Article
Overcoming Kinematic Singularities for Motion Control in a
Caster Wheeled Omnidirectional Robot
Oded Medina
†
and Shlomi Hacohen *
,†
Citation: Medina, O.; Hacohen, S.
Overcoming Kinematic Singularities
for Motion Control in a Caster
Wheeled Omnidirectional Robot.
Robotics 2021, 10, 133. https://
doi.org/10.3390/robotics10040133
Academic Editors: Dario Richiedei
and Marco Ceccarelli
Received: 25 October 2021
Accepted: 8 December 2021
Published: 13 December 2021
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Department of Mechanical Engineering, Ariel University, Ramat HaGolan St. 65, Ariel 4070000, Israel;
odedmed@ariel.ac.il
* Correspondence: shlomiha@ariel.ac.il
† These authors contributed equally to this work.
Abstract:
Omnidirectional planar robots are common these days due to their high mobility, for exam-
ple in human–robot interactions. The motion of such mechanisms is based on specially designed
wheels, which may vary when different terrains are considered. The usage of actuated caster wheels
(ACW) may enable the usage of regular wheels. Yet, it is known that an ACW robot with three actu-
ated wheels needs to overcome kinematic singularities. This paper introduces the kinematic model
for an ACW omni robot. We present a novel method to overcome the kinematic singularities of the
mechanism’s Jacobian matrix by performing the time propagation in the mechanism’s configuration
space. We show how the implementation of this method enables the estimation of caster wheels’
swivel angles by tracking the plate’s velocity. We present the mechanism’s kinematics and trajectory
tracking in real-world experimentation using a novel robot design.
Keywords:
kinematic singularity; caster-wheel; motion control; motion planning; omnidirectional
robot
1. Introduction
Omnidirectional mobile robots are capable of traversing in three dimensions from
any given configuration without steering ([
1
,
2
]), which enables driving through winding
paths with small tracking errors. This nature of omni robots makes them very popular for
industrial [
3
], as well as for academic applications [
4
]. Such robotic platforms commonly
use omni-wheels (e.g., [
5
,
6
]). However, researchers have presented other mechanisms for
omnidirectional robots. Jung and Kim [
7
] developed an omnidirectional wheeled robot
equipped with three conventional wheels actuated by only three motors resulting in no
actuation redundancy. Motors rotational motion is transmitted by a special gear train to the
wheels and to a revolute joint. Karavaev et al. [
8
] introduced a spherical omnidirectional
robot driven by an internal omni wheeled platform.
The use of omni-wheels involves some undesired side effects. For example, Ham-
aguchi [
9
] presented a mechanism and control scheme to reduce the vibrations of omni-
wheeled robots.
The use of caster wheels (CW) is widely used for mobile robots in many applications.
This use is divided into two kinds of operations. In the common one, the CW is not actuated.
For example, it serves as a third contact point with the ground for a differential-steering
mobile-robot, etc. (see for example [
10
,
11
]). Hooks et al. [
12
] presented a quadrupedal
robot having CW in its contact point with the ground. The CW enables the robot to enter
a wheeled mode by lowering itself onto its passive CW, which is far more efficient in
terms of power consumption. In such cases, the CW is not actuated and its velocity or
orientation is not considered. Furthermore, in many cases, as a result of the assumption
of no skidding and slipping, the caster wheels seemingly have no impact on the vehicle
kinematics. However, cases where this assumption does not hold have been investigated.
Robotics 2021, 10, 133. https://doi.org/10.3390/robotics10040133 https://www.mdpi.com/journal/robotics
