Abstract

Two-wheeled self-balancing robot (TWSBR) is a mobile robot with a wide application in security, rescue, entertainment, and other fields. To make the robot obtain a larger range of the controllable inclination angle, a reconfigurable mechanism of the moment of inertia is designed for the TWSBR, and the energy consumption of the reconfigurable mechanism is reduced by a gravity compensation mechanism. This paper constructs a virtual equivalent parallel mechanism (VEPM) to model the robot-ground system combining the robot and the ground. The kinematics, dynamic model, and performance indexes of the VEPM are solved based on the vector method, the Lagrangian dynamics, and the screw theory. Then, the dimensions of the mechanism are optimized based on the comprehensive performance analysis. Finally, the effectiveness of the optimization algorithm and gravity compensation mechanism is verified through simulation and motion experiments. The reconfigurable mechanism enables the TWSBR to stand up, step up, and surmount obstacles. The performance analysis and optimal design approaches proposed in this paper have positive significance for the systematic modeling and optimal design of two-wheeled and two-legged robots.

References

1.
Imtiaz
,
M. A.
,
Naveed
,
M.
,
Bibi
,
N.
,
Aziz
,
S.
, and
Naqvi
,
S. Z. H.
,
2018
, “
Control System Design, Analysis & Implementation of Two Wheeled Self Balancing Robot (TWSBR)
,”
Proceedings of the IEEE 9th Annual Information Technology, Electronics and Mobile Communication Conference
,
Vancouver, Canada
,
Nov. 1–3
, pp.
431
437
.
2.
Zhang
,
J.
,
Zhao
,
T.
,
Guo
,
B.
, and
Dian
,
S.
,
2022
, “
Fuzzy Fractional-Order PID Control for Two-Wheeled Self-balancing Robots on Inclined Road Surface
,”
Syst. Sci. Control Eng.
,
10
(
1
), pp.
289
299
.
3.
Vasudevan
,
H.
,
Dollar
,
A. M.
, and
Morrell
,
J. B.
,
2015
, “
Design for Control of Wheeled Inverted Pendulum Platforms
,”
ASME J. Mech. Rob.
,
7
(
4
), p.
041005
.
4.
Nemec
,
D.
,
Adamkovic
,
D.
,
Hrubos
,
M.
,
Pirnik
,
R.
, and
Mihalik
,
M.
,
2021
, “
Fast Two-Wheeled Balancing Robot
,”
Proceedings of the IEEE 22nd International Carpathian Control Conference
,
Velké Karlovice, Czech Republic
,
May 31–June 1
, pp.
1
9
.
5.
Cui
,
L.
,
Wang
,
S.
,
Zhang
,
J.
,
Zhang
,
D.
,
Lai
,
J.
,
Zheng
,
Y.
,
Zhang
,
Z.
, and
Jiang
,
Z.
,
2021
, “
Learning-Based Balance Control of Wheel-Legged Robots
,”
IEEE Robot. Autom. Lett.
,
6
(
4
), pp.
7667
7674
.
6.
Zhang
,
C.
,
Liu
,
T.
,
Song
,
S.
,
Wang
,
J.
, and
Meng
,
M.
,
2021
, “
Dynamic Wheeled Motion Control of Wheel-Biped Transformable Robots
,”
Biomimetic Intell Rob.
,
2
(
2
), p.
100027
.
7.
Zhao
,
L.
,
Yu
,
Z.
,
Chen
,
X.
,
Huang
,
G.
,
Wang
,
W.
,
Han
,
L.
,
Qiu
,
X.
,
Zhang
,
X.
, and
Huang
,
Q.
,
2021
, “
System Design and Balance Control of a Novel Electrically-Driven Wheel-Legged Humanoid Robot
,”
Proceedings of the IEEE International Conference on Unmanned Systems
,
Beijing, China,
pp.
742
747
.
8.
Luo
,
Z.
,
Shang
,
J.
,
Wei
,
G.
, and
Ren
,
L.
,
2018
, “
A Reconfigurable Hybrid Wheel-Track Mobile Robot Based on Watt II Six-Bar Linkage
,”
Mech. Mach. Theory
,
128
, pp.
16
32
.
9.
Wei
,
J.
, and
Dai
,
J. S.
,
2019
, “
Reconfiguration-Aimed and Manifold-Operation Based Type Synthesis of Metamorphic Parallel Mechanisms With Motion Between 1R2T and 2R1T
,”
Mech. Mach. Theory
,
139
, pp.
66
80
.
10.
Du
,
X.
,
Li
,
Y.
,
Wang
,
P.
,
Ma
,
Z.
,
Li
,
D.
, and
Wu
,
C.
,
2021
, “
Design and Optimization of Solar Tracker With U-PRU-PUS Parallel Mechanism
,”
Mech. Mach. Theory
,
155
, p.
104107
.
11.
Ye
,
W.
,
Chai
,
X.
, and
Zhang
,
K.
,
2020
, “
Kinematic Modeling and Optimization of a New Reconfigurable Parallel Mechanism
,”
Mech. Mach. Theory
,
149
, p.
103850
.
12.
Ahmad
,
A.
,
Andersson
,
K.
, and
Sellgren
,
U.
,
2015
, “
An Optimization Approach Toward a Robust Design of Six Degrees of Freedom Haptic Devices
,”
ASME J. Mech. Des.
,
137
(
4
), p.
042301
.
13.
Aginaga
,
J.
,
Iriarte
,
X.
,
Plaza
,
A.
, and
Mata
,
V.
,
2018
, “
Kinematic Design of a New Four Degree-of-Freedom Parallel Robot for Knee Rehabilitation
,”
ASME J. Mech. Des.
,
140
(
9
), p.
092304
.
14.
Huang
,
G.
,
Guo
,
S.
,
Zhang
,
D.
,
Qu
,
H.
, and
Tang
,
H.
,
2018
, “
Kinematic Analysis and Multi-objective Optimization of a New Reconfigurable Parallel Mechanism With High Stiffness
,”
Robotica
,
36
(
2
), pp.
187
203
.
15.
Wei
,
J.
, and
Dai
,
J. S.
,
2019
, “
Lie Group Based Type Synthesis Using Transformation Configuration Space for Reconfigurable Parallel Mechanisms With Bifurcation Between Spherical Motion and Planar Motion
,”
ASME J. Mech. Des.
,
142
(
6
), p.
063302
.
16.
Ma
,
X.
,
Zhang
,
K.
, and
Dai
,
J.
,
2018
, “
Novel Spherical-Planar and Bennett-Spherical 6R Metamorphic Linkages With Reconfigurable Motion Branches
,”
Mech. Mach. Theory
,
128
, pp.
628
647
.
17.
Gosselin
,
C. M.
,
1989
, “
Determination of the Workspace of 6-DOF Parallel Manipulators
,”
Proceedings of the ASME Design Engineering Technical Conference
, pp.
321
326
.
18.
Arian
,
A.
,
Isaksson
,
M.
, and
Gosselin
,
C. M.
,
2020
, “
Kinematic and Dynamic Analysis of a Novel Parallel Kinematic Schönflies Motion Generator
,”
Mech. Mach. Theory
,
147
, p.
103629
.
19.
Zhao
,
C.
,
Guo
,
H.
,
Zhang
,
D.
,
Liu
,
R.
,
Li
,
Z.
, and
Deng
,
B.
,
2020
, “
Stiffness Modeling of n (3RRlS) Reconfigurable Series-Parallel Manipulators by Combining Virtual Joint Method and Matrix Structural Analysis
,”
Mech. Mach. Theory
,
152
, p.
103960
.
20.
Liu
,
H.
,
Huang
,
T.
,
Chetwynd
,
D. G.
, and
Kecskeméthy
,
A.
,
2017
, “
Stiffness Modeling of Parallel Mechanisms at Limb and Joint/Link Levels
,”
IEEE Trans. Rob.
,
33
(
3
), pp.
734
741
.
21.
Cao
,
W.
,
Xu
,
S.
,
Rao
,
K.
, and
Ding
,
T.
,
2019
, “
Kinematic Design of a Novel Two Degree-of-Freedom Parallel Mechanism for Minimally Invasive Surgery
,”
ASME J. Mech. Des.
,
141
(
10
), p.
104501
.
22.
Zhang
,
D.
, and
Wei
,
B.
,
2017
, “
Modelling and Optimisation of a 4-DOF Hybrid Robotic Manipulator
,”
Int. J. Comput. Integr. Manuf.
,
30
(
11
), pp.
1179
1189
.
23.
Wang
,
J.
,
Wu
,
C.
, and
Liu
,
X.-J.
,
2010
, “
Performance Evaluation of Parallel Manipulators: Motion/Force Transmissibility and Its Index
,”
Mech. Mach. Theory
,
45
(
10
), pp.
1462
1476
.
24.
Wang
,
Z.
,
Zhang
,
N.
,
Chai
,
X.
, and
Li
,
Q.
,
2017
, “
Kinematic/Dynamic Analysis and Optimization of a 2-URR-RRU Parallel Manipulator
,”
Nonlinear Dyn.
,
88
(
1
), pp.
503
519
.
25.
Wang
,
X.
,
Wu
,
J.
, and
Wang
,
Y.
,
2021
, “
Dynamics Evaluation of 2UPU/SP Parallel Mechanism for a 5-DOF Hybrid Robot Considering Gravity
,”
Rob. Auton. Syst.
,
135
, p.
103675
.
26.
Milica
,
L.
,
Năstase
,
A.
, and
Andrei
,
G.
,
2020
, “
A Novel Algorithm for the Absorbed Power Estimation of HEXA Parallel Mechanism Using an Extended Inverse Dynamic Model
,”
Proc. Inst. Mech. Eng. Part K J. Multi-body Dyn.
,
234
(
1
), pp.
185
197
.
27.
Tang
,
H.
,
Zhang
,
D.
, and
Tian
,
C.
,
2022
, “
An Approach for Modeling and Performance Analysis of Three-Leg Landing Gear Mechanisms Based on the Virtual Equivalent Parallel Mechanism
,”
Mech. Mach. Theory
,
169
, p.
104617
.
28.
Ozgur
,
E.
,
Gogu
,
G.
, and
Mezouar
,
Y.
,
2014
, “
Structural Synthesis of Dexterous Hands
,”
Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems
,
Chicago
, pp.
1676
1681
.
29.
Hu
,
Y.
, and
Guo
,
W.
,
2021
, “
A New Concept of Contact Joint to Model the Geometric Foot-Environment Contacts for Efficiently Determining Possible Stances for Legged Robots
,”
Mech. Mach. Theory
,
162
, p.
104327
.
30.
Tang
,
H.
,
Zhang
,
D.
, and
Tian
,
C.
,
2022
, “
A Method for Comprehensive Performance Optimization of Four-Leg Landing Gear Based on the Virtual Equivalent Parallel Mechanism
,”
Mech. Mach. Theory
,
174
, p.
104924
.
31.
Gamba
,
J. D.
, and
Featherstone
,
R.
,
2021
, “
Balancing on a Springy Leg
,”
Proceedings of the IEEE International Conference on Robotics and Automation
,
X’ian, China
,
May 30–June 5
, pp.
4970
4975
.
32.
Nguyen
,
V. L.
,
Lin
,
C. Y.
, and
Kuo
,
C. H.
,
2020
, “
Gravity Compensation Design of Delta Parallel Robots Using Gear-Spring Modules
,”
Mech. Mach. Theory
,
154
, p.
104046
.
33.
Chew
,
D. X. H.
,
Wood
,
K. L.
, and
Tan
,
U.
,
2019
, “
Design of a Passive Self-Regulating Gravity Compensator for Variable Payloads
,”
ASME J. Mech. Des.
,
141
(
10
), p.
102302
.
34.
Zhang
,
L.
, and
Ren
,
X.
,
2020
, “
Comparison of Three Different Wheeled-Hopping Robots
,”
Proceedings of the IEEE 9th Data Driven Control and Learning Systems Conference
,
Liuzhou, China
,
Nov. 20–22
, pp.
1394
1397
.
35.
Vatterott
,
K. H.
,
1978
, “
Berechnungs-und Anwendungsmöglichkeit Einer Polygonzahl
,”
Mech. Mach. Theory
,
13
(
3
), pp.
301
309
.
36.
Zou
,
Q.
,
Zhang
,
D.
, and
Huang
,
G.
,
2022
, “
Dynamic Performance Evaluation of the Parallel Mechanism for a 3T2R Hybrid Robot
,”
Mech. Mach. Theory
,
172
, p.
104794
.
37.
Chen
,
X.
, and
Sun
,
C.
,
2019
, “
Dynamic Modeling of Spatial Parallel Mechanism With Multi-Spherical Joint Clearances
,”
Int. J. Adv. Rob. Syst.
,
16
(
5
), pp.
1
13
.
38.
Wang
,
R.
, and
Zhang
,
X.
,
2017
, “
Parameters Optimization and Experiment of A Planar Parallel 3-DOF Nanopositioning System
,”
IEEE Trans. Ind. Electron.
,
65
(
3
), pp.
2388
2397
.
39.
Zhang
,
D.
,
2013
, “
Improving the Accuracy in Software Effort Estimation: Using Artificial Neural Network Model Based on Particle Swarm Optimization
,”
Proceedings of 2013 IEEE International Conference on Service Operations and Logistics, and Informatics
,
Dongguan, China
,
July 28–30
, pp.
180
185
.
40.
Yang
,
Y.
,
Yao
,
C.
, and
Xu
,
D.
,
2020
, “
Ecological Compensation Standards of National Scenic Spots in Western China: A Case Study of Taibai Mountain
,”
Tour. Manag.
,
76
, p.
103950
.
41.
Wang
,
M.
,
Song
,
Y.
,
Lian
,
B.
,
Wang
,
P.
,
Chen
,
K.
, and
Sun
,
T.
,
2022
, “
Dimensional Parameters and Structural Topology Integrated Design Method of a Planar 5R Parallel Machining Robot
,”
Mech. Mach. Theory
,
175
, p.
104964
.
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