Journal of Robotics, Networking and Artificial Life, Vol. 4, No. 1 (June 2017) 45–48___________________________________________________________________________________________________________Obstacle Avoidance Method for Electric Wheelchairs
Based on a Multi-Layered Non-Contact Impedance Model
Haruna Kokubo, Taro Shibanoki

4-12-1 Nakanarusawacho, Hitachi, 316-8511, Ibaraki University, Japan
16nm712n@vc.ibaraki.ac.jp, taro.shibanoki.ts@vc.ibaraki.ac.jp
http://bs.cis.ibaraki.ac.jp/
Takaaki Chin

1070 Akebonocho, Nishi-Ku, Kobe, 651-2181, Hyogo Rehabilitation Center, Japant-chin@pure.ne.jp
Toshio Tsuji

1-3-2 Kagamiyama, Higashi-Hiroshima, 739-8511, Hiroshima University, Japantsuji@bsys.hiroshima-u.ac.jp

Abstract
This paper proposes an obstacle avoidance method based on a multi-layered non-contact impedance model forcontrol of the biosignal-based electric wheelchair. The proposed system can calculate a virtual repulsive force
before the collision by multi-layered impedance fields covered around it. This system therefore regulates desired
path to avoid obstacles in a variety of situations. In the experiments, the mobile robot passed through obstacles
smoothly, and could stop emergently to avoid the obstacle in front of the robot owing to virtual forces calculated by
the proposed model.
Keywords: obstacle avoidance, non-contact impedance, electric wheelchairs, people with disabilities

allow robots to avoid obstacles based on virtual force
and so on, but tend to focus only on maintaining theminimum distance necessary for avoidance. The
application of such technology to biosignal-controlled
electric wheelchairs requires consideration of how toachieve natural movement rather than simple obstacle
avoidance.
In this regard, a method known as non-contact
impedance control supports natural collision prevention[7] – [9]. The technique can be used to generate virtual
external forces that act on the robot based on virtual
impedance between the robot and obstacles. (including
other robots), which allows the robot to steer away fromanything in its path. However, this requires the settingof appropriate parameters for various situations.
Additionally, as such approaches are premised on thecontrol of mobile robots, it is necessary to develop anatural obstacle-avoidance method for biosignalcontrolled electric wheelchairs.
This paper proposes an obstacle avoidance system forelectric wheelchairs based on a non-contact impedancemodel. The system helps to prevent collisions using
mechanical impedance-based covered virtual walls
around the robot. It supports smooth avoidance ofobstacles and enables collision-preventing emergency
stops using virtual walls with different impedance
parameters.

1. Introduction
According to the World Health Organization (WHO),the population of people with disabilities worldwide
accounts for almost 15% and is gradually increasing [1].
Electric wheelchairs and other mobility aids are used
to support disabled people in independent living bycompensating for lost function. In particular, an electric
wheelchair that can be controlled with biosignals suchas electroencephalograms (EEGs) and electromyograms(EMGs) has recently attracted attention [2] - [4]. The
authors’ research group also developed the Cybernetic
Human Robot Interface System (CHRIS), which can beused to operate wheelchairs, domestic appliances, video
games and other equipment using biosignals [4]. The
system has a number of distinctive features, such as
adaptability to input signal variations and various input
types in line with user requirements. However, thesesystems can malfunction due to biosignal fluctuations
associated with unintended motions. It is also necessary
to provide a motion assistance method with theseapproaches, as obstacle avoidance depends on theoperator.
A number of conventional techniques are applied todetermine appropriate paths for distinction based on
artificial potential fields and fuzzy logic using neuralnetworks and other methods [5], [6]. These systems

Copyright © 2017, the Authors. Published by Atlantis Press.
This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).
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Journal of Robotics, Networking and Artificial Life, Vol. 4, No. 1 (June 2017) 45–48___________________________________________________________________________________________________________(1)

1I

(2)

II
I

I

Fig. 1. Kinematics of a mobile robot

2. Control of the mobile robot based on a MultiLayered Non-Contact Impedance ModelIn this study, the mobile robot was compressed into amass point with two translational degrees of freedom(Fig. 1), and motion planning was performed.
The robot can determine the distance between itself
and nearby obstacles using an internal sensor. Multiplevirtual walls based on mechanical impedance are used
to avoid collision with obstacles via calculation ofrelated virtual external forces.
Figure 2 illustrates the concept of the multi-layered
non-contact impedance model. It is considered that 𝑃
obstacles are present in the direction of movement of
the robot, which is surrounded by virtual circles(referred to here as virtual walls) with radii of 𝑞𝑖 ,( 𝑖 = 1, 2, … , 𝐼 ) based on a mechanical impedancemodel.
When the obstacle comes within the 𝑖th virtual wall,the norm vector from the wall’s surface to the obstacle
𝑑𝑿𝑖𝑜 ∈ ℜ2 is represented as𝑑𝑿𝑖𝑜 = 𝑿𝑟 − 𝑞𝑖 𝒏.

Fig. 2. Structure of the proposed multi-layered non-contact
impedance model

Here, 𝑴𝑖 ， 𝑩𝑖 and 𝑲𝑖 are the inertia, damping andspring matrices of the non-contact impedance,respectively. It should be noted that if the obstacle isoutside the 𝑖th virtual wall, the virtual force 𝑭𝑖𝑜 is zero.
The proposed method supports obstacle avoidancewith multi-layered non-contact impedance using various
parameters. The virtual extra force from all obstacles infront of the robot is calculated as𝑃(𝒑)𝑭𝑖𝑜 = � 𝑭𝑖𝑜 .
𝑝=1

Finally, the resultant force acting on the mobile robot in
the non-contact impedance model is defined as𝐼

𝑭𝑜 = � 𝑭𝑖𝑜 .

(1)

𝑖=1

Here, 𝑿𝑟 is the vector of displacement from the centerof the sphere (the mobile robot’s position) 𝑿𝑒 ∈ ℜ2 to(𝑝)the pth obstacle
𝑿𝑜 ∈ ℜ2 ( 𝑝 = 1, 2, … , 𝑃 ). The
direction vector 𝒏 reflecting the distance between themargin of the virtual wall and the obstacle 𝑝 is definedas
𝑿𝑟 = 𝑿𝑒 −𝑿(𝑝)𝑿𝑜 .

𝑟, ‖𝑿𝑟 ‖ ≠ 0.
𝒏 = �‖𝑿𝑟 ‖0, ‖𝑿𝑟 ‖ = 0

(5)

(6)

Additionally, the dynamic equation for the robot
regarding non-contact impedance control is expressed as𝑴𝑒 ∆𝑿̈ + 𝑩𝑒 ∆𝑿̇ + 𝑲𝑒 ∆𝑿 = 𝑭𝑒 + 𝑭𝑜 .
(7)
Here, 𝑴𝑒 ， 𝑩𝑒 and 𝑲𝑒 are the inertia, damping andspring matrices of the robot, respectively.
A displacement vector ∆𝑿 is given using the reference
position 𝑿𝑡 = (𝑥𝑡 , 𝑦𝑡 )T and the current position of therobot 𝑿𝑒 = (𝑥𝑒 , 𝑦𝑒 )T based on ∆𝑿 = 𝑿𝑡 − 𝑿𝑒 . Thelimitations of ∆𝑿 and ∆𝑿̈ [6] and the elements 𝑲𝑒 ∆𝑿and 𝑴𝑒 ∆𝑿̈ in Equation (7) are ignored. Thus, theequation translates to(2)(3)

If the obstacle is inside the virtual wall ( 𝑞𝑖+1 <‖𝑿𝑟 ‖ ≤ 𝑞𝑖 ), the virtual impedance between the robot
and the obstacle causes exertion of a virtual external
force on the robot:
𝑭𝑖𝑜𝑴 𝑑𝑿𝚤̈ + 𝑩𝑖 𝑑𝑿𝚤𝑜̇ + 𝑲𝑖 𝑑𝑿𝑖𝑜 , 𝑞𝑖+1 < ‖𝑿𝑟 ‖ ≤ 𝑞𝑖. (4)=� 𝑖 𝑜0, 𝑜𝑜ℎ𝑒𝑒𝑒𝑒𝑒𝑒

𝑩𝑒 ∆𝑿̇ = 𝑭𝑒 + 𝑭𝑜 .

(8)1∆𝑿̇ = (𝑭𝑒 + 𝑭𝑜 ).

(9)

In Equation (8), the velocity increment ∆𝑿̇ is calculatedas𝑩𝑒46

Journal of Robotics, Networking and Artificial Life, Vol. 4, No. 1 (June 2017) 45–48___________________________________________________________________________________________________________Finally, 𝑿𝑣̇ is defined as the velocity of control thatallows the robot to avoid an obstacle using
3.

𝑿𝑣̇ = 𝑿𝑒̇ − ∆𝑿̇.

(10)

Simulation Experiment3.1. Experimental Conditions
To evaluate the efficacy of the proposed method, twosimulation experiments were performed with immobile
obstacles located (1) randomly and (2) along the path ofmovement. Simulations confirm whether the robot canemergently stop before collision as well as pass throughobstacles using proposed method only.
The robot had an initial position of (0.0, 0.0) [m] andmoved toward a target position (5.0, 0.0) [m] with an
initial speed of (0.6, 0.0) [m/s] in experiment (1). In
experiment (2), the robot moved in a straight line at a
speed of (0.2, 0.0) [m/s]. The parameters used in thesimulation were 𝐼 = 1 , 𝑞1 = 0.6 [m], 𝑴1 =(10.0, 10.0) [kg], 𝑩1 = (5.0, 5.0) [Nm/s], 𝑲1 =(10.0, 10.0) [N/s] for experiment (1), and 𝐼 = 2 ,𝑞1 = 0.6 [m], 𝑴1 = (0.21, 0.21) [kg], 𝑩1 = (0.8, 0.8)
[Nm/s], 𝑲1 = (1.0, 1.0) [N/ m], 𝑞2 = 0.4 [m], 𝑴2 =(16.8, 16.8) [kg], 𝑩2 = (12.6, 12.6) [Nm/s], 𝑲2 =(1000.0, 1000.0) [N/s] for experiment (2).

Fig. 3. Trajectories of each experiment3.2. Results and discussion

Fig. 4. Velocities and virtual forces of each experiment

Figures 3 and 4 show the results of the experiments((a) for (1) and (b) for (2)). Figure 3 shows the paths of
the robot in each experiment, and Fig. 4 shows, from
top to bottom, velocities (overall and x-/y-axis) andvirtual forces in each direction under the proposed
method.
It can be seen from Fig. 3 (a) that the robot passed
straight by two obstacles and altered its path to avoid
another on the right. After the avoidance maneuver, therobot corrected its path toward the target position,
avoided obstacles on the left and finally arrived at thetarget position. Figure 4 (a) shows that the robot slowed
down due to virtual forces from the presence of twoobstacles under the proposed method at around 1.0 [s]before sensing virtual forces from behind andaccelerating to avoid an obstacle at 1.8 [s]. The robot
adjusted its velocity as appropriate in response to virtual
impedance forces indicating the distance from obstacles
on each side.

Figures 3 (b) and 4 (b) show other obstacles in therobot’s path after collision avoidance. The robot
decelerated gradually, and finally stopped before
collision under the influence of virtual forces from thevirtual wall with higher stiffness parameters from theobstacle at around 9.4 [s].
The results indicate that the proposed method supports
collision avoidance in various situations.
4. Practical Experiment
A trajectory-tracking control experiment using an
actual mobile robot (iRobot Create 2, iRobot Corp.) was
performed with the position coordinates detailed inSection 3. The target electric wheelchairs generally havepairs of propulsion and caster wheels, but a control
method for a robot with two independently driven
wheels was considered here for simplicity. Sufficient
friction between the drive wheels and the floor to avoid
wheel spin was assumed.

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Journal of Robotics, Networking and Artificial Life, Vol. 4, No. 1 (June 2017) 45–48___________________________________________________________________________________________________________multiple virtual walls based on a mechanical impedancemodel are located around the robot, enabling natural
avoidance of obstacles and emergency stops to prevent
collisions. In simulation and practical experiments using
the method, the robot avoided obstacles in response tovirtual forces based on the model.
In future research, the authors plan to implement themethod using distance image sensors and apply it inoperation of an actual biosignal-controlled wheelchair[4] to evaluate its effectiveness.
Acknowledgements
This work was supported by JSPS KAKENHI Grant
Number JP26330226.

Fig. 5. Experimental results for practical experiment

References

The position coordinates were regarded as target points
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and target position coordinates were used to determine
target velocity, which was defined for each wheel (𝑣𝐿 ,𝑣𝑅 )T using the distance 𝐿 𝑇 and direction 𝜃𝑇 between therobot and the target position as(11)𝑣𝐿 = 𝐾𝑣 ∙ 𝐿 𝑇 + ∆𝑣,(12)𝑣𝑅 = 𝐾𝑣 ∙ 𝐿 𝑇 − ∆𝑣,∆𝑣 = 𝐾𝑡 𝜃𝑇 + 𝐾𝑡𝑡 𝜃𝑇̇ .
(13)Here, 𝐾𝑣 , 𝐾𝑡 and 𝐾𝑡𝑡 are pre-set constants.
Figure 5 (a) shows the paths observed in the simulationand practical experiments. Solid lines show the resultsof 10 trials in the practical experiment. Hardly any
difference between the results of the two conditions isobserved. Figure 5 (b) shows tracking in the sixth trial.
As in the simulation experiment, the robot detected theobstacle and decelerated to pass by it with individual
wheel velocity regulation in response to virtual reaction
forces with the proposed model. The robot subsequently
decelerated to avoid collision with other obstacles along
its path in response to alternate contact with outer andinner virtual walls.
These results indicate that the proposed multi-layered
non-contact impedance model enables obstacle
avoidance in various situations. However, the scope ofthe tracking experiment was limited to the conditions
reported here; no experiment using an actual biosignalcontrolled electric wheelchair was conducted. The
authors plan to verify the efficacy of the proposed
method with implementation of the model using range
sensors.
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Conclusion

This paper proposes a multi-layered non-contact
impedance model and its application to obstacle
avoidance for electric wheelchairs. In this method,48