Learning Spatial Constraints using Gaussian Process for Shared Control

of Semi-autonomous Mobile Robots

Kun Qian

1,2

, Dan Niu

1,2

, Fang Fang

1,2

and Xudong Ma

1,2

Key Laboratory of Measurement and Control of CSE, Ministry of Education, No.2, Sipailou, Nanjing 210096, China

School of Automation, Southeast University, No.2, Sipailou, Nanjing 210096, China

Keywords:

Mobile Robot, Gaussian Process, Shared control, Semi-autonomous, Wi-Fi Signal Strength.

Abstract:

In this paper, a novel human-robot shared control approach is proposed to solve the problem of semi-

autonomous mobile robot navigation with the spatial constraints of maintaining reliable Wi-Fi connection.

In particular, the presented approach beneﬁts from using Gaussian Process Regression method to learn the

distribution of indoor Wi-Fi signal strength (WSS) and to fuse it with the environmental occupancy probabil-

ity. The resulting WSS-Occupancy hybrid map is further utilized for generating paths that prevent the robot

from violating the spatial restriction. A shared control strategy is designed to implement the WSS-aware nav-

igation behaviour. The approach is evaluated by both simulation and real-world experiments, in which the

results validate the practicability and effectiveness of the approach.

1 INTRODUCTION

With the increasing prevalence of wireless LAN

in indoor environments, tele-operated mobile robots

have been applied to environment inspection and

monitoring applications(Sgouros and Gerogiannakis,

2003)(Pitzer et al., 2012). In situations that spatial

constraints other than obstacles are imposed to such

a networked mobile robot, full tele-operation may not

be reliable enough and semi-autonomous robots(Tang

et al., 2009) with human-robot collaboration have be-

come important in network robotic system.

In the context of this study, the focus is particu-

larly on an unknown spatial constraint of maintain-

ing reliable Wi-Fi connections during robot naviga-

tion. Our motivation originates from the fact that in

indoor environments, when a robot navigates through

an area with poor Wi-Fi signal strength (WSS), the

tele-operation system may temporarily lose control

over the robot, neither can continuous and high qual-

ity tele-presence (visual and audio) feedback be en-

sured.

By treating the Wi-Fi distributionas a static spatial

constraint here, the solution is to design a WSS-aware

navigation behavior for ensuring continuous and reli-

able Wi-Fi connection during the robots exploration.

We deﬁne the problem mentioned above as spatially

restricted navigation of a tele-operated mobile robot.

Intuitively, learning the distribution of spatial con-

straints in the environment can be beneﬁt to prevent

a robot from violating the restriction. Learning the

spatial distribution of an indoor environment from a

mobile platform can be formulated as a well-known

regression problem, i.e., to predict sensor values at

locations where the robot doesn’t traverse. Gaussian

Process(Rasmussen and Williams, 2006)(Qian et al.,

2016) is a powerful formalism for predict the prob-

ability distributions over sensor values at uncovered

locations. In Jadaliha’s work(Jadaliha et al., 2012),

the authors employed Gaussian Processes (GPs) to

build non-parametric probabilistic models using data

from a pilot sensor work deployment, for monitoring

spatial phenomena of interest. In order to handle the

diffusion and patches effects of complex interaction

of gas, Stachniss(Stachniss et al., 2009) proposes to

learn two-dimensional spatial models of gas distribu-

tions using a sparse Gaussian process mixture model,

which accurately represents the smooth background

signal and the areas with patches of high concentra-

tions. These recent studies(Krause et al., 2008)(Fer-

ris and D. Hahnel, 2006)(Xu et al., 2011)(Xu and

Choi, 2011)(Engel et al., 2003)(Ko et al., 2007) have

shown that Gaussian processes are an attractive mod-

eling technique in this context since they do not only

provide an estimate of sensory data for each point in

the space but also the predictive uncertainty. To our

best knowledge, the GPs approach has not yet been

applied to model the indoor Wi-Fi signal strength dis-

Qian, K., Niu, D., Fang, F. and Ma, X.

Learning Spatial Constraints using Gaussian Process for Shared Control of Semi-autonomous Mobile Robots.

DOI: 10.5220/0006382902010208

In Proceedings of the 14th International Conference on Informatics in Control, Automation and Robotics (ICINCO 2017) - Volume 2, pages 201-208

ISBN: Not Available

201

tribution.

Another challenge is how to utilize the recovered

spatial constraints to implement spatially restricted

navigation behaviors of a robot. Semi-autonomous

navigation will outperform full tele-operation when

spatial constraints are considered. Two major prob-

lems are concerned in this paper:

• Firstly, if the spatial distribution of WSS is recov-

ered by the GPs, the distribution should be inte-

grating with the occupancy grid map in order to

achieve a WSS-aware navigation behaviour.

• Secondly, a semi-autonomous behaviour of robot

is desired to correct the path designated by the re-

mote user and prevent itself from entering the ar-

eas with low WSS.

To deal with semi-autonomous control of mobile

robots, human-robot shared control methods(Li et al.,

2015) have been applied when multiple inputs and

multiple constraints are considered. The concept of

shared control is to select between the two sources

of commands and combine them to ensure task ac-

complishment while satisfying dynamic constraints.

However, to our best knowledge, there is little re-

search towards the solution of the WSS-aware navi-

gation problem.

In this paper, we propose a practical problem

called WSS-aware navigation of a tele-operated mo-

bile robot, which is an example of a general con-

cept of spatially restricted navigation. To tackle

this problem, we present an approach that enables

semi-autonomous navigation of a tele-operated mo-

bile robot by learning WSS-Occupancy hybrid map,

in which Gaussian Process is used as an effective

model to learn the WSS distribution with limited

number of training samples and predict the WSS dis-

tribution in a coordinate frame that is consistence

with the robots occupancy grid map. The concept

of shared control is introduced to implement a semi-

autonomous navigation behaviour of mobile robot

that can avoid the risk of violating the constraints, i.e.,

continuous and reliable Wi-Fi connection during nav-

igation is ensured.

2 WEB-BASED ROBOTIC

SYSTEM FOR MONITORING

A web-based robotic system is developed for re-

mote environment monitoring. The mobile robot is

equipped with a HOKUYO laser range ﬁnder for self-

localization and obstacle avoidance and a video cam-

era for capturing local video streams. The onboard

computer integrates a network card to measures the

Wi-Fi signal strength (WSS). The web-based robotic

system is built with three-layer architecture, as shown

in Figure 1:

• Web Client Layer (WCL). The WCL provides a

user with a client GUI to monitor the remote envi-

ronments as well as to get access to the direction

control of a robot.

• Network Service Layer (NSL). The NSL is com-

prised of a Web server and an Audio/VideoServer.

Another key role of NSL is to conduct the shared

control strategy, and thus the shared control effect

is transparent to the user.

• Local Robot Control Layer (LRCL), The

LRCL runs various ROS (Robot Operating

System)(Quigley et al., 2009) based nodes to

access robot hardware and to perform perception,

localization, navigation, mapping and other mod-

ules. The proposed WSS distribution mapping

function is also deployed in LRCL for creating

and storing the robots knowledge about the

spatially constrained environment.

Mobile

client

Streaming

x Recognition

x Decision making

Perception

x Localization

x Navigation

Navigation

x Audio

x Video

Mapping

Web Client Layer Network Service Layer Local Robot Control Layer

Shared control

Web server(LAMP)

A/V server

Service management

Autonomous control

Sensor data acquisition

Motor control

Node management

Full supervision Full autonomousSemi-autonomous

Roles of human

intervene

Browser

client

Internet

LAN

x SLAM

x WSS mapping

Direct control

Monitoring

Server

Figure 1: Web-based robotic system architecture.

A browser-based GUI is also provided to receive

human input commands from keyboard, joystick and

other types of interface, as shown in Figure 2. Given

the direction human input commands and the robots

autonomous control commands, the concept of shared

control is to select between the two sources of com-

mands and combine them to ensure task accomplish-

ment while satisfying dynamic constraints.

In our remote monitoring application, a typical

constrain concerned in this paper is to maintain solid

Wi-Fi connection for ensuring smooth video stream-

ing. With regard to this, the key to shared control

is to model the distribution of indoor Wi-Fi signal

strength and fuse such spatial distribution with the en-

vironment occupancy probability distribution, which

we deﬁne as WSS-Occupancy hybrid map building.

ICINCO 2017 - 14th International Conference on Informatics in Control, Automation and Robotics

202

Based on this a decision making module is proposed

to select or combine the commands from human in-

puts and the robots autonomous control inputs gener-

ated from a navigation controller based on the WSS-

Occupancy hybrid map. The shared control frame-

work is shown in Figure 3.

Figure 2: Browser-based GUI.

Direct control

command

Autonomous control

command

Keyboard,

joystick

interface

Task

allocation

Localization & Navigation

WSS-Grid hybrid map

learning

Decision making

Audio/Video

feedback

GUI

Sever

Shared control

Figure 3: Shared control framework.

3 LEARNING WSS SPATIAL

DISTRIBUTION

3.1 WSS Samples Accquisition

A robot explores the environment and constructs the

grid map of the environment using its onboard laser

sensor readings. In the situation of both robot posi-

tion and environmental map are unknown, the popu-

lar GMapping algorithm(Grisetti et al., 2007) is em-

ployed to implement highly efﬁcient SLAM (simulta-

neously localization and mapping).

As the exploration and mapping proceeds, the

robot simultaneously captures the Wi-Fi signal

strength (WSS) from the network card of the onboard

computer along the path it travels. At every ﬁxed time

interval t the robot encapsulates the WSS data as each

data packet:

D = (x

)|i = 1, 2,...,n (1)

in which x

is the positions of sample points, and y

is the WSS measured at the corresponding position

timestamp t

3.2 Learning WSS Distribution with

Gaussian Processes

A Gaussian process deﬁnes a distribution over a space

of functions. Let D = {{x

, ¯y

},{x

, ¯y

},...,{x

, ¯y

}}

be a set of training data generated from a noisy pro-

cess ¯y

= f(x

) + ε

, where x

∈ R

is an input sam-

ple data and y

∈ R is a target or an observation. ε

is additive Gaussian noise with zero mean and un-

known variance σ

, i.e.,ε ∼ N(0,σ

). A Gaussian

Process considers f(·) as a random function and esti-

mates the posterior distribution p( f|D) based on the

prior p( f) and the training data D. A GP prior p( f)

is completely speciﬁed by its mean function and co-

variance function,i.e., f ∼ GP(m

),which can be

formulated as:

p( f (x)) ∼ N(m

(x),k

(x,x)) (2)

Assuming that we have two input points x

and x

and the corresponding function values at these points

are f(x

) and f(x

), respectively. We consider a prior

mean function m

≡ 0 and a typical squared exponen-

tial (SE) covariance function, or called kernel func-

tion:

cov(y

) = k

) + δ

(3)

in which:

) := α

exp



−

− x

)

−1

− x

)



(4)

with x

∈ R

. In the above equation,

Λ = diag([l

,..., l

]) is a diagonal matrix of squared

characteristic length-scales l

, i = 1, ...,d. α

is the

signal variance and δ

is the Kronecker symbol that

is unity when p = q and zero otherwise.

If we denote X as the entire set of input values,

Equation (3) can be rewritten as:

cov(y) = K + σ

I (5)

where K is the n×n covariance matrix with K[p,q] =

). The prior over function f depicted by

Equation (5) indicates that one can generate the ma-

trix K from a set of input values X and then sample a

set of corresponding target values y ∼ N(0,K + σ

I).

Given a training dataset D of n input-

output pairs that contains samples positions

Learning Spatial Constraints using Gaussian Process for Shared Control of Semi-autonomous Mobile Robots

203

X = {x

|i = 1,2,..., n} and their corresponding

WSS values y = {y

|i = 1,2,..., n}, a GP model is

trained. Based on the trained GP model the posterior

distribution can be computed. For a new input x

∗

that represents a position where WSS at this position

is never measured, the joint conditional distribution

of the estimated target value y

∗

can be estimated by

the prediction distribution p(y

∗

,D). The posterior

over function values, conditioned on the training

data X and y is Gaussian with mean µ

∗

and variance

∗

(Deisenroth et al., 2014):

p( f (x

∗

)|x

∗

,X,y) = N(µ

∗

,σ

∗

) (6)

where

∗

= k

∗

(K + σ

−1

y (7)

∗

= k(x

∗

) − k

∗



K + σ



−1

∗

(8)

The chosen kernel function determines the perfor-

mance of the GP regression. The hyper-parameters

of a GP with Gaussian kernel for a particular dataset

can be learned from the training data, in which the

hyper-parameters are derived by maximizing the log

marginal likelihood using empirical Baysian infer-

ence(Rasmussen and Williams, 2006).

3.3 Fusion of Grid Map with Wi-Fi

Signal Strength Distribution

The learned WSS distribution map models the spa-

tial distribution of WSS within a given indoor context.

We use Equation (9) to transfer raw WSS data S into

that takes similar value as a grey image pixel:

= 255(S + S

min

)/(S

max

− S

min

) (9)

, in which S

min

and S

max

are the lower bound and the

upper bound of transformation, which are set as:

min

= −113dBm (10)

max

= 0dBm (11)

, according to our inspection of the range of sam-

ple WSS values in typical indoor environments. We

deﬁne the minimal value of WSS that ensures reli-

able network connection in the environment is S

and thus the corresponding value after the transform

is G

. Furthermore, since the Wi-Fi distribution

map is learned on actual sensor readings recorded at

locations in the world coordinate that is consistent

with the occupancy grid map of the environment, the

WSS distribution map can be fused with the occu-

pancy grid map, resulting in a WSS-Occupancy hy-

brid grid map. Denote G

as the grey value of a pixel

in the occupancy grid map and G

are deﬁned in

Equation (9). The resulting grey value G

of the cor-

responding pixel in the WSS-Occupancy hybrid grid

map is given in Equation (12):

= {

< min(G

)

else

. (12)

4 SHARED CONTROL

STRATEGY

Using the WSS-Occupancy hybrid grid map de-

scribed in Section 3, a desired trajectory can be com-

puted by a regular navigation controller that is com-

prised of a global path planner and a reactive local

planner. The path will ensure goal-directed naviga-

tion while avoid the robot to pass through the areas

with low WSS, so that continuous network connec-

tion will be strictly ensured.

Using a local path planner such as VFH or ND

algorithm(Minguez and Montano, 2005), the au-

tonomous control set u

is obtained. Given the hu-

man direct control u

= [v

]

and the output of the

reactive local planner u

= [v

]

, in which v and

w represent the translational speed and the rotational

speed of the robot, respectively, the shared controller

adopted in this work can be formulated as a combi-

nation of both two sources of command as shown in

Equation (12). ρ is the allocation weight with domain

0 ≤ ρ ≤ 1.

= (1− ρ)u

+ ρu

(13)

Since a robot control command will not exactly

cause ideal movement but introducing certain uncer-

tainties, we roughly predict the distribution of the

robot’s possible future positions in a small time inter-

val ∆t ahead by adding Gaussian noises to the transla-

tional and rotational velocity. Firstly we assume that

the robot’s heading is constant but the translational

velocity is v, thus the robot’s possible movements are

placed along a vector

−→

OA after ∆t. Then we assume

that the robot’s rotational velocity changes randomly

within [−∆w, ∆w] in ∆t. The result is a fan-shaped

area as shown in Figure 4 that contains all possible

Let the feasible autonomouscontrol input set asU

and feasible human input set asU

. Four types of rela-

tionships between U

and U

as shown in Figure 5 are

considered. If U

is a subset of U

, i.e.,U

⊆ U

, the

tele-operation command is regarded safe for ensuring

both goal-reaching and obstacle avoidance. In this

case, any ρ that satisﬁes 0 ≤ ρ ≤ 0.5 can be taken to

generate a synthetic control command. In three other

situations such asU

⊆ U

, U

∩U

6= {O,U

} and

ICINCO 2017 - 14th International Conference on Informatics in Control, Automation and Robotics

204

ƸwƸt

vƸt

Figure 4: Deﬁnition of U

∩U

= {O}, the tele-operation commands exceed

the safe range of the autonomous decision and it is

therefore difﬁcult for the user to manually direct the

robot to achievethe goal while meeting the constrains.

In this case, we simply assign the allocation weight

ρ = 1 to ensure successful task accomplishment by

robot’s autonomy only.

(a) (b) (c) (d)

Figure 5: Four types of relations between U

and U

5 EXPERIMENTS

5.1 WSS-Occupancy Hybrid Mapping

We ﬁrstly verify the performance of WSS distribu-

tion mapping in a simulation experiment. A Wi-Fi

signal generator is utilized to simulate the Wi-Fi sig-

nal that travels in a simulated indoor environment as

shown in Figure 6(a). In the simulation, we use In-

door Propagation model, a.k.a, the MK model(Motley

and Keenan, 1988), to generate the ground truth Wi-Fi

distribution. This model takes into consideration the

signal decline when it travels through various kinds

of obstacles. Table 1 gives the signal attenuation rate

when the signal propagates through different types of

obstacles, such as walls, wood or glasses, et al.

The MK model based simulator uses Equation

(14) to compute the predicted path loss for a testing

receiver place:

pico

= S

+ 10× n

× log(x) + (N

+ L+ N

)

(14)

in which S

equals to the pass loss at 1m from the

transmitter, n

is the signal attenuation rate long the

Table 1: WI-FI Signal attenuation rate.

Types of obstacles Attenuation rate

electromagnetic interference 30 ∼ 50dBm

Concrete walls 12 ∼ 32dBm

Block walls 5 ∼ 15dBm

Wooden walls 3 ∼ 8dBm

Glasses 1 ∼ 5dBm

propagation path due to electromagnetic interference,

x is the distance between the transmitter place and

the testing receiver place, N

is the number of inte-

rior walls between the transmitter and testing receiver

place and S

is the loss factor of different interior wall

materials. The result of the simulated WSS distribu-

tion is shown in Figure 6(b), which is taken as the

ground truth.

Wireless AP

(a) (b)

Figure 6: Simulated environment and the ground truth.

Using a Stage(Vaughan, 2008) based robot sim-

ulator, a robot travels through the environment and

obtains the training dataset. Figure 7 shows the re-

sults of occupancy grid map and the robot trajectory

for collecting the WSS sample data. Subsequently, a

WSS distribution map is trained with Gaussian Pro-

cess Regression method and the predicted WSS spa-

tial distribution in shown in Figure 8. The result is

evident that by utilizing a limited number of training

samples, a smooth 2D spatial distribution of WSS can

be inferred and the WSS at positions that is not mea-

sured can be predicted.

Figure 7: Robot trajectories for collecting the training sam-

ples.

In addition, a WSS-Occupancy hybrid map is ob-

tain by fusing the WSS distribution map with the oc-

cupancy grid map, resulting in WSS-aware path plan-

ning results. A comparison of WSS-aware and non

Learning Spatial Constraints using Gaussian Process for Shared Control of Semi-autonomous Mobile Robots

205

-40

-60

-80

-100

-120

WSS/dBm

Figure 8: Learned WSS distribution.

WSS-aware path planning results are shown in Figure

9. The result implies that using a WSS-Occupancy

hybrid map instead of a traditional occupancy grid

map, the robot detours to avoid entering areas with

poor WSS. In the experiment the threshold is taken

as S

= −75dBm, i.e., G

= 68 to obtain the

shaded area in Figure 9(b). A comparison of the WSS

captured along two different paths is shown in Fig-

ure 10, which indicates that the WSS-aware naviga-

tion behavior guarantees continuous and reliable Wi-

Fi connection.

Path

(a) Without WSS-constrain

Area with low

WIFI signal

strength

Path

(b) With WSS-constrain

Figure 9: Path planning results.

5.2 Shared Control using

WSS-Occupancy Hybrid Map

The shared control performance was further validated

in two other real world environment scenarios. The

Area with low

WSS

Non WSS-

aware path

WSS-aware path

Figure 10: The WSS along two paths.

experiment made use of Turtlebot mobile robot plat-

form in an ofﬁce environment of size about 100m

where Wi-Fi networks were deployed over multiple

Access Points (APs). Scenario 1 was designed as a

WSS-aware navigation trial experiment. The actual

position of the Access Point (AP) in the testing en-

vironment was outside the room as marked in Figure

11. By building the WSS-Occupancy hybrid map of

the environment the robot was aware of the area with

low WSS, depicted by the shaded area in Figure 11.

When the robot was steered by a remote user to travel

from point A toward the top-right corner of the map

as shown in Figure 11, the shared controller drove the

robot to avoid the area with low WSS, as shown by

the Part B of the trajectory in Figure 11. The results

of the translational and rotational velocity of the robot

during the corresponding trial test are given in Fig.12,

which reveal the decision making results of the shared

controller. The result implies that a robot is capable of

adapting its behavior to reduce the risk that confronts

with the spatial constrains we have exerted.

Full autonomous to

avoid the area with low

WIFI signal

Part A: Tele-operation only

Part B: Full autonomous

Part C: Tele-operation only

Area with low WIFI signal

Wireless

Access Point

Figure 11: Shared control result in scenario1.

Scenario 2 validates the effectiveness of human

supervision for assisting robot’s autonomy. The task

ICINCO 2017 - 14th International Conference on Informatics in Control, Automation and Robotics

206

A B C

Translational velocity

Shared control result

Tele-operation input

Autonomous control input

(a) Translational Velocity

A B C

Rotational velocity

Shared control result

Tele-operation input

Autonomous control input

(b) Rotational Velocity

Figure 12: The robot’s velocity in scenario1.

assigned to the robot in this scenario was to travel

from P1 to P3 autonomously, but the robot had to

travel through a short part of corridor which is too

narrow for a robot to pass on its own. When the

robot’s path planner failed to report a path across the

corridor, the shared controller with ρ = 0 led to full

human supervision, which was achieved by receiving

human direction control through the GUI. The robot

therefore successfully reached the goal. This experi-

ment indicates that the proposed shared control strat-

egy is also beneﬁcial to the general purposes of semi-

autonomous control in a web-based robotic system.

6 CONCLUSIONS

In this paper, a novel human-robot shared control

approach is proposed to solve the problem of semi-

autonomous navigation with a static spatial constraint

of maintaining reliable Wi-Fi connection. In the train-

ing mode, a robot explores the environment while

building the WSS-Occupancy hybrid map based on

Gaussian Process Regress method. In the runtime

Pass through the

narrow corridor by

human supervision

Part A: Full autonomous

Part B: Tele-operation only

Part C: Full autonomous

Wireless

Access Point

Figure 13: Shared control result in scenario2.

mode, the robot utilizes the WSS-Occupancy hybrid

map in a shared control framework to generate paths

that prevent itself from entering areas with low Wi-

Fi signal strength. A series of experimental stud-

ies have been performed, where promising results are

obtained. The presented approach can be extended

to solve other similar problem of spatially restricted

navigation of a tele-operated mobile robot to reduce

the risk of violating the constraints while reaching the

goal.

ACKNOWLEDGEMENTS

This work is supported by supported by the Na-

tional Natural Science Foundation of China (Grant

No. 61573101, 61573100 and 61504027) and the

NSF of Jiangsu Province(NO.BK20140647).

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