognized as Internet standards.
TCP is a complex protocol initially designed for the reliable transmission of static data, such as emails and files, over low-bandwidth, high-error-rate networks It establishes a virtual connection between sender and receiver, acknowledges received data packets, and retransmits lost packets While there have been attempts to utilize TCP in Networked Real-Time Systems (NRSs), its focus on reliability is not suitable for scenarios where timely transmission is critical The retransmission mechanism is ineffective for real-time data delivery, and its strict congestion control can lead to increased delay jitter, significantly degrading Quality of Service (QoS) in congested networks.
UDP, on the other hand, is based on the idea of sending a datagram from a de- vice to another as fast as possible without due consideration of the network state
[57] This protocol does not maintain a connection between the sender and receiver
UDP does not ensure the delivery or the sequence of transmitted data at the receiving end Its primary benefit lies in significantly reduced transmission delays and jitter, especially in optimal network conditions This makes UDP a popular choice for real-time applications.
RTP, a new protocol for delivering real-time multimedia data, is built on UDP and incorporates features for jitter compensation and out-of-sequence detection Typically used alongside the RTP Control Protocol (RTCP), RTP transmits audio and video streams, while RTCP monitors transmission statistics and assesses quality of service.
Conclusion
It is able to summarize the system model as follows:
The state-space representation of the overall Networked Control System (NRS) is detailed in equation (2.15) This network functions as an intermediary between the process and the controller, transmitting input signals and observation measurements that may experience delays, losses, and out-of-order delivery, as illustrated in figure 2.2 The delays are treated as random yet measurable at each sampling instance, while out-of-order delivery is characterized as a long delay, as outlined in equation (2.21) Additionally, packet loss is represented as a binary random variable, as defined in equation (2.22).
The robot features a differential drive system with two wheels, governed by both continuous and discrete kinematic models Its hardware setup includes actuators and sensors for navigation and interaction, alongside remote control devices for user engagement Data communication is facilitated through a multi-protocol model that leverages various transport protocols to improve real-time performance and reliability for the navigation and remote sensing (NRS) system.
The result of this chapter are published in [1, 2, 3, 4, 5, 10].
Localization Using Optimal Filter
Robot localization
Localization refers to a robot's ability to determine its position within an environment, specifically its x and y coordinates and heading direction in a global coordinate system This capability is crucial for mobile robotics, as accurate localization enables robots to perform tasks autonomously Some researchers consider localization the "most fundamental problem" for achieving true robotic autonomy Over the past decade, significant advancements have been made in this area, leading to various localization methods, including dead reckoning, absolute positioning, and sensor fusion.
Dead reckoning, also known as relative positioning, estimates a robot's location by considering its speed, direction, and the time elapsed since its last known position A common method of dead reckoning is odometry, which integrates incremental data over time using wheel encoders to track wheel revolutions, allowing the robot to calculate the distance traveled and changes in direction This technique is favored for its short-term accuracy, high sampling rates, and low cost However, odometry can accumulate errors over time, potentially leading to unbounded inaccuracies without proper compensation Therefore, it is frequently combined with absolute positioning methods to correct these errors after a set duration.
Absolute positioning utilizes measurements relative to a global frame for robot localization, with map matching being a widely used technique This method leverages geometric features of the environment, such as lines and points that represent walls and corners, or specific shapes like rectangles and triangles, to determine the robot's location The primary benefit of absolute positioning is its independence from prior estimations and accumulated errors, although it does face challenges related to implementation complexity and reliance on the environmental structure.
Sensor fusion is a method that combines both relative and absolute measurements to enhance environmental perception Since different sensors may detect varying features—some being occluded for certain sensors while visible to others—integrating data from multiple sensors effectively addresses these limitations This fusion results in a more accurate and comprehensive understanding of the surroundings Various fusion techniques have been developed, including the central limit theorem, Kalman filter, Bayesian networks, and Dempster-Shafer Notably, the Kalman filter stands out as a powerful tool for synthesizing information from multiple sources, providing optimal statistical estimates, making it particularly advantageous for Non-Rigid Structures (NRSs).
Localization of NRSs
In NRSs, localization encounters significant challenges due to communications networks, including unavoidable delays, out-of-order data, intermittent observations, and unreliable bandwidth Various studies, as outlined in section 1.3.1, have explored solutions to these issues through advanced interface techniques and optimal filters.
Advanced interface techniques involve determining a robot's pose locally before sending it to the network At the remote site, this pose is extrapolated based on the network's state While this method is easy to implement, it suffers from low accuracy and struggles to manage mixed uncertainties related to delays, data loss, and out-of-order transmission.
Optimal filters can effectively address the limitations posed by network influences in robotic systems By incorporating network effects into the system model, optimal estimation theory can be utilized to accurately determine the robot's state While current filters primarily target specific issues like network delay or message loss, many studies have explored multiple challenges but fall short in optimizing for out-of-order message delivery Additionally, most existing filters are tailored for linear systems, necessitating further adjustments for application in nonlinear systems such as Nonlinear Robot Systems (NRSs).
In this study, we introduce a novel filtering technique for localization known as the past observation-based extended Kalman filter (POEKF) This filter effectively addresses challenges such as delay, data loss, and out-of-order information caused by network issues The POEKF is derived from Kalman filter theory, focusing on a "relevance factor" that quantifies the significance of past observations in relation to the current state This relevance factor acts as a multiplier, allowing the integration of delayed or out-of-order measurements into the posterior estimation Additionally, when measurements are missing, the filter executes a prediction step that combines the kinematic model with the input signal to maintain accuracy.
Localization of NRSs using past-observation based extended Kalman filter 45
This section provides a concise overview of the Kalman filter, which serves as the foundation for our algorithm It details the derivation of the optimal filter specifically for linear Nonlinear Regression Systems (NRS) and concludes with an explanation of how the filter can be adapted for nonlinear systems.
The Kalman filter is a mathematical tool designed to efficiently estimate the state of a process while minimizing the mean squared error It operates through two key steps: the time update, which predicts the state prior to measurement, and the data update, which refines the predicted estimate once the measurement is obtained.
Consider the following discrete time linear stochastic system:
= + x x u w z x v (3.1) where k∈, x, w∈ n , z, v∈ m , u∈ l , A∈ n n × , B∈ n l × , H∈ m n × , ( , , )x w v 0 are Gaussian, uncorrelated, white, with mean ( ,0,0)x and covariance ( , , )P Q R 0 re- spectively The steps to calculate the Kalman filter can be summarized as follows:
• The time update equations (prediction phase):
P − = A P A − + − − +Q − (3.3) where ˆx k − ∈ n is the priori state estimate at step k given knowledge of the process prior to step k, and P k − denotes the covariance matrix of the priori estimate error
• The data update equations (correction phase):
The equation P + = −I K H P − (3.6) represents the posteriori state estimate at step k, denoted as ˆx k + ∈ n, based on the measurement z k In this context, K k signifies the Kalman gain, while P k + indicates the covariance matrix associated with the posteriori estimate error For further information on the Kalman filter, please consult references [10, 70].
3.3.2 Optimal filter for linear NRSs
The NRS described in equation (2.15) defines the state vector x as [x, y, θ]ᵀ, where (x, y) represents the robot's position and θ indicates its orientation Consequently, localization transforms into the task of estimating the state vector x When the functions f and h are linear, the system can be reformulated as outlined in equation (2.15).
(3.8) where u k n − − 1 , z i k , H k m − , v k m − , and i are defined by the above equations We now de- rive the optimal filter to estimate the state of the linear system given in equations (3.7) and (3.8)
The priori state estimate, denoted as ˆx k −, represents the expected value of the state x k based on all measurements collected up to the previous step, k-1 By applying the expected value to both sides of equation (3.7), we can effectively articulate this estimate.
As E(x k − 1 ) is the posteriori state estimate at time k-1, u k n − − 1 is a known input and
1 k − w is Gaussian zero-mean white noise, equation (3.9) becomes:
Priori Error Covariance: Let e k − and e k + be the priori and posteriori estimate er- rors, respectively: k k ˆ k
From equations (3.7) and (3.10) we obtain:
Taking the expected value of both sides of equation (3.13) and noting that k + 1 e − is un- correlated with w k − 1 , we obtain the covariance of the priori estimate error:
The posteriori state estimate indicates that the measurement \( \tilde{z}_k \) updates the system state at a prior time \( i \) instead of the current time \( k \) Due to delays or out-of-order issues, this measurement may not be received by the estimator until time \( k \) Consequently, we formulate the data update equation as follows: \( \hat{x}_{k+1} = \hat{x}_k + K_k (\tilde{z}_i - H_i \hat{x}_i) \).
That is, the correction term is the past residual at which the measurement is taken This can be explained by computing the mean of estimation error:
From equations (3.7) and (3.10) we get:
Substituting equation (3.17) to (3.16) and noting that w k − 1 and v i are zero-mean ob- tain:
Equation (3.18) suggests that when the initial estimates of x are aligned with its expected value, the posteriori estimate ˆx + will, on average, accurately reflect the true value of x This characteristic is a key advantage of our estimator.
The Kalman gain (Kk) and the posteriori error covariance are calculated to optimize the filter's performance The primary objective is to minimize the total variance of estimation errors, which is represented by the cost function.
Assume that the measurement is fused using equation (3.15) with an arbitrary gain K k From equation (3.16), the covariance of the posteriori estimate error, P k + , is determined as:
Due to the independence between e − and v , equation (3.20) can be simplified to:
To minimize the cost function J k, the matrix K k is selected as the gain or blending factor This minimization involves taking the derivative of J k with respect to K k, setting it to zero, and solving for K k It's important to note that tr A tr A( )= ( ) T and tr XA( ) A T during this process.
∂ , the derivative of J k is obtained as:
Setting equation (3.22) to zero gives:
In order to compute L, the priori state estimate at time k needs determining from the estimate at time i Through the time update equation (3.10) and the data update equation (3.15), e − becomes:
After m updating steps, the estimation error becomes:
=∏ − (3.27) and ξ 1 and ξ 2 are the functions of noise sequences w and v From equation (3.26) and the independence between e − and noise sequences, the covariance L becomes:
Substituting equation (3.28) in (3.24) and (3.23) yields: k k k i i T
Summary: The optimal filter for the linear NRS can be summarized as follows:
We call this filter past observation-based Kalman filter (PO-KF)
Remark 1: When the delay n is zero, the time update equation (3.31) reduces to the standard form (3.2) When the delay m is zero, F I= and the Kalman gain (3.30) reduces to the standard form (3.4) and the error covariance (3.29) reduces to (3.6)
Remark 2: Equation (3.30) can be rewritten as: k i *
The Kalman gain at time i, denoted as K_i*, is defined by the equation K = FK (3.37) In the standard Kalman filter (3.4), the past residual, represented as (z̃_k - H_i x̂_i), can be updated to the posterior estimate at time k, similar to the process at time i However, it is essential to adjust the Kalman gain by the factor F, which reflects the relevance of the measurement updated at time i in relation to the state at time k.
Remark 3: From equations (3.33) – (3.36), the computation of the PO-KF de- pends on values of the random variables λ and m As analyzed in chapter 2, these values are determined and measurable at each sampling time: λ k is determined by equation (2.14) and m is measured by the time stamp included in the receiving mes- sage (see section 2.2.2) Thus, the implementation of the PO-KF is feasible
Remark 4: Equation (3.35) can be rewritten as: ˆ k + = ˆ k − +λ i K k ( i k −H i i ˆ − ) x x z x (3.38)
If a measurement is not obtained (λ i =0), a "dummy" measurement is utilized, but this does not provide any information for the estimate Consequently, the posterior estimate defaults to the prior estimate, indicating that there is no correction phase involved As a result, the estimator operates in an open-loop manner, leading to reduced accuracy This outcome is logical, as the loss of feedback measurement means there is no information available to refine the prediction.
Network delay, while not resulting in information loss, introduces additional complexity to the system However, if the network delay is measurable, it can be incorporated into the computation process to enhance the retrieval of relevant information for estimates Simulations will demonstrate that although network delay leads to initial estimate errors, these errors diminish rapidly as delayed measurements are received, ultimately stabilizing at a steady state.
3.3.3 Optimal filter for nonlinear NRSs
To adapt the PO-KF for nonlinear systems, it is essential to implement modifications due to the inherent nonlinearity of NRSs Our primary approach involves linearizing the nonlinear system based on its previously estimated states.
Performing a Taylor series expansion of the state equation (2.15) around
(3.39) where A k − 1 , W k − 1 are defined by the above equation The known signal u * k n − − 1 and the noise signal w * k − 1 are defined as follows:
Similarly, the measurement equation (2.15) is linearized around ˆ( ,0)x i − to obtain ˆ ˆ
(3.42) where h i , H i , V i are defined by the above equation The known signal ε * i and the noise signal v * i are defined as follows:
The system (3.39) and the measurement (3.42) now become linear and the PO-
KF can be applied to obtain the optimal filter for networked robot localization as fol- lows:
• The time update equations at the prediction phase:
• The data update equations at the correction phase:
We call this filter past observation-based extended Kalman filter (PO-EKF) It is noted that the PO-EKF is suboptimal rather than optimal due to the linearization process.
Implementation of the PO-EKF for the differential-drive network robot
The previously discussed PO-EKF is a versatile tool designed for various network control systems This section focuses on its specific implementation for the differential-drive NRS, detailing how the PO-EKF can be effectively applied in this context.
To effectively implement the PO-EKF, it is essential to understand the network state, which includes factors such as message loss, delay, and out-of-order delivery at each sampling instance In our system, the message arrival, denoted as λ k, is calculated using equation (2.14).
In this system, a message is marked as "1" if received within the time frame from k-1 to k, and "0" otherwise Network delays, denoted as n and m, are assessed by comparing the sending time in the received message with the actual receiving time, necessitating clock synchronization for accuracy (refer to section 2.2.2) Additionally, out-of-order messages are identified through the sequential number present in the received message, with the associated time delay calculated using equation (2.21).
3.4.2 Implementation of the prediction phase
The estimation of the priori estimate ˆx k − in equation (3.45) is carried out via the kin- ematic equation (2.8) of the robot where the function f is defined The input
The pre-determined velocity [ω ω L R] T u= is essential for defining the robot's desired trajectory To calculate the prior covariance P k −, it is necessary to identify the matrices A k − 1, W k − 1, and Q k − 1 This identification is based on the kinematic equation (2.8) and equation (3.39), which provide the framework for determining A k − 1 and k 1.
The process noise, denoted as Q k, is influenced by the angular velocities of the left and right wheels, ω L and ω R Variances are represented as δω L 2 and δω R 2, with δ being a constant derived from experimental data This constant is calculated by assessing the deviations between the actual robot position and the position predicted by the kinematic model during straight movements and rotations at various speeds The estimated value for δ in our system is 0.01, which is used to formulate the input-noise covariance matrix Q k.
In the implementation of the PO-EKF, the initial estimate \( \hat{x}_0^+ \) is initialized to zero, establishing the origin of the global coordinate system at the robot's starting position The initial error covariance \( P_0^+ \) is set equal to the measurement error \( R_0 \) (as shown in equation (3.50)) However, in practice, the choice of \( P_0^+ \) has minimal impact on the operational performance of the PO-EKF, as the error covariance \( P_k^+ \) rapidly converges to a steady state.
3.4.3 Implementation of the correction phase
The correction phase implementation relies on equation (3.46) and requires the parameters z, R, H, and V According to equation (2.14), if a data packet is lost (λ i = 0), these parameters will be zero, resulting in the absence of a correction phase, as noted in remark 4 of section 3.3.2 Conversely, when the packet is received (λ i = 1), the parameters are defined as z, R, H, and V, which we will now determine.
The output z of the robot encompasses both its position and orientation, which are measured using an optical encoder for position and a compass sensor for orientation The measurement noise's covariance matrix, R k, is established by comparing these measurements with true values across various configurations multiple times to estimate the expectation and variance of the noise In our system, we identify the covariance matrix of the measurement noise accordingly.
Finally, matrices H k and V k are identity matrices due to equations (2.13) and (3.42): k k
In next sections, the performance of the PO-EKF will be evaluated via simulations and experiments.
Simulations
In order to evaluate the efficiency of the PO-EKF for the localization of NRSs, sim- ulations have been carried out in MATLAB [24] The setup is as follows
The robot's identity is defined by its motion and sensory systems In our simulation, the robot's motion is modeled using its kinematic equation (2.8), with parameters established based on the actual NRS.
• Radius of the driven wheel: R = 5 cm
• Distance between the driven wheels: L = 60 cm
The angular velocities of the left and right wheels, represented as u = [ω L, ω R], range from -26 rad/s to 26 rad/s and are pre-determined and stored in the controller to enable the robot to follow specific trajectories, as illustrated in figures 3.1 and 3.2 The selection of these trajectories will be elaborated upon in the "simulating scenario" section At each execution step k, a value u k is retrieved from the controller and transmitted over the network to the actuator.
• The output includes the position and orientation of the robot, z = [ x y θ ] T Its initial values are chosen to be zeros, z 0 = 0 0 0 0 T , corresponding to the origin of the global coordinate system
In MATLAB, the representation of robot motion by its kinematics is carried out as follows:
% Compute the tangential and angular velocities (noise in- cluded)from the angular velocities (without noise) wL=wL(i-1)+PNoise_L(i); wR=wR(i-1)+PNoise_R(i); v=r_wheel*(wR+wL)/2; w=r_wheel*(wR-wL)/b_wheel;
% Time-based propagation of robot pose by its kinematics x(i)=x(i-1)+ dt*v*cos(theta(i-1)); y(i)=y(i-1)+ dt*v*sin(theta(i-1)); theta(i)=theta(i-1)+ dt*w;
In the simulation, the robot is equipped with a sensory system capable of measuring the output z in a manner similar to the actual system The sensor values are identified as the system output, incorporating measurement noise for accuracy.
% Values measured by sensors pos_mes_X(i)=pos_true_X(i)+ONoise_x(i); pos_mes_Y(i)=pos_true_Y(i)+ONoise_y(i); pos_mes_Theta(i)=pos_true_Theta(i)+ONoise_theta(i);
The network is designed as a module that incorporates delay, data loss, and out-of-order delivery, as outlined in equation (2.15) Experimental measurements indicate that the time delay ranges from 100 ms to 800 ms, with a data loss rate of 2% and an out-of-order rate of 5% at each sampling interval.
In MATLAB, the loss rate is initialized using binary random variables, specifically for the controller to actuator (lamdaCA) and sensor to controller (lamdaSC) connections, with a success probability of 0.98 over N execution steps Additionally, out-of-order and delay conditions are introduced by generating a binary random variable, where 5% of the values indicate a loss.
“1” corresponding to the occurrence probability of the out-of-order: lamdaOCA = binornd(1,0.05,N,1);
Then, at the time at which the lamdaOCA = 1, the time delay will be added an extra delay (j i T− ) s as in equation (2.21):
% Network delay a1=1;a2=8; % range of random delay b1=5;b2; % range of out-of-order
Delay(i)=round(a1+(a2-a1)*rand()+lamdaOCA(i)*(b1+(b2- b1)*rand()));
In some simulations, those network parameters will be set to be higher in order to simulate extremely bad network conditions
Implementation of the PO-EKF
In section 3.4, the parameters for the PO-EKF, including A, W, Q, H, and R, are selected based on specific criteria The MATLAB definitions of these matrices are simple and derived from their respective formulas Additionally, the input and measurement noises are characterized through covariance matrices, with the measurement noise component x being explicitly defined.
Std_ONoise_x = sqrt(Var_ONoise_x)'; %1x1
ONoise_x = Std_ONoise_x* randn(1,N+2); %1x1 * 1xN = 1xN
In robotic simulations, a set of noise-free input velocities is applied to the kinematic model at each sampling time to create theoretical trajectories, as illustrated in Figures 3.1 and 3.2 The first trajectory represents a standard movement, while the second depicts a more complex maneuver However, due to input disturbances and network effects, the robot follows a different path known as the true trajectory Observations are then measured to produce an output trajectory, which is affected by measurement noise Figure 3.3 presents a comparison of the trajectories in the X direction, showing only 100 sample points for clarity Finally, a localization algorithm is utilized to estimate the trajectory accurately.
(corresponding to ˆx + ) This trajectory is expected to close to the true trajectory x
The difference between the estimate and the true trajectories determines the accura- cy of the localization algorithm
In this evaluation, we compare the PO-EKF with two well-known localization algorithms: the extended Kalman filter (EKF) and the Lucas-Extended Kalman filter (LEKF) proposed in [64] The EKF operates under the assumption that it cannot detect measurement delays, incorporating all incoming data as if it were timely Conversely, the LEKF is specifically tailored for systems experiencing random delays and packet loss, utilizing an infinite buffer to manage and reorder delayed or out-of-sequence measurements, while treating lost measurements as zero values During each estimation step, the LEKF iteratively applies the Kalman equations from the initial state to the current estimate, demonstrating its optimal performance in handling such challenges.
Figure 3.1: An ordinary theory trajecto- ry of the robot in the motion plane
Figure 3.2: An extreme theory trajectory of the robot in the motion plane
Figure 3.3: The theory, true and observation trajectories in X direction
The first simulation utilized network parameters with a time delay ranging from 100ms to 800ms, an out-of-order rate of 5%, and a loss rate of 1% Figure 3.4 illustrates the estimated and actual trajectories in the motion plane, where their overlap indicates effective estimation To compare the algorithms, the root mean square error (RMSE) was calculated, and Figures 3.5–3.7 display the comparative curves in the X, Y, and θ directions, derived from 100 Monte Carlo tests The results indicate that the Extended Kalman Filter (EKF) exhibits the largest error, while both the PO-EKF and LEKF demonstrate comparably small errors.
EKF PO-EKF LEKF True value
Figure 3.4: The EKF, LEKF, PO-EKF, and true trajectories in the motion plane
Figure 3.5: RMSE of the EKF, LEKF,
PO-EKF estimation and the true trajec- tories in X direction
Figure 3.6: RMSE between the EKF,
LEKF, PO-EKF and the true trajectories in Y direction
Figure 3.7: RMSE between the EKF,
LEKF, PO-EKF and the true trajectories in orientation
When evaluating filter performance, both accuracy and computational efficiency are essential Standard MATLAB functions, including tic, toc, and flops, were utilized to measure the floating-point operations and execution time of various filters As presented in Table 3.1, the performance results indicate that the PO-EKF has approximately double the computational burden of the EKF, yet it remains significantly more efficient, being nearly one hundred times less demanding than the LEKF.
Table 3.1: Normalized computational burden of filters
Parameter EKF LEKF PO-EKF
Figure 3.8: The EKF, LEKF, PO-EKF, and true trajectories of the robot in the motion plane
Figure 3.9: RMSE between the EKF,
LEKF, PO-EKF and the true trajectories in X direction
Figure 3.10: RMSE between the EKF,
LEKF, PO-EKF and the true trajectories in Y orientation
Figure 3.11: RMSE between the EKF,
LEKF, PO-EKF and the true trajectories in orientation
In the second simulation, an extreme scenario is analyzed where the time delay ranges from 800ms to 1500ms, accompanied by a 15% out-of-order rate and a 10% loss rate, as the robot navigates a sinusoidal path The LEKF employs a finite buffer of 50 slots to alleviate computational demands, assuming bounded time delays Figure 3.8 illustrates the estimated versus true trajectories, revealing that while the EKF experiences significant drift at curvature points, both the PO-EKF and LEKF maintain strong tracking performance This is further highlighted by the RMSE comparisons in figures 3.9–3.11 Additionally, table 3.2 outlines the computational burden of the filters, indicating that although the LEKF's use of a finite buffer reduces computation, it remains higher than that of the PO-EKF.
Table 3.2: Normalized computational burden of filters
Parameter EKF LEKF PO-EKF
Simulations indicate that the Extended Kalman Filter (EKF), which was not specifically designed to address network-induced issues, is significantly impacted by network conditions In contrast, both the PO-EKF and LEKF demonstrate improved performance; however, the PO-EKF is notably less demanding in terms of computational resources.
Experiments
Experiments were carried out to assess the performance of the PO-EKF using the NRS hardware detailed in section 2.3, with the software developed in Microsoft Visual C++.
The experiments involve two distinct network configurations: the local configuration and the VPN configuration In the local configuration, the robot connects to the Internet via Viettel's 3G network, while a control computer at a remote site uses VNPT's ADSL network for localization algorithms Conversely, the VPN configuration links both the robot and control computer to remote servers in the United States through a virtual private network These configurations aim to accurately simulate varying network conditions, both favorable and unfavorable.
Figure 3.12: Experimental configuration with local Internet service providers
Figure 3.13: Experimental configuration with VPN connections to the servers locat- ed at the United State
In experiments, the robot operates in manual mode, following predefined paths while its position is tracked by optical encoders and its orientation by a compass sensor Localization occurs at two sites: one with direct input and measurement data, and another with delayed data from a remote controller However, measurement errors make it impossible to determine the true trajectories during the experiments Consequently, the estimation using the Extended Kalman Filter (EKF) with no-delay data will serve as the reference for comparison and evaluation.
In the local configuration experiment, network parameters were assessed, revealing a time delay of 300ms to 500ms, an out-of-order rate of 2.4%, and a loss rate of 1.3% The estimated trajectories in the motion plane are illustrated in Figure 3.14(a), while Figures 3.14(b)–(d) display the errors of the EKF, LEKF, and PO-EKF trajectories in the X, Y, and θ directions, with the no-delay estimation serving as a reference The results indicate that the PO-EKF achieves superior accuracy compared to the EKF and matches the LEKF's accuracy at steady state, which is notable as the LEKF is recognized for its optimal performance in network-induced issues However, the estimation error observed in this experiment is approximately 10 cm, higher than the 5 cm error noted in simulations, attributed to unforeseen factors such as wheel slip, robot dynamics, and non-Gaussian noise Despite efforts to minimize these influences during calibration, they were not the primary focus of this study Notably, the 10 cm accuracy is adequate for our system, which requires a precision of 30 cm for effective control and navigation operations.
Figure 3.14: Comparison between the EKF, LEKF and PO-EKF in local configu- ration: (a) Trajectories in the motion plan; (b) Errors in X direction; (c) Errors in Y direction; (d) Errors in orientation.
In the VPN configuration experiment, network parameters were assessed, revealing an average time delay of 600ms to 800ms, an out-of-order rate of 2.9%, and a loss rate of 1.4% (refer to Table 3.3) The estimation results, illustrated in Figure 3.15, align with previous findings in terms of accuracy.
The results indicate that both the PO-EKF and LEKF exhibit significant estimation errors during the initial steps, primarily due to the absence of feedback measurements caused by network delays During this period, the filters rely solely on open-loop estimation through time update equations However, as delayed measurements are received, the filters begin to refine their estimations, ultimately achieving a steady state.
Table 3.3: Network parameters during experiments Parameter Local configuration VPN configuration
Time delay 300ms – 500ms 600ms – 800ms
Figure 3.15: Comparison between the EKF, LEKF and PO-EKF in VPN configura- tion: (a) Trajectories in the motion plan; (b) Errors in X direction; (c) Errors in Y direction; (d) Errors in orientation.
Discussion
In our experiments, we observed a relatively high rate of message loss and out-of-order delivery, significantly exceeding the typical network performance benchmark of below 1% This issue primarily stems from the 100 ms sampling rate in our system, during which the sensor update must compete with other tasks such as motion control, data storage, and network communications Factors like sensor adaptation, timing errors, and clock mismatches can lead to incomplete task execution, resulting in missed measurements Although increasing the sampling time could mitigate this problem, it would also decrease the filter's efficiency due to slower measurement updates.
(b) Figure 3.16: Estimate by the PO-EKF with uniform distribution noise: (a) RMSE in X and Y directions; (b) RMSE in orientation
(b) Figure 3.17: Estimate by the PO-EKF with non-zero mean noise: (a) RMSE in X and Y directions; (b) RMSE in orientation
The performance of the PO-EKF was assessed with non-Gaussian and non-zero mean noises, revealing that the accuracy with uniform distribution noise is comparable to that observed with Gaussian noise However, when the noise has a mean of 20 cm, the accuracy decreases in comparison to estimates with zero-mean noise Overall, the findings indicate that while the PO-EKF remains effective across various noise types, its accuracy may be somewhat compromised.
This study primarily focuses on addressing network-induced issues The results demonstrate that the proposed PO-EKF achieves superior accuracy compared to the Extended Kalman Filter (EKF), which is not tailored for networked systems, while matching the accuracy of the Linearized Extended Kalman Filter (LEKF), specifically optimized for such environments Additionally, the PO-EKF offers lower computational demands than the LEKF, highlighting its efficiency in networked applications.
Conclusion
The localization of NRSs faces challenges caused by the communications network
To address existing challenges, we introduce the PO-EKF filter, which effectively integrates system kinematics, network state, and feedback measurements to achieve optimal estimates by minimizing mean squared errors The theoretical foundation for this optimality is established, and extensive simulations and experiments validate that the proposed algorithm delivers accurate estimates without significant computational demands The findings of this study are documented in references [12, 13].