Journal of Robotics, Networking and Artificial Life
Vol. 7(3); December (2020), pp. 190–193
DOI: https://doi.org/10.2991/jrnal.k.200909.010; ISSN 2405-9021; eISSN 2352-6386
https://www.atlantis-press.com/journals/jrnal

Research Article

Apply Model-Free Adaptive Control Approach for Mobile
Robot Path Following
Chia-Jen Lin1, Chun-Chi Lai2,*, Kuo-Hsien Hsia2, Chin-Sheng Chen1
Graduate Institute of Automation Technology, National Taipei University of Technology, 1, Sec. 3, Zhongxiao E. Rd., Taipei, Taiwan 10608, R.O.C.
Bachelor Program in Interdisciplinary Studies, National Yunlin University of Science and Technology, 123 University Road, Section 3,Douliou, Yunlin, Taiwan 64002, R.O.C.
12ARTICLE INFOABSTRACT

Article History

The state of the art of mobile robot path planning is composed with global planner and local planner. For example, the global
planner majorly establishes a suitable path from a knowing map based on the shortest path. And the local planner which
computes the velocity command that includes obstacle clearance and progress toward the goal. However, due to the 2D laser
ranger on a mobile service robot just detects the part of the meal table or misses it, this will cause robot often hits the mealtable. In this work we apply adaptive control method to feed the goals for Dynamic Window Approach’s (DWA) computing. The
experimental result shows that DWA will follow the pre-defined path closely and smoothly.

Received 14 October 2019
Accepted 29 May 2020
Keywords
Mode-free adaptive control
dynamic window approach
path follower
mobile service robot© 2020 The Authors. Published by Atlantis Press B.V.
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

1. INTRODUCTION
With the rapid development of robotics and artificial intelligence technology, mobile service robots have begun to be used in
our lives. Based on the design of the automatic navigation function, the mobile service robot is allowed to move autonomously
and perform daily human services, such as automatic cleaning
and automatic delivery. Based on Simultaneous Localization andMapping (SLAM) [1], the autonomous navigation of mobile robot
will become a reality. If exclude the SLAM, the remaining works
of autonomous navigation are including path planning and pathfollowing.
The state of the art of mobile robot path planning is composedwith global planner and local planner. For example, the global
planner majorly establishes a suitable path from a knowing
map. And the local planner not only follows the global path but
also obstacle avoidance consideration. In this work, we apply
the pre-defined path and design a path follower to replace theautonomous global planner to overcome the actual navigation
problem when a mobile service robot is delivering the meal in afast food restaurant.

2. MOBILE ROBOT PATH PLANNING
Path planning is the most basic part of mobile robot navigation.
It refers to how the robot can find collision free waypoints as anappropriate motion path from the starting point to the end point
Corresponding author. Email: cclai@yuntech.edu.tw*

in a working environment. In general, the path planning mainly
involves these two major issues:•• Obstacles avoidance•• Optimizing the path
According to the environmental information, mobile robot path
planning can be divided into global path planning and local planning as shown in Figure 1.

2.1. Global Planner
The global planner is a pre-planning method that depends on theanalysis of known map. For example, the artificial potential field[2] algorithm was proposed in 1989. Its’ concept is to apply a virtual attraction and repulsive force to a robot. The target gives therobot attractive force, and the obstacle is the repulsive force. After
combining the force, a moving path of the robot to the target point
can be obtained. The Rapid Exploration Random Tree [3] method
was originally proposed in 1998. Its’ idea is to growth with the initial point as the root in the space and add child nodes by random
sampling. Connect the closest child node to the root node until
the child gradually reaches the target point, and then a feasible
path could be selected. The other well-known methods of safe pathcreation are such as the generalized Voronoi diagram [4] and theProbabilistic Roadmaps (PRMs) [5]. The PRMs applies a sampling to the environment in order for a graph to be created, eachedge of which is considered safe for robot traversing and a graphsearch algorithm such as Dijkstra [6] or A* [7] is applied to theresulting graph to determine a path between the starting and goal.

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In nowadays, the occupancy grid map [8] is popular to represent
the posterior probability model of environment. And the graphsearch algorithm Dijkstra or A* is also suit for finding the optimal path which is a collection of cells. After the success of finding
the global path from the start to the goal, all the selected cells aretranslated into positions as the point vector.

2.2. Local Planner
In order to transform global path into a suitable waypoints, local
planner applies sensors to detect the robot’s environment to obtainpose or geometric information of obstacles. Therefore, using the
updated local sensing information, the local planner generates anobstacle avoidance strategy and attempts to match the trajectory
provided by the global planner. Some local trajectory generationof local planner may apply Bezier lines [9], arcs, segments [10], orsplines [11]. In nowadays, one of the most popular local path planmethod is Dynamic Window Approach (DWA) [12], the basic ideaof the DWA algorithm is as follows:•• The DWA method is a local response obstacle avoidance controller, which searches for the best action (translation velocity v
and angular velocity w) in the velocity space.
•• Considering the dynamic constraints of the robot to reduce thesample space.
•• The trajectories corresponding to different velocities can berepresented by a series of arcs with different curvatures.
•• In order to obtain a fast response, it is assumed that the speed ofthe robot is constant in all future intervals.
The sampled trajectories are evaluated by an objective function
O(v, w), which is consisted with the goal heading, obstacle clearance, and velocity as below criteria:   191the fast food restaurant is shown in Figure 2. Although this pedestal column could be sensed via the laser ranger equipped on robot
platform, but sometimes it misses the detection and the upper bodyof robot hits the corner of table that causes the meal deliver task tobe failed. In this work, we apply the pre-define path and path follower to replace the autonomous global planning to overcome theactual navigation problem which causes by the meal table.

3. PATH FOLLOWER DESIGN
There are four sequences for path follower:•• Get the pre-defined path from file or Topic.
•• Prune the Waypoints: Erase the unsuitable waypoints in the path.
•• Segment Regulation: Adjust the segment length between waypoints.
•• Send out or publish the modified path for DWA.

3.1. Prune the Waypoints
The first work in prune the waypoint is to check if the waypointshould be discarded. Assume for a given path with five waypoints
P0 ~ P4, if the initial waypoint P0 is in front of robot as shown inFigure 3a the angle q between v1 and v 2 will greater than p/2, where
v1 is the vector of robot pose and P0 and v 2 is the vector of P0 and
P1. On the other hand, if the angle q between v1 and v 2 are smaller
than p/2 as shown in Figure 3b, then the P0 point will be deleted
and the point data will be recorded as Ppast. In Figure 3c, L1 is thedistance between robot center pose and P0. L2 is distance between
robot center pose and Ppast. When L1 > L2 but robot cannot turn toP0 due to the local obstacle. In this situation the P0 point will also bedeleted and the point data will be recorded as Ppast.

O(v , w ) = s (a ´ heading(v , w ) + b ´ dist(v , w )(1)+ g ´ velocity(v , w ))The heading (v, w) is the angle difference between robot current
head orientation and robot to goal direction, the dist (v, w) is thedistance to the closest obstacle, and the velocity (v, w) presents
the forward velocity of the robot with kinematic constraints.

2.3. Problem in Actual Navigation
In practical applications, the navigation package released in ROS[13] framework are applied to an automatic meal delivery robot ina fast food restaurant. Due to the pedestal column of meal table in

Figure 1 | Mobile robot path planning flow diagram.

Figure 2 | Auto global path planning problem: the shortest global pathoften causes mobile service robot to hit the meal tablet.

abcdFigure 3 | Prune the waypoints of default path.

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192

3.2. Segment Regulation
At this stage, we need an indicator as the criterion for judging how
close that robot is following the original path. Calculate the verticaldistance “height1” as shown in Figure 3d between the robot pose andthe segment of Ppast to P0 as the performance criteria for following
the line. The “height1” distance can be calculated as below equation:

Table 1 | The circular path following error
Maximum distance error (m)Mean distance error (m)0.05620.0238abcd		 v3 ´ v4 = v3 v4 sinq (2) v ´ v4		height1 = 3
(3)v3

3.2.1. Model-free adaptive control
Model-free adaptive control was proposed by Hou and Huang[14] which can realize the parameter adaptive control and structure adaptive control of the controlled system which makes it more
applicable for many practical plants.
u(k) = u(k - 1) +rf (k)( y * (k + 1) - y(k)) (4)l + f 2 (k)f (k ) = f (k - 1) +hDu(k - 1)
(5)( m + Du (k - 1))(Dy(k) - f (k - 1)Du(k - 1))
2f (k) = f (1), if f (k) £ e or Du(k - 1) £ e (6)From the above Eqs. (4)–(6), consider the previously calculated
height1 as y(k) and u(k) as control variables to regulate the lengthof the path.

4. EXPERIMENTAL RESULTS
The experiment is firstly to simulate in ROS rviz user interface forverifying the path following result. In Figure 4a, the predefined
path is shown as a green circle with a radius of 1 m. In Figure 4b,
the blue circular path represents the smooth following result.
Figure 4c shows the path following error with the time index. Theab

Figure 5 | Robot path following demo: (a) service robot in a real fast-foodrestaurant, (b) service robot starts to follow a long path, (c) robot turn inright-down corner, (d) robot will reach final goal.

maximum distance error of following the circle is about 0.0562 m
and the mean distance error is about 0.0238 m as shown in Table 1.
Besides, Figure 5a shows the service robot in a real fast-food restaurant, and the pre-defined green path is established to move aroundthe restaurant as shown in Figure 5b. The service robot follows
the path well and finally reaches the pre-defined goal as shown in
Figure 5c to 5d.

5. CONCLUSIONc

Figure 4 | Robot path following simulation: (a) circular path generation,(b) circular path following simulation, (c) path following error.

The state of the art of mobile robot path planning is composed with
global planner and local path planner. However for meal deliver
application in a real fast food restaurant, the mobile service robot
often hits the corner of the meal table due to the 2D laser ranger
just detects the part of the meal table or misses it. In this work, weapply the pre-defined path and path follower to replace the autonomous global planning to overcome the actual navigation problem
which causes by the meal table. The experimental result shows that
DWA can also follow the pre-defined path closely and smoothly.

CONFLICTS OF INTEREST
The authors declare they have no conflicts of interest.

C.-J. Lin et al. / Journal of Robotics, Networking and Artificial Life 7(3) 190–193

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AUTHORS INTRODUCTION
Mr. Chia-Jen Lin

Dr. Kuo-Hsien Hsia

He received the M.S. degree in 2004 from
National Yang-Ming University, Taipei,Taiwan, where he is currently working
toward the PhD degree in National Taipei
University of Technology, Taipei, Taiwan.
He is also a R&D manager in TECO Group
Research Institute with TECO Electric andMachinery Co., Ltd. His research interests
are AGV control and service robot techniques.

Dr. Chun-Chi LaiHe received the PhD degree in ElectricalEngineering from the National Sun Yat-Sen
University, Taiwan, in 1994. He is currently
an Associate Pofessor of National Yunlin
University of Science and Technology inTaiwan. His research interests are in thearea of artificial intellgience, fuzzy controland image processing.

Dr. Chin-Sheng Chang
He received the PhD degree in ElectricalEngineering from National Chung Cheng
University, Chiayi, Taiwan, in 2014. Heis currently an Assistant Professor ofNational Yunlin University of Science andTechnology in Taiwan. His research interests include multisensor fusion and intelligent robotics.

He received the PhD degree in MechanicalEngineering from National Chiao TungUniversity, Hsinchu, Taiwan, in 1999. In2002, he joined the Graduate Institute ofAutomation Technology, National Taipei
University of Technology, Taipei, Taiwan,
as an Assistant Professor, where he is currently a Professor and the Director. He has
authored or coauthored more than 150 journal and conference
papers and book chapters on the research. His research interests include intelligent motion control, robotics, mechatronics,and machine vision. Dr. Chen was recipient of the Outstanding
Research Award from the College of Mechanical and ElectricalEngineering, Taipei TECH, in 2013and 2014.