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Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science
ISSN: 0954-4062 Online ISSN: 2041-2983 Copyright © 2018 by Institution of Mechanical Engineers
Engineering Science
Engineers, Part C: Journal of Mechanical
Proceedings of the Institution of Mechanical
The online version of this article can be found at:
DOI: 10.1177/0954406213518523
2278 originally published online 16 January 2014
Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 2014 228:
Naoki Uchiyama, Tresna Dewi and Shigenori Sano
Collision avoidance control for a human-operated four-wheeled mobile robot
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Original Article Collision avoidance control for a human-operated four-wheeled mobile robot Naoki Uchiyama, Tresna Dewi and Shigenori Sano
In human-operated robotic systems, controllers are required to incorpor- ate the human operator commands and compensate for operator’s mistakes without hampering the ease of operation. Collision avoidance functions are neces- sary for easy and safe operation of a robot operated by an elderly or disabled person. We consider a colli- sion avoidance control for human-operated four wheeled mobile robots that are widely used in common vehicle systems.
Department of Mechanical Engineering, Toyohashi University of Technology, Toyohashi, Aichi, Japan Corresponding author: Naoki Uchiyama, Department of Mechanical Engineering, Toyohashi University of Technology, 1-1 Hibarigaoka, Tempaku, Toyohashi, Aichi 441-8580, Japan. Email: uchiyama@tut.jp
In this approach, the mobile robot destination is given and the robot motion is generally determined by
12,13
The potential field method based on the idea of imaginary forces acting on a robot is one of the most popular approaches to obstacle avoidance. This approach has been extended by many studies. Because the four-wheeled robot is a nonholonomic system, the obstacle avoidance func- tion must consider this dynamic property. The robot manipulator dynamics is considered and decoupled in the implementation of the obstacle avoidance func- tion presented in Ref. 7; however, this decoupling approach cannot be applied to the nonholonomic four-wheeled mobile robot. The dynamic window approach is one of the most efficient approaches that consider the nonholonomic constraint and can be applied to unknown environments.
7–11
Much research has been conducted on obstacle avoidance for mobile robots.
5,6
Abstract Because the collision avoidance function is indispensable for providing safe and easy operation of human-operated robotic systems, this paper deals with the collision avoidance control for a human-operated mobile robot in unknown environments. A typical four-wheeled mobile robot with infrared distance sensors for detecting obstacles is considered. The robot cannot move in an arbitrary direction owing to a nonholonomic constraint. Therefore, we propose a simple control approach in which a human operator’s control input is modified in real time to satisfy the nonholonomic constraint and avoid collision with obstacles. The proposed controller has steering- and brake-like functions that are adjusted according to the distance sensor information. The stability of the proposed control system is analyzed with a linear model. The effectiveness of the proposed method is confirmed by experiments in which several operators control the robot in an environment with obstacles.
and executing missions in remote or hazardous environments.
3,4
pro- viding precise and smooth operations in difficult phys- ical tasks,
1,2
Fully automated robots are desirable to support household chores, nursing and welfare work, and industrial tasks performed by skilled workers. However, from the viewpoint of cost efficiency, it is impractical to produce such robots using the currently available technology. Human-operated robotic sys- tems are a suitable solution, and hence, widely stu- died. The objectives of human-operated robots include extending human mechanical power,
Date received: 10 June 2013; accepted: 26 November 2013 Introduction
Keywords Four-wheeled mobile robot, collision avoidance, human-operated mobile robot
Proc IMechE Part C: J Mechanical Engineering Science 2014, Vol. 228(13) 2278–2284 ! IMechE 2014 Reprints and permissions: sagepub.co.uk/journalsPermissions.nav DOI: 10.1177/0954406213518523 pic.sagepub.com optimizing a certain cost function such as the distance to the destination.
In the field of autonomous vehicle control, Reichardt and Schick
ylf
, force acting on each wheel [i: force direction (x or y), j: right(r) or left(l) wheel, k: front(f) or real(r) wheel]; , steering angle; m, vehicle mass; a, b, distance between the center of gravity and the rear or front wheel; d, distance between rear wheels (front wheels); and ( ) is the time derivative.
ijk
, vehicle velocity in the lateral direction; !, vehicle angular velocity; f
y
is the vehicle velocity in front–rear direction; u
x
where u
ylr
þ f
yrr
¼ f
yr
, f
þ f
xr
yrf
¼ f
yf
, f
xlr
þ f
xrr
¼ f
xr
, f
xlf
þ f
xrf
We assume that f
and are inputs provided by an operator, f
xf
¼ c
Uchiyama et al.
Figure 1. Four-wheeled robot model.
f ylf f xrf f yrf f b a
δ xlf
ω f γ
d ylr f xlr f x u y u xrr f yrr f
γ
r
þ !a u x ð6Þ
y
u
1
f tan
f f
xrr
f yf ’ c
15
are approximated as follows
yr
and f
yf
are zero (i.e. rear- wheel drive), and vehicle parameters m, I, a, b, and d are known and constant. The forces f
xlf
and f
xrf
, f
xlr
¼ f
¼ f
Þ cos g ð5Þ f
14
This subsection briefly explains the concept of the social force model. The social force model is defined as follows dw dt
x
m _u
15
Figure 1 shows a schematic of the four-wheeled mobile robot. The dynamics of the four-wheeled mobile robot is represented as follows
Dynamics and control of the four-wheeled mobile robot
conducted computer simula- tions of interacting pedestrians and showed that the social force model can describe the pedestrian behav- ior including obstacle avoidance. The following sec- tion applies this concept to the robot vehicle control.
18
F ¼ F þ F þ F ð2Þ Helbing and Molnar
The social force vector F defined in equation (2) con- sists of the attractive force from the desired position F , the repulsive force from other pedestrians and walls F , and attractive force from the objects of inter- est F
l is the fluctuation vector.
ð1Þ where w is the pedestrian velocity vector, F is the social force vector, and F
l
¼ F þ F
19,20
xr
first introduced the social force model to explain pedestrian motion. The social forces are considered to act on a pedestrian in order to avoid collisions with other people or walls and to enable motion in a specific direction at a given speed. The social forces for collision avoidance are modeled as repulsion forces from obstacles such as other people or walls. Follow-up studies on this concept have been conducted.
18
Helbing and Molnar
Controller design for collision avoidance Social force model
considers the dynam- ics of a pedestrian and the imaginary social forces acting on him/her in order to avoid collisions with other people or walls. Based on this concept, we pro- pose a control approach for collision avoidance in which the control input signal is modified according to the distance sensor information. The proposed con- trol system is an extension of that in Ref. 21 to a four- wheeled robot. A stability analysis is performed to validate the proposed approach. The effectiveness of the proposed approach is demonstrated by experi- mental results obtained when several unskilled oper- ators control the four-wheeled robot in a corridor-like environment.
18–20
The social force model, which has been used to explain pedestrian motion,
presented a set of potential function components to assist automated and semiautomated vehicles. However, these approaches require computational effort and expen- sive sensors to construct and employ the risk map and artificial potential fields. This paper aims to present a simple approach that employs inexpensive distance sensors.
17
proposed an approach based on the concept of artificial potential fields, which ensures safe motion in the absence of driver inputs. Wolf and Burdick
16
15 and Rossetter et al.
proposed the concept of risk map to achieve human-like behavior. A risk map is an egocentric map of potentials reflecting the risk at a certain position in the environment. Gerdes and Rossetter
¼ f
þ f
xlf
ð4Þ
f
xrf
þ ð f
xlr
f
xrr
þ d 2 ff
yr
cos bf
yf
sin þ af
xf
I _! ¼ af
x
xf
cos m!u
yf
sin þ f
xf
þ f
yr
¼ f
y
ð3Þ m _u
y
sin þ m!u
yf
cos f
2279
Proc IMechE Part C: J Mechanical Engineering Science 228(13)
2280 u
y where and f are the steering angle and driving force
!b d d
1
f yr r r r tan ’ c ¼ c ð7Þ designated by an operator, respectively, and f corres- u x
d
ponds to the accelerating or braking force of a typical where c and c are the cornering stiffness and and vehicle. The virtual steering angles g and g are
f r f ri li
are the sliding angles of the front and rear wheels. assumed to be proportional to the distance measure-
r
From equations (3) to (7), we have the following ment at each sensor location as follows dynamics , g ki i d ki i
¼ p þ q k ¼ l, r ð13Þ u y þ !a
1
m tan
x xr f y
_u ¼ f þ c sin þ m!u where the subscript l or r denote that the correspond- u
x
ing sensor is located on the left or right side of the ð8Þ robot body, i the sensor number, and p and q are
i i
positive constants. In this study, g and g are
ri li
u
y
!b
1
m tan
y r
_u ¼ c assumed to be positive. Equation (11) indicates that u
x
the controller steers to the left when the distance to u
y
þ !a
1
the obstacle measured by the sensor located at the tan
f x
c cos m!u ð9Þ u x right-hand side of the robot becomes small and vice versa. u y
þ !a
1 Because we cannot directly apply the social force to
I f tan cos _! ¼ ac u x the dynamics in equations (3) to (5), we propose to u y include the similar effect in the steering angle and
!b
1
tan
r
þ bc ð10Þ driving force, as given in equations (11) and (12), u
x
which are common control variables in four-wheeled This study assumes that several distance sensors are vehicle systems. This controller design has not been located on the robot. Figure 2 shows an example of a presented as far as the author’s knowledge. sensor location for the rectangular shaped robot. For simplicity, the virtual forces h and h in equa-
ri li
Because the distance information to obstacles is avail- tion (12) are assumed to be proportional to the dis- able, we include this information in steering angles tance measurement at each sensor location as follows and driving force generated by rear wheels for colli-
, sion avoidance as follows h ki i d ki i ¼ ^p þ ^q k ¼ l, r ð14Þ X m m X where and are positive constants. From equation i i
^p ^q g g
d ri li
¼ þ ð11Þ (12), it can be seen that the smaller the distance, the
i¼1 i¼1 larger the braking force provided by the controller. m m The effect of g and h can be interpreted as in the X X ki ki
f h h social force model, in which the social force is mod-
xr d ri li
¼ f ð12Þ
i¼1 i¼1 eled as a virtual repulsive force to avoid collisions with obstacles.
Stability analysis
Using the test case presented in Figure 2, we consider
Y
the validity of the proposed method for realizing the Distance
d collision avoidance function in the human-operated φ r 2
sensors robot. Namely, this subsection is devoted for analyz-
d r 1
ing the validity of the control in equations (11) and
d l 2 l l 2 1 (12), and the measurement of rotational deviation and l 2
forward speed as well as actual parameter values is
d l 1 l 1
not required for the control and the analysis in this subsection. Although the vehicle system has nonlinear
B dynamics in equations (3) to (5), we apply a linear
Robot
x
analysis at a certain operating point that is generally effective to predict the fundamental property of the Wall
L
control system. Experiments were conducted to fur- ther verify the effectiveness, and their results are
X
shown in ‘‘Experiments’’ section. For simplicity, the robot is assumed to have a rectangular shape. It is further assumed that the human operator intends to
Figure 2. Robot moving between walls. move the robot along the centerline between two parallel walls. Because of operational mistakes, the robot deviates from the centerline as shown in Figure 2. The lateral and rotational deviations are denoted by x and , respectively. The position in the vertical direction is denoted by y. In addition, we assume that all distance sensors are located symmet- rically with respect to the centerline and only above the robot’s center of gravity, as shown in the figure. The number of sensors located at the left or right half side of the robot is denoted by N.
The distance between each sensor and the walls is given as follows d
i
f
mu x _
þ 2c
f P N i¼1
p
i
l
m ð25Þ
r
€ ¼ ac f bc
r
Iu
x
_x 2ac f P N
i¼1
p i l i
ac
bc
2
m ð24Þ
u ys b!
s
u
x
ð23Þ Furthermore, assuming that the angle is small and substituting equations (17) to (19) after linearization, controller equations (11) and (12), and distance equa- tions (15) and (16) into equations (21) to (23) yields the following dynamics
€y ¼ f
xr
€x ¼ c r þ c
x
f
mu
x
_x 2c f P N
i¼1
p i l i m x
þ u
I x a
c
þ bc
x ð27Þ where c
, respectively. Then, we can rewrite equation (26) as follows
€ þ c
1
_ þ c
2
¼ c
3
1
’ c
c
3
are positive constants. Equation (27) is a stable system with respect to . In addition, the positive value of x provides a positive steady- state value for , which makes the robot turn left and reduces the magnitude of x. Similarly, when x has a negative value, the negative steady-state value for causes the robot to turn right and reduces the magnitude of x. Hence, this approach is expected to provide the appropriate collision avoidance function.
Experiments
Figure 3 shows the experimental robot equipped with distance sensors and the controller for human operators. The measurable range of the distance sensor is 10–80 cm. Rotary encoders (500 PPR) attached to the motors are used for measuring the robot position and orientation by assuming that the wheel slip is negligible. The proposed controller design is verified in the environment shown in Figure 4, where the robot controlled by six operators is expected to move from the start position to the destination.
In order to achieve the effective collision avoid- ance, it is reasonable to employ a function that pro- vides a larger steering angle and breaking force near obstacles compared with equations (13) and (14).
Uchiyama et al.
r
f
f
f P N i¼1
þ b
2
c
r
Iu
x
_ 2ac
p
To validate the proposed method, we simply con- sider the case that the vehicle’s front and rear sides and the cornering stiffness satisfy a ’ b and c
i
l
i
I ð26Þ where we assume the desired steering angle
d
¼ 0. The breaking force effect appears as in equation (24), and it is obvious that the motion is decelerated when f
xr
is negative. Because the control objective is to reduce the deviation in the x and directions, we only consider equations (25) and (26) for the stability analysis. It should be noted that owing to the nonholonomic con- straint, the robot cannot move instantaneously in the x direction. Hence, we only consider the dynamics in equation (26) for the stability analysis.
r
f
ri
x
Assuming that the robot moves with approximately the constant speed (operating point) ðu
x , u y
, !Þ ¼ ðu
x
, 0, 0Þ as follows u
x
¼ u
þ u
sin ð18Þ
xs
, u
y
¼ u
ys
, !
¼ !
_ ¼ ! ð19Þ
y
ð20Þ where ðu
tan B ð16Þ where L is the half distance between the walls and B is the half width of the robot. l
¼ L x cos
þ l
i
tan B ð15Þ d
li
¼ L þ x cos l
i
i
cos u
is the distance from the robot’s center of gravity to the ith distance sensor along the robot’s center line.
From Figure 2, we obtain the following relations _x ¼ u
x
sin u
y cos
ð17Þ _y ¼ u
x
s
xs , u ys , ! s
þ ac
ð22Þ
x
þ c
f
m!
s
u
x
I _!
s
s
¼ ac
f
u ys þ a!
s
u
x
u
þ a!
Þ is the deviation from the operat- ing point and the steering angle is small. Linearizing equations (8) to (10), we obtain the following linear- ized dynamics m
r
_u
xs
¼ f
xr
ð21Þ m _u
ys
¼ c
u
ys
ys
b!
s
u
x
c
f
u
2281
Proc IMechE Part C: J Mechanical Engineering Science 228(13)
2282
(a) Steering wheel α i n =
1 n d ij
3 n
2 = Accelerator Distance n
=
5 sensors
0.8 d ij
° d
(b) l 1
22.5 Figure 5. Function profile used for collision avoidance.
°
45 d l 2 Distance sensors
°
45 Table 1. Experimental parameters.
Parameter Value Parameter Value d
° r 2
45 2 1=3
3 m
° ) 1 ) 1.33 (kg m 2.0 10 (rad m
22.5 d r 1
2 1=3
3 I ) 2 ) 0.02 (kg m 4.6 10 (rad m
1=3 a
0.09 (m) 1 ) 0.4 (N m 1=3 Figure 3. Experimental robot system. b
0.07 (m) 2 ) 0.5 (N m C f n
15.0 (N/rad)
3 C r 15.0 (N/rad) (a) 900
Goal 27°
10 Start Table 2. Number of collisions occurred for each operator.
600
17 Operator No. Manual Proposed 1200 500
1
3 (b)
2
2
3
1
4
3
5
1
6
2
operating point in ‘‘Stability analysis’’ section is still valid for linearized equations of (28) and (29). Table 1 lists the parameters used in the experiment. Each operator operates the robot under the following conditions: Figure 4. Experimental environment.
1. Without the collision avoidance function (if the We consider the following nonlinear functions instead robot collides with the wall, the operator operates of equations (13) and (14) the robot from the start position again).
2. With the collision avoidance function.
i
g ,
ki
¼ p ffiffiffiffiffiffi k ¼ l, r ð28Þ n d ki In case 2, we consider the worst case that the operator
i
can control only on/off of the translational motion, h ,
ki ffiffiffiffiffiffi
¼ p k ¼ l, r ð29Þ n d
ki
and the breaking and the steering are controlled automatically. Figure 5 shows the profile of these functions in which Table 2 presents the number of collisions for each the parameters are set as operator. No collisions occurred while operating the
i ¼ 0.5 and n ¼ 1, 2, 5.
Regarding to the stability analysis, linearizing equa- robot with the collision avoidance function. tions (28) and (29) leads to equations (13) and (14), Figure 6 compares the time required for each oper- and hence the linear analysis assuming a certain ator to reach the goal. Because the robot collided the
Uchiyama et al.
2283
20 (a)
5 Accelerator ]
Proposed control
15 Voltage [V]
10 Steering
5 Manual control Required time [s
10 Time [s]
1
2
3
4
5
6 Operator’s No. (b)
0.6 y Figure 6. Comparison of required time to reach the goal.
[m]
- 0.6
0.8
1.6 x [m]
5 (a)
Accelerator
1 (c)
Voltage [V] Steering [rad]
10 Time [s]
- –1 Time [s]
10
0.6 (b)
Figure 8. Manual control results. (a) Commanded control y input voltage, (b) robot position, and (c) robot orientation.
[m]
- 0.6
0.8
1.6 x [m]
f d f ¼ 0:23 ðV V Þ ½N ð31Þ
1 (c)
where V and V are control input voltages com-
f
manded by the human operators and V ¼ 2.65 V. In
Figure 7, although the operator does not steer the
[rad]
robot, it successfully moves to the goal by automatic- ally adjusting the steering angle . In Figure 8, the
- –1
10 Time [s]
operator frequently adjusts both the steering wheel and accelerator. However, a collision occurs at
Figure 7. Proposed control results. (a) Commanded control approximately x ¼ 1.8 m in Figure 8(b). These results
confirm the effectiveness of the proposed controller input voltage, (b) robot position, and (c) robot orientation. design using inexpensive distance sensors and simple control input calculations. wall during the trial of all operators, they performed Experimental results show that the proposed con- several trials and the required time was reduced in the trol in equations (11) and (12) can provide successful last trial. The figure shows the required time recorded collision avoidance for the worst case that the oper- in the last trial of the manual control case. On an ator can control only on/off of the translational average, there is no significant difference in the motion. For the case that the operator can control required time to reach the goal with and without the the speed and the steering, the effect of functions g
ki
proposed method. The average times were 9.42 s for and h in equations (11) and (12) may be tuned by
ki
the manual control case and 10.12 s for the proposed changing the values and n in Figure 5. If the oper-
i method.
ator is skillful, the effect should be reduced, otherwise, Figures 7 and 8 compare the operator control with it should be increased. Hence, the proposed control and without the proposed method. Figures 7(a) and may be useful for any level of operators in collision
8(a) show the control input voltage commanded by avoidance. the operator. The control input voltage has the fol- lowing relation to the steering angle and acceler-
d Conclusions
ation force f in equations (11) and (12), respectively
d
This paper presents a new approach to collision avoidance for four-wheeled human-operated mobile
d
¼ f16:2 ðV V Þg ½rad ð30Þ 180 robots using inexpensive infrared distance sensors. Because the proposed method considers the nonholo- nomic constraint of a mobile robot, it provides prac- tical collision avoidance control. The effectiveness of the proposed approach is demonstrated by the results of the experiment, in which all unskilled operators could maneuver the robot to the destination without collisions. In future studies, the presented linear ana- lysis will be extended to more general cases and the proposed robot system will be applied to more com- plex environments.
Funding
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Proc IMechE Part C: J Mechanical Engineering Science 228(13)