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IEEJ International Workshop on Sensing, Actuation, Motion Control, and Optimization
Obstacle Avoidance of Omnidirectional Mobile Robots
in Consideration of Motion Performance
Yuta Ando∗Non-member, Masahide Ito∗a) Senior Member
This paper addresses an obstacle avoidance problem of omnidirectional mobile robots. To resolve the problem, the
authors present a trajectory tracking controller based on model predictive control. The main feature of the proposed
controller is to design it under linear approximation so as to keep motion performance. The proposed controller was
validated by experimental results including comparison with the conventional one.
Keywords: omnidirectional mobile robots, obstacle avoidance, model predictive control, linear approximation
1. Introduction
Nowadays, our society has been trying to introduce au-
tonomous technologies increasingly such as autonomous driv-
ing and artificial intelligence. To advance such technologies,
RoboCup (1) provides us with a good research and/or develop-
ment platform. In particular, the Soccer Small Size League
(SSL) focuses on autonomous robotic soccer by using omni-
directional mobile robots.
In the SSL, each team has 11 robots to compete a soc-
cer game automatically thanks to global vision and wire-
less communication. An automatic referee system was in-
troduced in 2018 because no human referee could have cor-
rectly judged plays occurred in a fast-paced game on a large
field (12 m ×9 m). Since then, crashing between two robots
of different teams has been severely and frequently detected
during a game. A foul taken by crashing means to disadvan-
tage the team. On the other hand, to dominate a game, even
basic skills such as passing and keeping the ball require high-
performance motion control. Therefore, obstacle avoidance
while keeping motion performance is important.
To achieve such obstacle avoidance, this paper presents a
trajectory tracking controller based on model predictive con-
trol (MPC). Kimura, et al. (3) have proposed an MPC-based
controller for vehicles. Their controller achieves obstacle
avoidance even though limiting constraints to be linear re-
duces computational cost. The motion performance, however,
can be deteriorated under a certain condition. To overcome
the drawback, the authors propose introducing another linear
constraints in this paper. The effectiveness of the proposed
method is demonstrated by experimental results.
2. MPC-based Obstacle Avoidance in Considera-
tion of Motion Performance
MPC is a real-time optimal control method with two main
features—the one is to exploit prediction of system behavior
based on its mathematical model and another is to handle
constraints of the system. For an obstacle avoidance problem,
a) Correspondence to: masa-ito@ist.aichi-pu.ac.jp
∗School of Info. Sci. and Tech., Aichi Prefectural University,
1522-3 Ibaragabasama, Nagakute, Aichi 480-1198, Japan.
this paper concentrates on designing the constraints.
The authors have designed a trajectory tracking controller
based on linear MPC to improve motion performance of an
omnidirectional robot under certain constraints (2). This pa-
per also use the same model and performance index with in
Ref. (2). A omnidirectional mobile robot can be modeled as
𝒙(𝑘+1)=𝒙(𝑘) + 𝑇𝑠𝜶𝒖 (𝑘−𝐻𝑤)
𝒚(𝑘)=𝒙(𝑘)(1)
where 𝒙is state, 𝒖is input, 𝒚is output, 𝑇𝑠is sampling time,
𝐻𝑤is time delay, and 𝛼is scaling parameter, respectively; the
performance index for trajectory tracking is represented as
𝑉(𝑘)=
𝐻𝑝
Õ
𝑗=𝐻𝑤
ˆ
𝒚(𝑘+𝑗|𝑘) − 𝒚★(𝑘+𝑗|𝑘)
2
Q ( 𝑗)
+
𝐻𝑢
Õ
𝑗=0
ˆ
𝒖(𝑘+𝑗|𝑘) − 𝒖★(𝑘+𝑗|𝑘)
2
R ( 𝑗)(2)
where ˆ·is a predicted variable, ·★is a reference variable, and
Qand Rare the weight matrices, respectively.
In this paper, consider an obstacle avoidance problem that
a robot starting from an initial position moves to a target po-
sition so as not to collide an obstacle on the way (see Fig. 1).
Suppose that any obstacle is static and also is shaped as a
circle. Let 𝑤𝒑𝑟(𝑘),𝑤𝒑𝑜𝑖, and 𝑟𝑜𝑖be a robot position, the
position and radius of the 𝑖th obstacle. If a obstacle itself is
considered as a prohibited area (PA), the PA is formulated by
the following inequality:
Fig. 1. A robot, an obstacle, and two kinds of PAs
©2021 The Institute of Electrical Engineers of Japan.
Fig. 2. Four target positions and three obstacles
k𝑤𝒑𝑟(𝑘) − 𝑤𝒑𝑜𝑖k2≥𝑟𝑜𝑖.(3)
To handle a quadratic constraint (3) in a linear MPC manner,
it must be approximated to the linear one. Instead of the
constraint (3), Ref. (3) has introduced
(𝑤𝒑𝑐−𝑤𝒑𝑜𝑖)⊤𝑤𝒑𝑟(𝑘)>𝑤𝒑⊤
𝑐(𝑤𝒑𝑐−𝑤𝒑𝑜𝑖),(4)
which corresponds to a linear approximation based on Taylor
series expansion at a tangent point 𝑤𝒑𝑟(𝑘)=𝑤𝒑𝑐. Their
method, however, deteriorates the motion performance under
a certain condition. To overcome the drawback, this paper
proposes another linear constraint instead of Eq. (4). The
point of our proposed constraint is to limit the tangential lines
of the obstacle circle to the one crossing the robot position.
Using such tangential lines can introduces the following in-
equalities based on different PAs from the conventional one:
±sin(𝜙±𝛾) ∓ cos(𝜙±𝛾)𝑤𝒑𝑟(𝑘)<0,
where
𝜙:=atan2(𝑤𝑦𝑜𝑖−𝑤𝑦𝑟,𝑤𝑥𝑜𝑖−𝑤𝑥𝑟),
𝛾:=asin 𝑑𝑜𝑖
k𝑤𝒑𝑟(𝑘) − 𝑤𝒑𝑜k2
.
3. Experiment
This section evaluates the proposed method via experi-
ments using a real robot. In the experiments, the robot
drives along the four sides of a rectangular as shown in
Fig. 2. Each vertex is a target position for the robot on
each side. On three of the four sides, there are virtual and
static obstacles that the robot should avoid. The target posi-
tions are 𝑤𝒑1=[−2.8 m,−2.8 m]⊤,𝑤𝒑2=[2.8 m,−2.8 m]⊤,
𝑤𝒑3=[2.8 m,2.8 m]⊤,𝑤𝒑4=[−2.8 m,2.8 m]⊤, and
𝑤𝒑5=𝑤𝒑1; the obstacles is placed at 𝑤𝒑𝑜1
=[2 m,−2 m]⊤,
𝑤𝒑𝑜2
=[3.3 m,1.8 m]⊤, and 𝑤𝒑𝑜3
=[2.7 m,0 m]⊤with ra-
dius 𝑟𝑜𝑖
=1 m, 𝑖 =1,2,3. The target position is changed
to the next one, i.e., its index is increased, when satisfying
k𝑤𝒑𝑟−𝑤𝒑𝑖k2<0.02 m on the way. Generating a reference
trajectory for every side is based on a trapezoid profile of
velocity consisting of a constant velocity 3 m/s and accelera-
tion/deceleration ±4 m/s2.
The experimental results are summarized in Fig. 3. For
comparison, Fig. 3 includes not only a result when using the
proposed method but also results when using the conventional
one and when not avoiding obstacles.
Firstly, from Fig. 3 (a), it can be seen that the proposed
method achieves obstacle avoidance better than the conven-
tional one. In the case of the conventional method, the robot
(a) trajectories on the field
0 2 4 6 8 10 12 14 16
time (s)
-4
-2
0
2
wy (m)
(b) time history of 𝑤𝑦
Fig. 3. Experimental results
completely traversed the second and third obstacles; in the
case of the proposed method, the robot slightly traversed the
first and second obstacles. For as much penetration as in the
latter case, it can be resolved by enlarging the size of the PA
more than that of the obstacle. Secondly, Fig. 3 (b) shows
that the robot using the proposed method reached at the last
target position about 2.70 s faster than the case using the con-
ventional one; motion when using the proposed method is
only about 0.75 s slower than that without avoiding obstacles.
Therefore, it can be said that the proposed method realizes
obstacle avoidance while keeping motion performance.
4. Concluding Remarks
This paper presented an MPC-based trajectory tracking
controller that achieves both avoiding obstacles and keeping
the motion performance. The effectiveness of the proposed
method was experimentally validated. Our future works in-
clude extending this method so as to avoid moving obstacles.
Acknowledgment
This work was partially supported by JSPS KAKENHI
Grant Number JP16K00430.
References
( 1 ) RoboCup Objective, RoboCup Federation official website, accessed on Jan
2021. [Online]. Available:https://www.robocup.org/objective
( 2 ) R. Suzuki and M. Ito: “Trajectory tracking controller based on linear model
predictive control for omni-wheeled mobile robots with velocity command
limits,” Proc. SAMCON’19, Paper No. V1-7, Chiba, Japan, 2019.
( 3 ) K. Kimura, et al.: “Real-time model predictive obstacle avoidance control
for vehicles with reduced computational effort using constraints of prohibited
region,” Mech. Eng. J., Vol.2, No. 3, 2015; DOI: 10.1299/mej.14-00568.
