2020 International Conferences on Internet of Things (iThings) and IEEE Green Computing and Communications (GreenCom)
and IEEE Cyber, Physical and Social Computing (CPSCom) and IEEE Smart Data (SmartData) and IEEE Congress on
2020物联网国际会议(iThings)、 IEEE 绿色计算及通讯(GreenCom)、 IEEE 网络、物理及社会计算(CPSCom)、 IEEE 智能数据
(SmartData)及 IEEE
A Switching Offloading Mechanism for Path
Planning and Localization in Robotic
Applications
机器人应用中路径规划和本地化的切换卸载
机制
Dimitrios Spatharakis
∗
, Marios Avgeris
∗
, Nikolaos Athanasopoulos
†
, Dimitrios Dechouniotis
∗
Dimitrios Spatharakis * ，Marios Avgeris * ，Nikolaos Athanasopoulos † ，Dimitrios Dechouniotis *
Symeon Papavassiliou
∗
Symeon Papavassiliou
∗
National Technical University of Athens, Greece
希腊雅典国立技术大学
† School of Electronics, Electrical Engineering and Computer Science, Queen’s University Belfast, Northern Ireland, UK
英国北爱尔兰贝尔法斯特女王大学电子、电子工程和计算机科学学院
{dspatharakis, mavgeris}@netmode.ntua.gr, n. .uk, .gr, .gr
{ dspatharakis，mavgeris }@netmode. ntua.g，n. .uk， .g，
.g
Abstract—Industry 4.0 applications rely on mobile robotic agents
that execute many complex tasks that have strict safety and time
requirements. Under this setting, the Edge Computing service
delivery model allows the robotic agents to offload their
computationally intensive tasks to powerful computing infrastructure
in their vicinity. In this study, we propose a novel switching
offloading mechanism for such robotic applications. In particular, we
design opportunistic offloading strategies for the path planning and
localization services of mobile robots. The offloading decision is
based on the uncertainty of the robot’s pose, the resource availability
at the Edge of the network and the difficulty of the path planning. Our
switching offloading framework is implemented and evaluated using
a robot in a real Edge Computing testbed, where the trade-off
between execution time and the successful completion of the robot
trajectory is highlighted.
工业 4.0应用程序依赖于移动机器人代理来执行许多复杂的任
务，这些任务有严格的安全性和时间要求。在这种情况下，边缘
计算服务交付模型允许机器人代理将计算密集型任务卸载到附近
强大的计算基础设施中。在这项研究中，我们为这种机器人应用
程序提出了一种新的切换卸载机制。特别是，我们为移动机器人
的路径规划和定位服务设计了机会主义卸载策略。卸载决策基于
机器人姿态的不确定性、网络边缘的资源可用性和路径规划的难
度。我们的切换卸载框架是在一个真实的边缘计算实验平台上实
现和评估的，其中执行时间和机器人轨迹的成功完成之间的权衡
是突出的。
Index Terms—IoT, Edge Computing, Computational Offload-ing,
Robotics, Switching Control.
索引术语ー物联网，边缘计算，计算卸载，机器人，切换控制。
I. INTRODUCTION
引言
Computation offloading in current and next-generation
net-works is becoming increasingly important due to the
prolifer-ation of Internet of Things (IoT) real world
applications [1]. These applications introduce a vast number
of low-capability, low-energy devices to the networking
ecosystem, which regu-larly need to perform computationally
intensive and/or energy-hungry tasks. However, when
latency and energy consumption minimization are required,
the limited resources of the IoT devices prove inadequate [2].
For example, in Industry 4.0 and especially in collaborative
robotics, where humans and robots work together in dynamic
environments, computation-ally heavy algorithms enable IoT
devices in sensing and actuating [3]. Consequently, large
amount of information has to be processed and complex
algorithms need to be executed in real-time.
随着物联网在现实世界中的应用越来越广泛，当前和
下一代网络中的计算卸载正变得越来越重要[1]。这些应
用程序为网络生态系统引入了大量低容量、低能耗的设
备，这些设备通常需要执行计算密集型和/或耗能的任务。
然而，当需要延迟和能源消耗最小化时，物联网设备的
有限资源证明是不够的[2]。例如，在工业 4.0 中，特别
是在人类和机器人在动态环境中一起工作的协作机器人
中，计算量大的算法使物联网设备能够感知和执行[3]。
因此，必须处理大量的信息，并且需要实时执行复杂的
算法。
The increasing availability of networking in the Edge and
Cloud supports new approaches, where processing is per-
formed remotely, with access to extensive computing and
memory resources. In this direction, Edge Computing (EC)
alongside Fog Computing (FC) [4] constitutes a particularly
prominent way of dealing with the aforementioned shortcom-
ings of IoT devices. FC offers an attractive alternative pro-
viding low-latency and high energy efficient operation, while
maximizing system performance. This paradigm is currently
more relevant than ever, especially in the context of the
Edge 和 Cloud 中不断增加的网络可用性支持新的方法，
在这些方法中，处理是远程执行的，可以访问广泛的计算
和内存资源。在这个方向上，边缘计算(EC)和光纤计算
(FC)[4]构成了处理上述物联网设备缺陷的一种特别突出的
方法。FC 提供了一个有吸引力的替代方案，提供低延迟
和高能效的操作，同时最大化系统性能。这种模式目前比
以往任何时候都更加相关，特别是在
much-anticipated Industry 4.0 revolution [5] and Industrial
IoT (IIoT), where Fog Robotics (FR) is introduced. FR can be
defined as the architecture that distributes computing, storage
and networking functions at the Edge/Cloud continuum in a
federated manner [6], i.e. where robots and automation
systems rely on data or code from a network to support their
operation.
备受期待的工业 4.0 革命[5]和工业物流(IoT) ，其中引入
了雾化机器人技术(FR)。FR 可以定义为以联邦方式在
Edge/Cloud 连续体上分配计算、存储和网络功能的体系结
构[6] ，即机器人和自动化系统依赖网络中的数据或代码
来支持其运行。
Suitable as it may seem, solely utilising remote computa-
tional resources is not enough; a number of unwanted
phenom-ena potentially take place in the transmission and
processing of the information, such as network latency,
variable Quality of Service (QoS), and downtime. For these
reasons, autonomous mobile robots often have some capacity
for local processing when targeting low-latency responses,
and during periods where network access is unavailable or
unreliable. Conse-quently, a major challenge, from a control
design, estimation, and network optimization point of view is
to combine local and remote resources in an efficient way.
仅仅利用远程计算资源似乎是不够的，在信息的传输和
处理过程中可能会出现一些不必要的现象，例如网络延迟、
可变的服务质量(QoS)和停机时间。由于这些原因，自主
移动机器人在针对低延迟响应时，以及在网络访问不可用
或不可靠时，往往具有一定的本地处理能力。从控制设计、
估计和网络优化的角度来看，conse 通常是一个主要的挑
战，即以一种有效的方式将本地资源和远程资源结合起来。
In this work, we propose a computation offloading mecha-nism
for robotic applications. In particular, we realize an IoT-enabled
localization and path planning framework and verify the expected
gains of computation offloading by utilizing a real Edge
Computing setting. To achieve this, we design and implement
local and remote localization and path planning controllers,
followed by a scheduling mechanism. The offload-ing
mechanisms are treated as switches, leading to different dynamics
of the resulting closed-loop system. Specifically, the algorithms
involved in the localization process are decided to run remotely,
rather than locally, when the uncertainty of the robot’s pose is
high and at the same time the network and computing resources
status at the Edge is favorable. On the other hand, path planning is
offloaded when the robot navi-gates in a part of a map where
better planning strategies can be achieved through involved
algorithms that can only be ex-ecuted remotely. These switches
compose a switching system that is adaptive and can operate
under different scenarios and applications. This architecture
perspective, which constitutes the main contribution of this work,
offers our framework a degree of contextual awareness; that is the
ability to sense and dynamically adapt to the robot’s environment,
implicitly enhancing to an extent the robustness of its operation,
as well as improving the QoS of the supported applications.
在这项工作中，我们提出了一个计算卸载机制的机器人应
用。特别是，我们实现了一个 iot 支持的本地化和路径规划
框架，并通过使用一个真正的边缘计算设置来验证计算卸载
的预期收益。为了实现这一点，我们设计并实现了本地和远
程定位和路径规划控制器，然后是调度机制。卸载机制被视
为开关，导致不同的动态结果闭环系统。具体地说，当机器
人位姿不确定性较高且边缘网络和计算资源状况良好时，定
位过程所涉及的算法决定远程运行，而不是局部运行。另一
方面，当机器人在地图的某个部分进行导航时，路径规划就
被卸载了，在这个部分中，通过只能远程执行的相关算法可以
实现更好的规划策略。这些开关组成了一个自适应的切换系统，
可以在不同的场景和应用下运行。构成本文主要贡献的体系结
构视角为我们的框架提供了一定程度的上下文意识，即感知和
动态适应机器人环境的能力，在一定程度上隐含地增强了机
器人操作的健壮性，并提高了所支持应用程序的服务质量。
Open challenges in this area throughout the literature
在整个文献中，这个领域的开放挑战
978-1-7281-7647-5/20/$31.00 ©2020 IEEE
978-1-7281-7647-5/20/31.002020 IEEE 77
DOI 10.1109/iThings-GreenCom-CPSCom-SmartData-Cybermatics50389.2020.00031
DOI 10.1109/iThings-GreenCom-CPSCom-SmartData-Cybermatics50389.2020.00031
are concerned with developing adaptive multi-robot/machine
control, capturing, modelling, predicting and anticipating the
agent’s interactions and designing distributed control and path
planning algorithms that deliver flexible and safe working
environments. Approaches similar to ours include [7], where
gesture-based semaphore mirroring with a humanoid robot is
split to remotely and locally executed functionality; [8], in
which the authors identify a three-layered environment (Robot,
Edge and Cloud) to overcome the challenges of network
limits in a Deep Robot Learning application and [9] where
Dew Robotics is introduced; this concept posits that
研究开发自适应多机器人/机器人控制、捕获、建模、预
测和预测代理的交互作用，设计分布式控制和路径规划算
法，提供灵活和安全的工作环境。类似于我们的方法包括
[7] ，其中基于手势的信号量镜像与仿人机器人是分裂到
远程和本地执行功能; [8]在其中，作者确定了一个三层环
境(Robot，Edge 和 Cloud) ，以克服挑战的网络限制，在
一个深度机器人学习应用程序和[9] ，其中引入了 Dew
Robotics; 这个概念假定,
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critical computations are executed locally so that the robot can
always react properly, while less critical tasks are moved to
the Fog and Cloud, so to exploit the larger availability in
computing, storage, and power supply. However, none of the
aforementioned offloading decision schemes addresses the
dynamic nature of the robot’s environment.
关键计算是在本地执行的，这样机器人总是能够正确地作
出反应，而较不关键的任务则转移到 Fog 和 Cloud 上，以
便在计算、存储和电源供应方面利用更大的可用性。然而，
上面提到的卸载决策方案都没有考虑到机器人环境的动态
特性。
The rest of the paper is organized as follows. In Section
论文的其余部分组织如下
II the architecture overview is presented, while in Section III
the system model and local tracking controller are pre-sented.
The algorithms used in the scope of this work for localization
and path planning are presented in Section IV. The switching
offloading mechanism is presented in Section V. An
experimental evaluation in Section VI. Finally, conclusions
are drawn and future plans are set in Section VII.
第三部分介绍了系统模型和本地跟踪控制器。第四部分介
绍了在本工作范围内用于定位和路径规划的算法。切换卸
载机制在第五节中介绍。第六部分的实验评估。最后，得
出结论，并在第七部分制定未来的计划。
II. ARCHITECTURE OVERVIEW
建筑概述
The scenario addressed in this work involves a mobile robot
equipped with sensing, computing, and wireless communica-tion
capabilities, which makes its way from a starting position to a
target position in an operating ground (e.g. a factory floor),
navigating through obstacles. This functionality is a key com-
ponent to realizing autonomous robotic navigation in Industry 4.0
use cases, e.g. warehousing and logistic robots which automate
the process of storing and moving supply chain goods. Tracking
the robot location is essential for a robust and safe trajectory
planning. However, a common problem in such a scenario is that
the uncertainty in estimating the exact pose (i.e. position and
orientation) grows over time in motion, due to inaccuracies in
sensing, wheel slips, hardware failures, etc., [10]. Thus, the
importance of an accurate, dynamically adjusted localization
technique is evident.
这项工作涉及的场景涉及一个移动机器人装备了传感，计
算和无线通信能力，使其从起始位置到目标位置在一个操作
场地(例如工厂车间) ，导航通过障碍物。这个功能是在工业
4.0 用例中实现自主机器人导航的关键组成部分，例如仓储和
物流机器人，这些机器人可以自动化存储和移动供应链货物
的过程。跟踪机器人的位置对于一个稳健和安全的轨迹规划
是必不可少的。然而，在这种情况下，一个共同的问题是，
估计精确姿态(即位置和方向)的不确定性随着时间的推移而
增加，由于传感器的不准确性，车轮打滑，硬件故障等[10]。
因此，准确的，动态调整的定位技术的重要性是显而易见的。
In our case self-localization through landmark assisted pose
estimation is implemented; the robots are equipped with a
camera module, while in their proximity unique cylindrical
beacons are used as landmarks to assist in the pose estimation
process. In the computationally demanding involved algo-
rithms, two offloading opportunities are revealed in, namely,
pose estimation and path planning. To this purpose, a small-
scale network infrastructure is set up, connecting the robot to a
wireless LAN (WLAN) through an Access Point located
within the robots’ network range, which in turn connects via a
wired connection (LAN) to a server in the robot’s proximity,
the Edge Server.
在我们的例子中，通过路标辅助姿态估计实现了自定位;
机器人配备了一个摄像机模块，而在它们附近，独特的圆
柱形信标被用作路标，以协助姿态估计过程。在计算要求
高的涉及算法算法中，两个卸载机会被揭示出来，即姿态
估计和路径规划。为此，建立了一个小规模的网络基础设
施，通过位于机器人网络范围内的 Access Point 将机器人
连接到无线局域网(WLAN) ，后者又通过有线连接(LAN)
连接到机器人附近的服务器 Edge Server。
Locally, the intangible assets include the (i) the Tracking
Controller (TC), (ii) the Local Odometry-Based Estimator
在本地，无形资产包括(i)跟踪控制器(TC) ，(ii)基于本
地里程计算的估计器
Fig. 1: Architecture Overview. The locally executed com-
ponents are highlighted with blue color, while the remotely
executed ones with green.
图 1: 架构概述。本地执行的组件用蓝色突出显示，而远
程执行的组件用绿色突出显示。
(LOE), (iii) the Local Beacon-Based Estimator (LBE), (iv) the
Local Path Planner (LPP) and (v) the Offloading Decision
Mechanism (ODM) components, all located within the robot;
component (i) is responsible for carrying out movement-
related decisions, (ii), (iii) and (iv) are the locally executed
pose estimation and path planning applications respectively
and (v) encompasses the intelligence of our switching system
by monitoring the offloading-related metrics and realizing the
offloading decisions. On the remote side, containerized
counterparts of the path planning and pose estimation appli-
cations are co-hosted on the Edge Server; these are namely
(LOE)、(iii)基于本地信标的估计器(LBE)、(iv)基于本地
路径规划器(LPP)和(v)卸载决策机制(ODM)组件，这些组
件都位于机器人内部; 组件(i)负责执行与运动相关的决策;
(ii)、(iii)和(iv)分别是本地执行的姿态估计和路径规划应
用; (v)通过监测卸载相关度量和实现卸载决策，包含了我
们切换系统的智能。在远程方面，路径规划和姿态估计应
用程序的集装箱对应物共同托管在 Edge Server 上;
(vi) the Remote Beacon-Based Estimator (RBE) and (vii) the
Remote Path Planner (RPP) which are able to receive
offloaded requests from the robot. A more detailed discussion
on these components follows in Sections III, IV and V.
基于远程信标的估计器 (RBE)和 (vii)远程路径规划器
(RPP) ，它们能够接收来自机器人的卸载请求。关于这些
组件的更详细的讨论将在第三、第四和第五节中进行。
In order to outline the sequence of interactions between the
main components of the architecture, we showcase a repre-
sentative scenario in which our solution applies successfully.
Fig. 1 depicts an overview of this scenario. Without loss of
generality, we assume that only one robot operates in the field.
Also, its starting pose, the operating space dimensions and the
obstacles’ and beacons’ positions and shapes are considered
known a priori.
为了概述架构的主要组成部分之间的交互序列，我们展
示了一个代表性的场景，我们的解决方案在其中成功应用。
图 1描述了这个场景的概述。在不失一般性的情况下，我
们假设只有一个机器人在现场操作。此外，它的起始姿态、
操作空间的尺寸以及障碍物和信标的位置和形状也被认为
是已知的。
A typical activity flow of our scenario, initiates with Local
Path Planner component calculating locally a trajectory from
the starting position to the target position. This triggers the
ODM for the first time; should a quick analysis on the
projected trajectory indicate room for significant refinement of
the selected path, the Remote Path Planner is invoked. This
analysis is based on the trajectory curvature and the degree in
which the more elegant remote component is potentially able
to smooth it around obstacles; Section V-C provides more
insight on this process. Eventually, the resulted trajectory
dictates the intermediate positions the robot needs to reach. In
order to sequentially perform the transition to the each of them,
the Tracking Controller component is invoked.
我们场景中的一个典型的活动流，使用 Local Path
Planner 组件启动，在局部计算从起始位置到目标位置的
轨迹。这将首次触发 ODM; 如果对预测轨迹的快速分析表
明所选路径有显著改进的空间，则调用 Remote Path
Planner。这种分析是基于轨迹曲率和更优雅的远程部件可
能使其绕过障碍物的程度; V-C 节提供了关于这一过程的
更多见解。最终，由此产生的轨迹决定了机器人需要达到
的中间位置。为了顺序地执行到每一个的转换，追踪控制
器组件被调用。
After reaching the next position of its trajectory, an un-
certainty indicator of the pose estimation is calculated; this
indicator is a scalar that grows with time and actually ac-
cumulates the error between the estimated and the reference
到达轨迹的下一个位置后，计算姿态估计的不确定性指
标，该指标是一个随时间增长的标量，实际上累积了估计
和参考之间的误差
78
78
Fig. 2: The timing sequence in the
proposed scenario.
图 2: 拟议场景中的时间序列。
pose after each move, as explained thoroughly
Section V-A. Here, the second decision occurs;
if this indicator measures bellow a predefined
threshold, the robot continues to move based
on the feedback coming from the Tracking
Controller’s monitoring process, i.e. the Local
Odometry-Based Estimator, which leverages
the robot’s photoelectric sensors (encoders)
attached to each wheel to measure the wheels’
angular ve-locities during a period of time.
Else, it invokes the more precise, but
computationally heavy, Beacon-Based Pose
Es-timator, leveraging information coming
from the beacons in the environment. That
triggers the ODM once again; the Edge Server
is queried to provide an estimation on the
duration of the potentially offloaded pose
estimation task. As described by the
mathematical modelling in Section V-B1, this
duration is proportional to the availability of
the computational resources. Based on this
estimated duration, a decision is made on
whether to offload the pose estimation task to
the Remote Beacon-Based Estimator, or
execute it locally. The flow ends with the robot
checking if the target position is reached. If not,
it reverts to first step.
在每个动作之后摆好姿势，正如第 V-A 节
详细解释的那样。在这里，第二个决定发生
了; 如果这个指标测量低于预定义的阈值，
机器人继续根据来自追踪控制器的监测过程
的反馈移动，即基于局部里程的估计器，该
估计器利用机器人的光电传感器(编码器)连
接到每个车轮，在一段时间内测量车轮的角
速度。否则，它会调用更精确，但计算量更
大的，基于信标的姿态 es 估计器，利用来
自环境中信标的信息。这又一次触发了
ODM; 边缘服务器被查询来提供一个估计潜
在卸载姿态估计任务的持续时间。正如 v-
b1 部分中的数学建模所描述的，这个持续
时间与计算资源的可用性成正比。基于这个
估计的持续时间，决定是否将姿态估计任务
卸载给基于远程信标的估计器，或者在本地
执行它。流程结束时，机器人会检查是否到
达目标位置。如果没有，它会回到第一步。
It is worth highlighting that the tracking
controller, as well as the path planning and
pose estimation are aperiodic. The position of
the robot on the operating ground, is defined
by the generated by the path planning
algorithms, to approach the target position. Fig.
2 gives a brief insight on the timing sequence in which the rest of the sections will refer to. Let subscript i correspond to the step during which
the robot reaches the next reference position in ki actuation steps, while simultaneously tracking its pose. In particular, at time t0i the robot is in
the position xi. When the next reference position xiref+1 is close, the uncertainty about the current estimation is calculated. Thus, the time
duration Ti1 corresponds to the time spent for localization. When the local odometry-based estimator is used, this time is equal to zero, while the
beacon-based estimation algorithm is time consuming. The time duration Ti2 corresponds to the path planning algorithm running time either
remote or local, which generates the next reference position. Similarly, the time to execute the local path planning algorithm is equal to zero.
值得强调的是，跟踪控制器，以及路径规划和姿态估计都是非周期的。机器人在操作场上的位置，是由路径规划算法生成的，以接
近目标位置。图 2给出了一个关于时间序列的简要见解，其余部分将参考。下标 i 对应于机器人在激励步骤中到达下一个参考位置的
步骤，同时跟踪其姿态。特别是，在这个时候，机器人是在位置 xi。当下一个参考位置 xiref + 1接近时，计算当前估计的不确定性。
因此，ti1 的时间持续时间对应于用于本地化的时间。当使用基于局部里程计的估计器时，这个时间等于零，而基于信标的估计算法
是耗时的。时间持续时间 ti2 对应于路径规划算法的运行时间，无论是远程的还是本地的，这会产生下一个参考位置。同样，执行局
部路径规划算法的时间等于零。
state vector xi =
状态向量 xi =
x1
x2
X1 x2
. The robot has to move
towards
机器人必须向前移动
the next
reference
下一个参考
position xrefi = [x1,ref(ti)
x2,ref(ti)] ,
位置 xrefi = [ x1，ref (ti) x2，ref
(ti)] ,
III. SYSTEM DYNAMICS
系统动力学
A. Robot dynamics
机器人动力学
The differential drive robot used in this study has two wheels that can turn at different rates, allowing motion by changing the orientation and
the position (x1, x2) either sep-arately or simultaneously. For the robot dynamics, the 2D coordinates, i.e. position, and the orientation of the
robot are
本研究中使用的差速驱动机器人有两个可以以不同速率转动的轮子，通过分别或同时改变方向和位置(x1，x2)来实现运动。对于机
器人动力学，二维坐标，即位置，和机器人的方向是
d
e
n
o
t
e
d
b
y
t
h
e
s
t
a
t
e
v
a
r
i
a
b
l
e
s
z
1
,
z
2
a
n
d
z
3
.
H
e
n
c
e
w
e
c
o
n
s
i
d
e
r
z
=
z
1 z2 z3 = x θ . The robot is controlled by
由状态变量 z1，z2和 z3表示。因此，我们认为 z = z1 z2 z3 = x θ。机器
人由
the angular velocities w R and wL, accounting for the right and left wheel
respectively. The robot dynamics is defined by the following continuous time
system, based on the work in [11], using the aforesaid state-space
representation. Specifically, we have for any t ≥ 0,
角速度 w r 和 w，分别代表左轮和右轮。机器人动力学由以下连续时间
系统定义，基于[11]中的工作，使用上述状态空间表示。具体而言，我
们对于任何 t ≥0,
z˙1(t)
=
Z1(t)
=
z˙2(t)
=
Z 2(t)
=
z˙3(t)
=
Z3(t)
=
where l, r are the distance between the two wheels and the
其中 l，r 是两个车轮和
radius of each wheel respectively. The odometry measurements
每个车轮的半径。里程测量
w˜L(t
j
i ),w˜ R(t
j
i ) are taken at each time instant t
j
i , i = 0, 1, …, j = 0, . . . , ki of
the timing sequence introduced in Section
W l (tji) ，w r (tji)在每个时刻取，i = 0,1，… ，j = 0，… ，ki
II. The corresponding discretized system using Euler forward method is:
采用 Euler 正演方法的相应离散系统是:
j+
1
j
+
1 r j
z˜1(ti
Z 1(ti
) =
) =
( w˜L(ti ) + w˜R(ti )) cos
z˜3(ti )(ti
(w l (ti) + w r (ti)) cos
z3(ti)(ti) 2
j+
1
j
+
1 r j
z˜2(ti
Z 2(ti
) =
) =
( w˜L(ti ) + w˜R(ti )) sin
z˜3(ti )(ti
(w l (ti) + w r (ti)
sinz3(ti)(ti) 2
j+
1
j
+
1 r j
z˜3(ti
Z3(ti
) =
) =
(w˜L(ti ) −
w˜R(ti ))(ti
(w l (ti)-w r (ti))(ti l
B
.
T
r
a
c
k
i
n
g
c
o
n
t
r
o
l
l
e
r
跟
踪
控
制
器
A
s
p
r
e
v
i
o
u
s
l
y
m
e
n
t
i
o
n
e
d
,
t
h
e
r
o
b
o
t
m
o
v
e
s
t
o
w
a
r
d
s
the next reference position x
i
ref to reach the target position. For this
actuation phase, given the specific robot dynamics, we propose a tracking
controller executed locally on the robot, by fixing the control inputs wL, wR
to be either equal or opposite. Therefore, the control input is w, while |w| =
|wL| = |wR|. As a result, we restrict the motion of the robot to a straight line,
i.e. “translational motion”, or a rotation around the center of the wheel axle,
i.e. “rotational motion”, respectively. This control structure is chosen as it is
efficient for tracking pur-poses, leading to a simple structure of the closed-
loop system. Specifically, the closed-loop dynamics for the translational and
rotational motion are
如前所述，机器人移动到下一个参考位置 xiref 到达目标位置。针对
这一驱动阶段，给出了具体的机器人动力学，我们提出了一个跟踪控制
器执行机器人局部，通过固定控制输入 wL，wR 或相等或相反。因此，
控制输入是 w，而 | w | = | wL | = | wR | 。因此，我们将机器人的运动限
制在一条直线上，即“平移运动”，或者分别围绕轮轴中心的旋转，即
“旋转运动”。之所以选择这种控制结构，是因为它能有效地跟踪目标，
从而形成一个简单的闭环系统结构。具体来说，平移和旋转轴运动的闭
环动力学是
S1T ran :
z˙2
S1T 运
行: z2
S2Rot : S2腐败:
tra
n
Tra
n
where
S1
S1在
哪
is used for the translational motion
and S2
用于平移运动和 S2
the robot needs to rotate. Let R(ti )
= 机器人需要旋转。让 r (ti) =
the
是
的
be
distance
距离
and the
以及
reference
参考资
料
tan
−
古
铜
色
1
z˜2(tij )−z2
,ref (ti)
Z2(tij)-
z2，ref (ti)
be the angle between the robot’s
cur-
就是机器人的角度
z˜1(tij )−z1
,ref (ti)
Z1(tij)-
z1，ref (ti)
r
e
n
t
e
s
t
i
m
a
tion of orientation and the line connecting the robot and the reference position.
Here, z˜ accounts for the estimation of its current pose calculated by
Equations (4) – (6) at the time period of the actuation t = t
j
i , j = 0, 1, . . . , ki.
租金估计的方向和线连接机器人和参考位置。在这里，z 解释了由方程
(4)-(6)计算的当前位姿的估计在时间周期的驱动 t = tji，j = 0,1，。
79
79
Fig. 3: The hybrid automaton of our system.
图 3: 我们系统的混合自动机。
The closed-loop system with the tracking controller can be
modeled by a discrete-event systems, see, e.g., [23], as shown
in Fig. 3, where the control input can be calculated as follows:
带有跟踪控制器的闭环系统可以用离散事件系统建模，
如图 3所示，参见[23] ，其中控制输入可以计算如下:
w(ti )
=
W (ti)
=
L2
L2
φ(ti ),
Φ (ti)
φ(ti ) >
2
Φ (ti) >
2
R(ti ) >
1
R (ti) >
1
,
Rotational,
旋转,
L1R(tj )
,
l1R (tj)
φ(tij
)
Φ
(tij)
≤
2
R(tij ) >
1
R (tij) >
1
,
Translation
al,
翻译,
j
ji
译
者
注:
j
j
j Stop.
别说了。
0, 零,
R(ti ) R (ti) ≤ 1 ,
The quantities 1, 2 are positive constants, while the gains L1,
L2 are constant control parameters.
量 1,2是正常常数，而增益 L1，l2是常数控制参数。
The reference position is reached when the estimation of its
position is close, and in particular is inside a ball of radius 1
close to the reference, i.e., centered at B(x
i
ref , z(t
j
i )) = {z ∈
R
3
: z − z˜(t
j
i ) ≤ 1}. The effect of the uncertainty is taken into
account explicitly in the offloading decision that follows.
当其位置的估计值接近时，特别是在接近参考值的半径
为 1的球内，即以 b (xiref，z (tji)) = { z ∈ R3: z-z (tji)≤1}
为中心时，即可达到参考位置。不确定性的影响在随后的
卸货决策中被明确地考虑进去。
IV. LOCALIZATION AND PATH PLANNING
四、本地化和路径规划
In what follows, we present the algorithms chosen for
localization and path planning, with a varying degree of
complexity and accuracy, that are implemented locally and
remotely accordingly.
在接下来，我们提出的算法选择的定位和路径规划，与
不同程度的复杂性和准确性，是实现局部和远程相应。
A. Localization
A. 本地化
The localization problem is equivalent to the pose estimation
problem in our setting. Two algorithms of different complexity
are implemented, namely, (i) an odometry-based one, and (ii) a
camera-based estimation. The first estimation algorithm is light
enough to run efficiently on the robotic platform. Roughly, the
robot’s on-board wheel encoders readings are fed to the motion
model (4) – (6). While this is a lightweight and fairly accurate
localization technique when it comes to short trajectories,
odometry is known to be prone to accumulative errors [12].
在我们的设置中，定位问题等价于姿态估计问题。实现了
两种不同复杂度的算法，即: (i)基于里程的算法，和(ii)基于
摄像机的估计。第一种估计算法足够轻，可以在机器人平台
上有效运行。大体上，机器人的车轮编码器读数被提供给运
动模型(4)-(6)。虽然这是一种轻量级和相当准确的定位技术，
但是在短轨迹方面，已知里程计容易产生累积误差[12]。
The second localization technique is the computationally
heavier beacon-based estimator. Details on the technical parts
of the algorithm and its software and hardware implementa-
tion can be found in [13]. Roughly, the technique is based on a
bilateration method using principles of the projective
geometry. Distance calculation is based on feature extraction
from pictures depicting the landmarks, with the localization
algorithm relying on minimum two strategically positioned
landmarks. To address this requirement, the attached camera
scans the area in front of the robot, capturing pictures and
第二种定位技术是计算量更大的基于信标的估计器。关
于算法的技术部分及其软件和硬件实现的细节可以在[13]
中找到。大致上，该技术基于使用射影几何原理的双边方
法。距离计算基于描绘地标的图片的特征提取，定位算法
依赖于至少两个战略位置的地标。为了满足这个要求，附
加的摄像头扫描机器人前面的区域，捕捉图片和
analysing them until two landmarks are detected. Hence, com-
putationally intensive, real time image processing is required
to achieve highly accurate results. Relevant works include [14]
and [15].
分析它们，直到发现两个地标。因此，需要计算密集的实
时图像处理来获得高度准确的结果。相关工作包括[14]和
[15]。
B. Path Planning
乙、路径规划
Many works exist in the literature addressing the path
planning problem; a realistic robot navigation and smooth
trajectory planning is a major challenge [16], [17]. Planning
algorithms generate a trajectory consisting of intermediate
reference positions to reach the final target position. In this
work, we select and adapt graph-based methods of varying
complexity, see, e.g., [11, Chapter 8]. As a result, the algo-
rithms described below, take as input a graph that represents
the real-space grid space along with the target positions, the
obstacles and the starting position. This grid has a predefined
cell size, that depends on the length of the robot. Each cell
corresponds to a possible reference position. In our case, the
obstacles are rectangular-shaped, in the sense of simplicity,
however, arbitrarily-shaped obstacles could also be included.
在解决路径规划问题的文献中有许多作品; 一个现实的
机器人导航和平滑的轨迹规划是一个主要的挑战[16] ，
[17]。规划算法生成由中间参考位置组成的轨迹以达到最
终目标位置。在这项工作中，我们选择和适应不同复杂度
的基于图的方法，参见，例如，[11，Chapter 8]。因此，
下面所描述的算法以一个表示真实空间网格空间的图形作
为输入，该图形包括目标位置、障碍物和起始位置。这个
网格有一个预定义的单元格大小，这取决于机器人的长度。
每个单元对应一个可能的参考位置。在我们的例子中，从
简单的意义上讲，障碍物是矩形的，然而，任意形状的障
碍物也可以包括在内。
On the one hand, a lightweight implementation of the A
algorithm [18] acts as the Local Path Planner. Similar to [19],
four directions of movement are allowed in the grid. The cells
containing obstacles are not connected with the neighboring
cells. The A algorithm returns a sequence of positions to reach
the target position, according to a heuristic cost function; in
our case this is the Manhattan Distance. The implementation
is suitable for a robot with minimal computational resources
providing a solid and quick solution, however the generated
trajectory is not smooth.
一方面，a 算法[18]的轻量级实现充当本地路径规划器。
与[19]类似，网格中允许四个方向的移动。包含障碍物的
细胞与邻近的细胞没有连接。A 算法根据启发式成本函数
返回到达目标位置的位置序列; 在我们的例子中，这是曼
哈顿距离。该实现适用于计算资源最少的机器人，提供了
一个坚实而快速的解决方案，然而生成的轨迹并不平滑。
The computationally intensive algorithm acting as the Re-
mote Path Planner is deployed on the Edge Server. Similar to
[20], the main process of the proposed algorithm is to locate a
possible move towards a node that is closer to the target given
the aforesaid graph. To this purpose, a multiple sources single
destination problem is solved, utilising Dijkstra’s shortest path
algorithm, which calculates a path from each node towards the
target position, offline. These precalculated paths, along with
the total cost to reach the desired destination, are stored in a
database on server’s startup. When the Remote Path Planner is
invoked, given the current location of the robot, a neighbour
pruning is performed similar to [21]. A node of the graph is
considered to be a neighbor of the current position if (i) the
distance between them is less than twice the specified cell size
and (ii) no obstacle is in the line of sight of the current
position to that node. Consequently, to retrieve the set of
possible neighbours, it is sufficient to search for avoidance of
line clipping (intersection) between the line connecting the
current position to each of the adjacent cells and the set of
obstacles present in the real-space grid. The optimal path is
chosen by comparing all possible neighbours. In particular,
the cost to reach each one of them from the current position is
added to the cost from each neighbour to reach the desired
target. In this way, the algorithm allows “shortcuts’ to the
neighbouring nodes, while any-angle trajectories are feasible.
作为 Re-mote Path Planner 的计算密集型算法部署在
Edge 服务器上。类似于[20] ，提出的算法的主要过程是
定位一个可能的移动到一个节点，更接近目标给出上述图
形。为此，利用 Dijkstra 的最短路径算法，离线计算从每
个节点到目标位置的路径，解决了多源单目标问题。这些
预先计算的路径，以及到达目的地的总成本，存储在服务
器启动时的数据库中。当调用 Remote Path Planner 时，给
定机器人的当前位置，执行类似于[21]的邻居修剪。图的
一个节点被认为是当前位置的邻居，如果(i)它们之间的距
离小于指定单元大小的两倍，并且(ii)在该节点当前位置
的视线范围内没有障碍物。因此，为了检索可能的邻居集
合，在连接当前位置到每个相邻单元的直线与实际空间网
格中存在的障碍集合之间搜索避免直线剪切(交点)就足够
了。通过比较所有可能的邻居来选择最佳路径。特别是，
从当前位置到达每个邻居的成本加上每个邻居达到预期目
标的成本。通过这种方式，算法允许到邻近节点的“捷径”，
而任何角度的轨迹都是可行的。
80
80
Fig. 4: The block diagram of the switching system.
Component abbreviations and colors follow the pattern
introduced in Section II.
图 4: 开关系统的框图。组件的缩写和颜色遵循第二节介
绍的模式。
V. SWITCHING SYSTEM
交换系统
In this section, we present the switching mechanisms that
are realizing the Offloading Decision Mechanism of our
framework. We assume that starting from a position x0 =
[x1(0) x2(0)] , the closed-loop system converges asymptot-
ically to a reference position xref = [x1,ref(ti) x2,ref(ti)] when
exact measurements are available, i.e., when z˜(t) = z(t). We
identify two offloading opportunities related to the pose
estimation and the path planning problem. In Fig. 4 the
proposed switching system is presented. In particular,
switches S1 and S2 relate to the estimation procedure, and
switch S3 concerns path planning part.
在本节中，我们将介绍实现我们框架的卸载决策机制的
切换机制。我们假设从一个位置 x0 = [ x1(0) x2(0)]开始，
闭环系统渐近收敛到一个参考位置 xref = [ x1，ref (ti) x2，
ref (ti)] ，当有精确的测量值时，即当 z (t) = z (t)。我们确
定了两个与姿态估计和路径规划问题相关的卸载机会。在
图 4中给出了提出的交换系统。特别地，开关 s1和 s2涉
及估计过程，开关 s3涉及路径规划部分。
A. Sensor selection (Switch 1)
A. 传感器选择(开关 1)
The measurements of the onboard sensors are imperfect, thus
the pose estimation error is accumulated. When the error becomes
too large, the more precise, yet more computationally intensive
remote localization algorithm is invoked. In order to decide when
to offload, we introduce the variable δ(·) that describes the
uncertainty in estimation. We set measurements of the states z˜,
computed by the Equations (4) – (6) and the model-based
estimations z˘, i.e.
由于星载传感器的测量不完善，导致了位姿估计误差的积
累。当误差变得太大时，就会调用更精确、计算更密集的远
程定位算法。为了决定何时卸载，我们引入了描述估计不确
定性的变量 δ ()。我们设置状态 z 的测量值，由方程(4)-(6)和
基于模型的估计 z，即。
j+
1
j
+
1 j
˜ j
J
δ(ti
Δ (ti
) = δ(ti ) + b0 + b1δ(ti ),
) = δ (ti) + b0 + b1δ (ti) ,
j = 1, . . . , ki, i ∈ , ˜ is the deviation between δ
N
j = 1，… ，ki，i
∈ n
where
在哪
里
the
之间的偏差
δ˜(tij
) =
Δ (tij)
=
z˘(tij ) −
z˜(tij )
Z (tij)-z
(tij)
where z˘(t
j
i ) consists of:
其中 z (tji)包括:
j+
1
j +
1 r j j j
j+1
j +
1 j j
z˘1(ti
Z1(ti
) =
) =
(wL(ti ) + wR(ti )) cos
z˘3(ti )(ti
(wL (ti) + wR (ti)) cos
z3(ti)(ti)
− ti ) +
z˘1(ti ),
– ti) + z
1(ti) ,
2
j+
1
j +
1 r j j j
j+1
j +
1 j j
z˘2(ti
Z2(ti
) =
) =
(wL(ti ) + wR(ti )) sin
z˘3(ti )(ti
(wL (ti) + wR (ti) sin
z3(ti)(ti)(ti)
− ti ) +
z˘2
– ti) + z
2
(ti )
,
(ti)
,
2
j+
1
j +
1 r j
jj+1
Jj + 1 j j
z˘3(ti
Z3(ti
) =
) =
(wL(ti ) −
wR(ti ))(ti
(wL (ti)-wR (ti))(ti
− ti ) +
z˘3(ti ),
– ti) + z3(ti) ,
l
which are the model-based estimation of the dynamics at time
instants t
j
i , j = 1, . . . , ki and wL,wR are the outputs of the
tracking controller. At time t
0
0, the model-based estimation is
equal to a known initial position, i.e. z˘1(t
0
0) = z˘
0
1. As a result,
其中基于模型的时间瞬间动力学估计 tji，j = 1，… ，ki 和
wL，wR 是跟踪控制器的输出。在 t00 时，基于模型的估计
等于一个已知的初始位置，即 z1(t00) = z01。因此,
δ linearly depends on the deviation, and is getting bigger as
the robot actuates, especially when the actual motion of the
robot differs from what the model dictates.
线性依赖于偏差，并且随着机器人的驱动而变得越来越大，
特别是当机器人的实际运动与模型所要求的不同时。
The offloading mechanism, aiming to reset the uncertainty,
is triggered when δ becomes too large, namely larger than a
prespecified threshold δ , i.e.,
卸载机制，旨在重置不确定性，触发时，δ 变得太大，
即大于预先设定的阈值 δ，即,
S
1
S
1
(ti i )
=
(ti i)
=
ON,
关于,
else, i
否
则，
我 ≤
k
OFF,
关
闭,
if
δ(tki )
如果 δ
(tki)
δ ,
Δ,
where ki refers to the time instant, when the robot’s po-sition,
calculated by Equations (4) and (5), is close to the next
reference position xref,k. Moreover, ON corresponds to using
the beacon-based localization and OFF to proceeding based
on the local odometry estimation. In the scope of this work,
we assume that the uncertainty becomes equal to zero when
the beacon-based localization is used. Hence, when S1(t
k
i
i ) =
ON, then δ(t
0
i+1) = 0, which means we get a valid
measurement of the states z. Otherwise, δ(t
0
i+1) = δ(t
k
i
j ).
其中 ki 是指当机器人的位置(由方程(4)和(5)计算)接近下
一个参考位置时的时间瞬间，而 ON 是指基于信标的定位
和基于局部里程估计的 OFF。在这项工作的范围内，我
们假设不确定性变成等于零时，基于信标的定位被使用。
因此，当 S1(tkii) = ON 时，则 δ (t0i + 1) = 0，这意味着我
们得到了状态 z 的有效测量，否则，δ (t0i + 1) = δ (tkij)。
B. Estimation Offloading (Switch 2)
B. 估算卸载量(开关 2)
Switch S2 decides whether the localization algorithm will
be executed locally on the microcontroller mounted on the
robot, or remotely on the Edge Server. Although the execution
of such a computationally heavy algorithm on a battery-
powered IoT device is energy-consuming, it may be
preferable in some cases as offloading might result to larger
response times due to lack of available resources on the
remote server and network congestion.
Switch s2 决定定位算法是在机器人上安装的微控制器
上本地执行，还是在 Edge Server 上远程执行。尽管在电
池供电的物联网设备上执行这样一个计算量大的算法是耗
费能源的，但在某些情况下，由于远程服务器上缺乏可用
资源和网络拥塞控制，卸载可能会导致响应时间更长，因
此可能更为可取。
1) Resource modelling and estimation: We assume that the
resources of the localization service on the Edge Server are
managed by the resource orchestrator of the infrastructure
provider and we can only estimate the allocated resources through
measurements. Thus, we model the resource allocation strategy
on the Edge Server as a linear dynamical system subject to
process and measurements uncertainty disturbances
资源建模和估计: 我们假设 Edge Server 上本地化服务的资
源由基础设施提供者的资源协调器管理，我们只能通过度量
来估计分配的资源。因此，我们将边缘服务器上的资源分配
策略建模为一个受过程和测量不确定性干扰的线性动态系统
c((k + 1)Ts) = c(kTs) + w(kTs),
C ((k + 1) Ts) = c (kTs) + w (kTs) ,
z(kTs) = c(kTs) + v(kTs),
Z (kTs) = c (kTs) + v (kTs)
where c accounts for the virtual CPU cores of the container, z
is the measurement of c and Ts is a constant sampling time.
The terms w, v are the process and measurement noise
respectively, both following a normal distribution. Based on
previous measurements, we compute a current estimation of
the virtual CPU cores allocated to the container, cˆ, by
applying a Kalman Filter [22], which is a computationally
light prediction method.
其中 c 代表容器的虚拟 CPU 核心，z 代表 c 的测量值，t
代表恒定的采样时间。术语 w，v 分别是过程噪声和测量
噪声，它们都遵循正态分布。基于以前的测量，我们计算
当前估计的虚拟 CPU 核分配到容器，c，通过应用卡尔曼
滤波器[22] ，这是一个计算光预测方法。
2) Processing time estimation: Having acquired the estima-
tion of the available remote virtual CPU cores cˆ, the estimated
processing time of the beacon-based localization algorithm can be
calculated. To this purpose, the processing time, tp is modeled as
a linear relationship of the available resources, tp = acˆ+ b. The
coefficients a,b are calculated using the least squares fitting
method, on a set of pairs (tp, cˆ) produced offline while
experimenting with a dataset of pictures. Moreover, we consider
the wireless network induced delay tnet to be constant as a
standard network delay in a WLAN network.
处理时间估计: 在获得可用远程虚拟 CPU 核的估计值后，
可以计算基于信标的定位算法的估计处理时间。为此，处理
时间，tp 被建模为可用资源的线性关系，tp = ac + b。系数 a，
b 是使用最小二乘拟合方法计算的一组对(tp，c)离线产生，
同时实验与图片数据集。此外，我们认为无线网络诱导延迟
tnet 作为无线局域网中的标准网络延迟是恒定的。
81
81
3) Localization Offloading: The processing time is related
directly to the CPU availability. The local beacon-based local-
ization has an average time tloc to be executed based on the
robot’s resources. Hence, Switch S2 is formulated as:
本地化卸载: 处理时间与 CPU 可用性直接相关。基于本
地信标的本地化有一个基于机器人资源执行的平均时间
tloc。因此，Switch s2的公式如下:
S
2
S
2
(ti i )
=
(ti i)
=
OFF,
关闭,
els
e,
否
则, ≤
k
ON,
关
于,
if
tp
如
果
tp
+
tnet
+
tnet
tlo
c,
Tl
oc,
where ki refers to the time instant that the robot must decide
whether to offload or not the beacon-based localization algo-
rithm. Moreover, ON corresponds to the remote execution of
the self-localization algorithm and OFF to the local execution.
ki 指的是机器人必须决定是否卸载基于信标的定位算法算
法的时间瞬间。此外，ON 对应于自定位算法的远程执行，
OFF 对应于本地执行。
C. Path Planning Offloading (Switch 3)
C. 路径规划卸货(开关 3)
Two path planning algorithms are implemented. By default,
the computationally light A algorithm presented in Section IV-
B,provides a reference trajectory on the robot. However,
whenever a prediction cost indicates a possible amelioration
by choosing a more refined path, the remote path planning
algorithm is invoked. Both algorithms take as input the current
estimation of the position and the reference position and
generate a reference trajectory.
实现了两种路径规划算法。默认情况下，IV-B 节中提
出的计算轻 a 算法为机器人提供了一个参考轨迹。然而，
每当预测成本表明可能通过选择一个更精确的路径改进，
远程路径规划算法被调用。两种算法都将位置和参考位置
的当前估计值作为输入，并生成参考轨迹。
The offloading decision for the path planning depends on a cost
consisting of two parts; the first part estimates the closeness of the
generated reference trajectory to obstacles and the second part
evaluates the curvature of the trajectory. Both terms follow
theoretical aspects from standard works, e.g.,
路径规划的卸载决策取决于两部分的成本: 第一部分估计
生成的参考轨迹与障碍物的接近程度，第二部分估计轨迹的
曲率。这两个术语都遵循标准工作的理论方面，例如,
[24]. We define the function D(x) that quantifies the “density”
of obstacles according to the estimation of the current position
xˆ, either computed by the beacon-based localization or the
local odometry measurements.
我们定义了一个函数 d (x) ，该函数根据目前位置 x 的估
计来量化障碍物的“密度”，这个估计可以通过基于信标的
定位或局部里程测量来计算。
D(x) =
D (x) =
exp
实
际
上
− x −
xobs ,
– x-xobs,
xˆobs
Xobs
xobs
Xobs
and Xobs is the set of positions that correspond
to the centers of the cells that are unreachable,
e.g., occupied by an obstacle.
Xobs 是对应于无法到达的单元中心的一组
位置，例如被障碍物占据。
Let {xˇ(i)}i=1,….,M be the part of the path
sequence con- sisting of the first M positions,
generated by the local path planning
algorithm.
设{ x (i)} i = 1，… ，m 是由局部路径规划
算法生成的由第一个 m 位置组成的路径
序列的一部分。
The local path planning algorithm takes as
input the current position estimation xˆ(t
k
i
i ) at t
= Ti
ki + Ti
1
and creates a
局部路径规划算法将当前位置估计 x (tkii)
在 t = Tiki + ti1处作为输入，并创建一个
reference trajectory sequence {xˇ(i)}i=0,1,…,M ,
with xˇ(0) = xˆ(t
k
i
i + Ti
1
). We define:
参考弹道序列{ x (i)} i = 0,1，… ，m，x (0)
= x (tkii + Ti1) . 我们定义:
Jlocal (ˆx(t
k
i
i + Ti
1
)) =
Jlocal (x (tkii + Ti1)) =
M −1
– 1
xˇ(i + 1) − xˇ(i) − xˇ(M ) −
xˇ(0) ,
X (i + 1)-x (i)-x (m)-x (0) ,
i=0
i = 0
as a cost describing the curvature of the
reference local trajectory. The offloading
strategy can be formulated as:
作为描述参考局部轨迹曲率的成本。卸载策
略可以表述为:
S3(t
k
i
i + Ti
1
) =
S3(tkii + Ti1) =
OFF, if D(ˆx(t
k
i
i + Ti
1
)) − Jlocal
(ˆx(t
k
i
i + Ti
1
)) ≤ J , ON, else,
如果 d (x (tkii + Ti1))-Jlocal (x (tkii +
Ti1))≤ j，则,
where t
k
i
i + Ti
1
indicates the time instant after the actuation
and pose estimation. The constant J accounts for the degree of
difficulty of the next moves in terms of proximity to
其中 tkii + ti1 表示驱动和姿态估计后瞬间的时间。常数 j
说明了下一步移动的难度在接近
obstacles and curvature of the trajectory. When S3 in ON, the
remote path planning provides the next step to reach the target
position. Otherwise, the robot relies on the local path planning
trajectory. It should be mentioned that, contrary to Switch 2,
here, we do not include the CPU availability in the offloading
decision, as we noticed that the remote path planner chosen is
mainly memory intensive.
障碍物和轨道的曲率。当 s3 处于 ON 状态时，远程路径
规划提供了到达目标位置的下一步。否则，机器人将依赖
于当地的路径规划轨迹。应该指出的是，与 Switch 2相反，
在这里，我们没有将 CPU 可用性包括在卸载决策中，因
为我们注意到所选择的远程路径规划器主要是内存密集型
的。
VI. EXPERIMENTS AND EVALUATION
实验和评估
The experiments were conducted in an operating space of
2.5×2.5 meters, divided by 25×25 cells, with a cell size of
10×10cm. The robot chosen was the commercially available
AlphaBot
1
, equipped with a Raspberry Pi 3 device as the con-trol
unit. The length of the AlphaBot is 22cm and the radius of each
wheel is 6.6cm. The coloured beacons were placed at the
periphery of the grid for the localization procedure described in
Section IV. The rectangular-shaped obstacles were placed as
depicted with grey colour in Fig. 5. The map is considered known.
The Access Point used was a MikroTik wireless SOHO AP,
providing up to 100Mbs LAN connection, Single Band (2.4GHz).
The Edge Server deployed on the NETMODE, testbed part of
Fed4FIRE
2
initiative, was equipped an Intel Atom CPU, up to
1Gbit Ethernet port and 8GB of RAM. The services provided by
the edge server were deployed as Docker containers. For each
Docker container, one can set constraints, to limit a given
container’s access to the host machine’s CPU cores, by
provisioning a percentage of them as the virtual cores of the
containers. Thus, containers can be assigned with partial virtual
CPUs using decimal values. Using a collection of pictures from
the actual experimentation room, from different positions and
viewing angles, a dataset was created to estimate the time
duration of the remote beacon-based localization. In Table I, the
values of the set of pairs (tp, cˆ), introduced in Section V-B, are
presented. Using the least squares fitting method we calculated
the coefficients
实验在 2.5 × 2.5 m 的操作空间内进行，除以 25 × 25个细
胞，细胞大小为 10 × 10cm。选择的机器人是商用的
AlphaBot1，配备有 Raspberry Pi 3 设备作为控制单元。
AlphaBot 的长度为 22厘米，每个轮子的半径为 6.6厘米。有
色信标放置在网格的外围，用于第四节中描述的定位程序。
如图 5 中灰色所示放置矩形障碍物。该地图被认为是已知的。
使用的接入点是 MikroTik 无线 SOHO AP，提供高达 100mb
的局域网连接，单频(2.4 GHz)。部署在 NETMODE 上的
Edge 服务器(fed4fire2 计划的试验台部分)配备了一个 Intel
Atom CPU，最多 1gbit 以太网端口和 8gb 内存。边缘服务器
提供的服务被部署为 Docker 容器。对于每个 Docker 容器，
可以设置约束，以限制给定容器对主机 CPU 核心的访问，方
法是将其中的一个百分比作为容器的虚拟核心。因此，容器
可以使用十进制值分配部分虚拟 cpu。利用实际实验室的图
像，从不同的位置和视角，建立数据集来估计基于信标的远
程定位的时间持续时间。在表 i 中，给出了第 V-B 部分中引
入的一组对(tp，c)的值。使用最小二乘拟合方法计算系数
a = −1.34 and b = 1.675. Hence, the estimated processing time of the remote
beacon-based localization is given by tp = −1.34ˆc + 1.675. Provisioning over
1.5 cores resulted in similar computation time, thus, the maximum CPU
allocation was set to that value. In our experiments, the allocated cores of the
containerized application were updated every 10sec, following a Normal
Distribution with a mean value of 0.75 and 0.5 variance. The following values
were used for the aforesaid
=-1.34和 b = 1.675。因此，基于远程信标定位的估计处理时间由 tp =-1.34
c + 1.675 给出。超过 1.5 个内核的配置导致了相似的计算时间，因此，最
大 CPU 分配被设置为该值。在我们的实验中，容器化应用程序的分配核心
每 10秒更新一次，遵循平均值为 0.75和 0.5方差的正态分布。以下值用于
上述
constant values: b0 = 1; b1 = 0.2; e1 = 5cm e2 = 5°, L1 = 0.2, L2 = 0.6, δ
= 6 and J = 3. Finally, the average
常数值: b0 = 1; b1 = 0.2; e1 = 5cme2 = 5 ° ，L1 = 0.2，L2 = 0.6，δ = 6，j
= 3。最后，平均值
network delay of the WLAN was empirically measured to tnet = 1sec per
offloaded picture and the average time for each picture to be processed
locally on the AlphaBot was tloc = 3sec.
无线局域网的网络延迟经验性地测量为每个卸载图片 tnet = 1 秒，每个
图片在 AlphaBot 上进行局部处理的平均时间为 tloc = 3秒。
Three experiments were conducted, namely, local only
execution, remote only execution and the proposed switching
offloading scheme. In Table II the average completion time
and the average success rate for 10 experiments of each
分别进行了本地执行、远程执行和切换卸载方案三个实
验。在表 II 中，每个实验的平均完成时间和 10个实验的
平均成功率
1 https://www.waveshare.com/wiki/AlphaBot
https://www.waveshare.com/wiki/AlphaBot
2
https://www.fed4fire.eu/testbeds/netmode/
2 https://www.fed4fire.eu/testbeds/netmode/
82
82
Fig. 5: The experiment setup and the trajectories produced by
the three experiments.
图 5: 实验装置和三个实验产生的轨迹。
Average Time per picture
(sec), tp
每张图片的平均时间
(秒) ，tp
Virtual Allocated
Cores, cˆ
虚拟分配的核
心，c
2.41 0.25
1.06 0.5
0.56 0.75
0.39 1
0.30 1.25
0.26 1.5
TABLE I: The average time for remote beacon-based estima-
tion per virtual allocated core to the container.
表 i: 每个虚拟分配到容器的核心的基于远程信标的估计的
平均时间。
setting is presented. For the rest of the evaluation, we will
present the results of the best trials for each setting. Moreover,
in Fig. 5 the reference trajectories of these trials for the three
experiments, are illustrated, with green colour for local only
execution, red colour for remote only execution and purple
colour for the switching system. As outlined in Section IV, the
local A algorithm allows only four directions of movement,
while the remote path planner allows any-angle movements.
For better visualization, we uploaded timelapse videos
3
from
the conducted trials for each setting. In these experiments, the
starting position for the AlphaBot was the already known
position A(3, 14), while the desired target reference positions
were B(10, 5) and C(14, 18) in sequence. The scale of
uncertainty is illustrated as a percentage of δ , i.e. δ/δ , which
is the predefined quantity for Switch 1 to be ON.
提出了设置。在剩下的评估中，我们将介绍每个设置的最
佳试验结果。此外，在图 5 中，这三个实验的参考轨迹被
说明，用绿色表示局部执行，红色表示远程执行，紫色表
示开关系统。如第四节所述，局部 a 算法只允许四个方向
的运动，而远程路径规划器允许任何角度的运动。为了更
好的可视化，我们上传了每个设置的实验视频。在这些实
验中，AlphaBot 的起始位置是已知的位置 a (3,14) ，而期
望的目标参考位置依次是 b (10,5)和 c (14,18)。不确定性的
范围表示为 δ 的百分比，即 δ/δ，这是开关 1为 ON 的预定
义量。
1) Experiment A – Local Only Execution: In the first
experiment Switches 1 and 3 were ON, throughout the ex-
periment and Switch 2 was never used. This setting results
实验 a-仅局部执行: 在第一个实验中，开关 1和 3是 ON，
在整个实验中，开关 2从未使用过。这个设置结果
3 https://github.com/Dspatharakis/alphabot-ppl/tree/master/timelapsed-videos
Https://github. com/dspatharakis/alphabot-ppl/tree/master/timelapsed-videos
Experiment
实验
Average completion
time (sec)
平均完工时间(秒)
Success
Rate
成功率
Local Only
Execution
只在本地执行 61
40%
40%
Remote Only
Execution
仅远程执行 105
100%
100%
Switching System
开关系统 90
100%
100%
TABLE II: The average completion time and success rate of
10 experiments for each setting.
表二: 每组 10个实验的平均完成时间和成功率。
Fig. 6: Experiment B – Remote Only Execution.
图 6: 实验 b-仅远程执行。
to a fast, although not precise navigation with δ/δ growing
monotonically. The average duration was 61 seconds as the
main time consuming process was the actuation. The amount
of successful trials was low. Consequently, without a more
sophisticated localization algorithm and a more precise path
planning technique there is no guarantee the target reference
position is reached.
在 δ/δ 单调增长的情况下，尽管不是精确的导航。平均持
续时间为 61 秒，因为主要的耗时过程是驱动。成功试验
的次数很少。因此，没有更复杂的定位算法和更精确的
路径规划技术，就不能保证达到目标参考位置。
2) Experiment B – Remote Only Execution: In the second
experiment, whenever the uncertainty about AlphaBot’s pose
grew over the predefined threshold δ , beacon-based localiza-
tion was invoked (Switches 1 and 2 ON) on the Edge Server.
Moreover, the reference trajectory was always generated by the
remote path planning algorithm (Switch 3 ON). In this setting,
the robot always reached the target positions, as shown in Table II,
although the completion time was heavily affected, as shown in
Fig. 6. Beacon-based localization was executed twice during this
experiment and, as a result, δ/δ became equal to 0. The setup of
the particular experiment underlines the importance of a slower
but more precise navigation.
实验 b ——仅远程执行: 在第二个实验中，每当 AlphaBot
姿态的不确定性超过预定义的阈值 δ 时，Edge 服务器上就会
调用基于信标的定位(switch 1 和 2 ON)。此外，参考轨迹总
是由远程路径规划算法(Switch 3 ON)生成。在这种情况下，
机器人总是到达目标位置，如表 2 所示，尽管完成时间受到
严重影响，如图 6所示。在这个实验期间，基于 beacon 的定
位执行了两次，结果，δ/δ 变为等于 0。特定实验的设置强调
了更慢但更精确导航的重要性。
3) Experiment C – Switching System: As described in
Section V-C, Switch 3 decides which path planning algorithm
solution the AlphaBot will use to generate the next reference
position. When, the curvature function of the trajectory calcu-
lated by the A algorithm and the obstacle density function
exceeded the threshold value J , the remote path planning so-
lution was selected; e.g., from the beginning of the experiment
until the 25th sec of the simulation and from the 43rd sec till
the 67th sec, as illustrated with green dashed line in Fig. 7. In
the same figure, with red solid line, δ/δ is depicted. Two times
during the experiment the more precise beacon-based
estimation was invoked to reset δ/δ . The first estimation
attempt, at the 25th sec of the experiment, was executed on the
Edge Server, because S2 was ON. The second one, at the 71st
sec of the experiment, was executed locally, as S2 dictated
(OFF), because the estimation of the CPU availability of the
Edge Server, provided by the Kalman Filter, along
实验 c-切换系统 : 如 V-C 部分所述，切换 3 决定
AlphaBot 将使用哪种路径规划算法解决方案来生成下一个
参考位置。当 a 算法计算的轨迹曲率函数和障碍物密度函
数超过阈值 j 时，选择这样的远程路径规划方法: 例如，
从实验开始到模拟的第 25 秒，从第 43 秒到第 67 秒，如
图 7 中绿色虚线所示。在同一图中，用红色实线描绘了
δ/δ。在实验期间，两次调用更精确的基于信标的估计来
重置 δ/δ。在实验的第 25 秒，第一次估计尝试在 Edge 服
务器上执行，因为 s2 是 ON。第二个是在实验的第 71 秒，
按照 s2 的指示(OFF)在本地执行，因为边缘服务器的
CPU 可用性的估计是由 Kalman Filter 提供的
83
83
Fig. 7: Experiment C – Switching System.
图 7: 实验 c 开关系统。
with the network delay for each picture, at that time, would
have provided worse results than the local execution. This
setup provided a very precise and robust navigation for the
robot, leading to a very high success rate of the experiments,
achieving a balance between execution time and trajectory
accuracy.
当时，每张图片的网络延迟会比本地执行提供更糟糕的结
果。该装置为机器人提供了一个非常精确和鲁棒的导航，
导致了非常高的实验成功率，实现了执行时间和轨迹精度
之间的平衡。
VII. CONCLUSION
七、结论
In this study, we introduced a switching offloading mecha-
nism for localization and path planning applications of mobile
robots. The offloading decision for localization is based on pose
uncertainty and the availability of edge resources, while the
offloading decision for path planning depends on the difficulty of
the trajectory. The proposed framework achieves more precise
navigation than the case of exclusive local execution of the
applications, without paying the price of a slower execution time,
like in the case of remote only execu-tion of the algorithms. Also,
it is modular and applicable to various scenarios, applications and
objectives under the robot’s dynamic environment. Our future
work will focus on extend-ing the proposed mechanism to more
sophisticated control algorithms, providing theoretical guarantees
for stability and convergence of the proposed robot’s dynamics.
Furthermore, we plan to develop more precise estimation and
planning algorithms in multi-robot scenarios and more
sophisticated control algorithms in the co-design setting that will
take into account the available resources on the infrastructure side.
在这项研究中，我们介绍了一种用于移动机器人定位和路
径规划应用的切换卸载机制。定位的卸载决策是基于位姿不
确定性和边缘资源的可用性，而路径规划的卸载决策则取决
于轨迹的难易程度。提出的框架实现了比应用程序的独占本
地执行更精确的导航，而不需要付出较慢的执行时间的代价，
就像只远程执行算法的情况一样。此外，它是模块化的，适
用于各种场景，应用和目标下的机器人的动态环境。我们未
来的工作将集中在扩展所提出的机制到更复杂的控制算法，
提供稳定性和收敛性的理论保证所提出的机器人的动力学。
此外，我们计划在多机器人场景中开发更精确的估计和规划
算法，在共同设计环境中开发更复杂的控制算法，这将考虑
到基础设施方面的可用资源。
ACKNOWLEDGMENT
确认
The research work of Mr. Dechouniotis is co-financed by
Greece and the European Union (European Social Fund-ESF)
through the Operational Programme “Human Resources
Development, Education and Lifelong Learning” in the
context of the project “Reinforcement of Postdoctoral
Researchers – 2nd Cycle” (MIS-5033021), implemented by
the State Schol-arships Foundation (IKY).
Dechouiotis 先生的研究工作由希腊和欧洲联盟(欧洲社
会基金)通过”人力资源开发、教育和终身学习”业务方案，
在”加强博士后研究人员第二周期”项目(MIS-5033021)范
围内共同资助，该项目由国家学校奖学金基金会(IKY)执
行。
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