Abstract

Calculating the maximum obstacle-crossing ability accurately at the mechanism design stage can better ensure that the manufactured robot prototype meets the predefined indices. The obstacle-crossing task of the legged robot is achieved by the collaborative movement of the leg and body. The reachable workspace constrains the spatial movement boundary of the foot tip and the robot body. The reachable workspace of the foot tip is invariant, while the shape and volume of the reachable body workspace vary with the supporting footholds. In this study, the body movement is modeled as a six-bar mechanism, and the reachable body workspace means the reachable region of the specified target point located on the moving platform of the six-bar mechanism. Unlike the previous work, the analytical method of calculating the reachable workspace for the target point outside the moving platform, named the external target point, is further studied. The influence of supporting footholds and shank-ground interference on the reachable body workspace is considered. The selection of supporting footholds, the collaborative motion sequences of the robot body and legs, and the determination of the maximum ability for crossing a ditch and climbing a step are demonstrated as cases of implementing the analytical reachable body workspace for the internal target point and the external target point, respectively. Finally, simulations verify the correctness of the theoretical analysis.

References

1.
Wang
,
G. Y.
,
Ding
,
L.
,
Gao
,
H. B.
,
Deng
,
Z. Q.
,
Liu
,
Z.
, and
Yu
,
H. T.
,
2020
, “
Minimizing the Energy Consumption for a Hexapod Robot Based on Optimal Force Distribution
,”
IEEE Access
,
8
, pp.
5393
5406
.
2.
Peng
,
S. J.
,
Ding
,
X. L.
,
Yang
,
F.
, and
Xu
,
K.
,
2017
, “
Motion Planning and Implementation for the Self-Recovery of an Overturned Multi-Legged Robot
,”
Robotica
,
35
(
5
), pp.
1107
1120
.
3.
Lee
,
J.
,
Hwangbo
,
J.
,
Wellhausen
,
L.
,
Koltun
,
V.
, and
Hutter
,
M.
,
2020
, “
Learning Quadrupedal Locomotion Over Challenging Terrain
,”
Sci. Rob.
,
5
(
47
), p.
eabc5986
.
4.
Chen
,
J. W.
,
Xu
,
K.
, and
Ding
,
X. L.
,
2022
, “
Adaptive Gait Planning for Quadruped Robot Based on Center of Inertia Over Rough Terrain
,”
Biomim. Intelli. Rob.
,
2
(
1
), p.
100031
.
5.
Yang
,
C. Y.
,
Yuan
,
K.
,
Zhu
,
Q. G.
,
Yu
,
W. M.
, and
Li
,
Z. B.
,
2020
, “
Multi-Expert Learning of Adaptive Legged Locomotion
,”
Sci. Rob.
,
5
(
49
), p.
eabb2174
.
6.
Bellicoso
,
C. D.
,
Bjelonic
,
M.
,
Wellhausen
,
L.
,
Holtmann
,
K.
,
G
F
nther
,
F.
,
Tranzatto
,
M.
,
Fankhauser
,
P.
, and
Hutter
,
M.
,
2018
, “
Advances in Real-World Applications for Legged Robots
,”
J. Field Rob.
,
35
(
8
), pp.
1311
1326
.
7.
Tang
,
Z.
,
Qi
,
P.
, and
Dai
,
J. S.
,
2017
, “
Mechanism Design of a Biomimetic Quadruped Robot
,”
Ind. Rob.
,
44
(
4
), pp.
512
520
.
8.
Zhang
,
C. S.
,
Zhang
,
C.
,
Dai
,
J. S.
, and
Qi
,
P.
,
2019
, “
Stability Margin of a Metamorphic Quadruped Robot With a Twisting Trunk
,”
ASME J. Mech. Rob.
,
11
(
6
), p.
064501
.
9.
Zhang
,
C. S.
, and
Dai
,
J. S.
,
2018
, “
Trot Gait With Twisting Trunk of a Metamorphic Quadruped Robot
,”
J. Bionic Eng.
,
15
(
6
), pp.
971
981
.
10.
Xu
,
P.
,
Ding
,
L.
,
Wang
,
Z. K.
,
Gao
,
H. B.
,
Zhou
,
R. Y.
,
Gong
,
Z. P.
, and
Liu
,
G. J.
,
2022
, “
Contact Sequence Planning for Hexapod Robots in Sparse Foothold Environment Based on Monte-Carlo Tree
,”
IEEE Robot. Autom. Lett.
,
7
(
2
), pp.
826
833
.
11.
Li
,
H. Y.
,
Qi
,
C. K.
,
Chen
,
X. B.
,
Mao
,
L. H.
,
Zhao
,
Y.
, and
Gao
,
F.
,
2021
, “
Stair Climbing Capability-Based Dimensional Synthesis for the Multi-Legged Robot
,”
Proceedings of the IEEE International Conference on Robotics and Automation (ICRA)
,
Xi'an, China
,
May 30–June 5
, pp.
2950
2956
.
12.
Chen
,
Z. J.
,
Liu
,
J. M.
, and
Gao
,
F.
,
2022
, “
Real-Time Gait Planning Method for ix-Legged Robots to Optimize the Performances of Terrain Adaptability and Walking Speed
,”
Mech. Mach. Theory
,
168
, p.
104545
.
13.
Pan
,
Y.
,
Gao
,
F.
, and
Du
,
H.
,
2016
, “
Fault Tolerance Criteria and Walking Capability Analysis of a Novel Parallel-Parallel Hexapod Walking Robot
,”
Robotica
,
34
(
3
), pp.
619
633
.
14.
Wang
,
Z. Y.
,
Ding
,
X. L.
, and
Rovetta
,
A.
,
2010
, “
Analysis of Typical Locomotion of a Symmetric Hexapod Robot
,”
Robotica
,
28
(
6
), pp.
893
907
.
15.
He
,
J.
, and
Gao
,
F.
,
2015
, “
Type Synthesis for Bionic Quadruped Walking Robots
,”
J. Bionic Eng.
,
12
(
4
), pp.
527
538
.
16.
Zhang
,
J. Z.
,
Jin
,
Z. L.
, and
Feng
,
H. B.
,
2018
, “
Type Synthesis of a 3-Mixed-DOF Protectable leg Mechanism of a Firefighting Multi-Legged Robot Based on G(F) Set Theory
,”
Mech. Mach. Theory
,
130
, pp.
567
584
.
17.
Li
,
L. Q.
,
Fang
,
Y. F.
,
Guo
,
S.
,
Qu
,
H. B.
, and
Wang
,
L.
,
2020
, “
Type Synthesis of a Class of Novel 3-DOF Single-Loop Parallel Leg Mechanisms for Walking Robots
,”
Mech. Mach. Theory
,
145
, p.
103695
.
18.
Han
,
Y. C.
,
Guo
,
W. Z.
,
Peng
,
Z. K.
,
He
,
M. D.
,
Gao
,
F.
, and
Yang
,
J. Z.
,
2021
, “
Dimensional Synthesis of the Reconfigurable Legged Mobile Lander With Multi-Mode and Complex Mechanism Topology
,”
Mech. Mach. Theory
,
155
, p.
104097
.
19.
Chen
,
J.
,
Liang
,
Z. C.
,
Zhu
,
Y. H.
, and
Zhao
,
J.
,
2019
, “
Improving Kinematic Flexibility and Walking Performance of a Six-Legged Robot by Rationally Designing Leg Morphology
,”
J. Bionic Eng.
,
16
(
4
), pp.
608
620
.
20.
Kang
,
R.
,
Meng
,
F.
,
Chen
,
X. C.
,
Yu
,
Z. G.
,
Fan
,
X. X.
,
Ming
,
A. G.
, and
Huang
,
Q.
,
2020
, “
Structural Design and Crawling Pattern Generator of a Planar Quadruped Robot for High-Payload Locomotion
,”
Sensors
,
20
(
22
), p.
6543
.
21.
Guo
,
W.
,
Cai
,
C. R.
,
Li
,
M. T.
,
Zha
,
F. S.
,
Wang
,
P. F.
, and
Wang
,
K. N.
,
2017
, “
A Parallel Actuated Pantograph Leg for High-Speed Locomotion
,”
J. Bionic Eng.
,
14
(
2
), pp.
202
217
.
22.
Russo
,
M.
,
Herrero
,
S.
,
Altuzarra
,
O.
, and
Ceccarelli
,
M.
,
2018
, “
Kinematic Analysis and Multi-Objective Optimization of a 3-UPR Parallel Mechanism for a Robotic leg
,”
Mech. Mach. Theory
,
120
, pp.
192
202
.
23.
Semini
,
C.
,
Barasuol
,
V.
,
Goldsmith
,
J.
,
Frigerio
,
M.
,
Focchi
,
M.
,
Gao
,
Y. F.
, and
Caldwell
,
D. G.
,
2017
, “
Design of the Hydraulically Actuated, Torque-Controlled Quadruped Robot HyQ2Max
,”
IEEE/ASME Trans. Mechatron.
,
22
(
2
), pp.
635
646
.
24.
Davliakos
,
I.
,
Roditis
,
I.
,
Lika
,
K.
,
Breki
,
C. M.
, and
Papadopoulos
,
E.
,
2018
, “
Design, Development, and Control of a Tough Electrohydraulic Hexapod Robot for Subsea Operations
,”
Adv. Rob.
,
32
(
9
), pp.
477
499
.
25.
Han
,
Y. C.
,
Guo
,
W. Z.
,
Zhao
,
D. H.
, and
Li
,
Z. Y.
,
2022
, “
Multi-Mode Unified Modeling and Operation Capability Synergistic Evaluation for the Reconfigurable Legged Mobile Lander
,”
Mech. Mach. Theory
,
171
, p.
104714
.
26.
Wu
,
J. X.
,
Yao
,
Y. A.
,
Li
,
Y. B.
,
Wang
,
S.
, and
Ruan
,
Q.
,
2019
, “
Design and Analysis of a Sixteen-Legged Vehicle With Reconfigurable Close-Chain Leg Mechanisms
,”
ASME J. Mech. Rob.
,
11
(
5
), p.
055001
.
27.
Wu
,
J. X.
,
Yang
,
H.
,
Li
,
R. M.
,
Ruan
,
Q.
,
Yan
,
S. Z.
, and
Yao
,
Y. A.
,
2021
, “
Design and Analysis of a Novel Octopod Platform With a Reconfigurable Trunk
,”
Mech. Mach. Theory
,
156
, p.
104134
.
28.
Wei
,
C. R.
,
Yao
,
Y. A.
,
Wu
,
J. X.
, and
Liu
,
R.
,
2020
, “
Development and Analysis of a Closed-Chain Wheel-Leg Mobile Platform
,”
Chin. J. Mech. Eng.
,
33
(
1
), p.
80
.
29.
Loc
,
V. G.
,
Koo
,
I. M.
,
Tran
,
D. T.
,
Park
,
S.
,
Moon
,
H.
, and
Choi
,
H. R.
,
2011
, “
Improving Traversability of Quadruped Walking Robots Using Body Movement in 3D Rough Terrains
,”
Robot. Auton. Syst.
,
59
(
12
), pp.
1036
1048
.
30.
Mao
,
L. H.
,
Gao
,
F.
,
Tian
,
Y.
, and
Zhao
,
Y.
,
2020
, “
Novel Method for Preventing Shin-Collisions in Six-Legged Robots by Utilizing a Robot-Terrain Interference Model
,”
Mech. Mach. Theory
,
151
, p.
103897
.
31.
Loc
,
V. G.
,
Koo
,
I. M.
,
Tran
,
D. T.
,
Park
,
S.
,
Moon
,
H.
, and
Choi
,
H. R.
,
2012
, “
Body Workspace of Quadruped Walking Robot and Its Applicability in Legged Locomotion
,”
J. Intell. Rob. Syst.
,
67
(
3–4
), pp.
271
284
.
32.
Agheli
,
M.
, and
Nestinger
,
S. S.
,
2014
, “
Comprehensive Closed-Form Solution for the Reachable Workspace of 2-RPR Planar Parallel Mechanisms
,”
Mech. Mach. Theory
,
74
, pp.
102
116
.
33.
Rastgar
,
H.
,
Naeimi
,
H. R.
, and
Agheli
,
M.
,
2019
, “
Characterization, Validation, and Stability Analysis of Maximized Reachable Workspace of Radially Symmetric Hexapod Machines
,”
Mech. Mach. Theory
,
137
, pp.
315
335
.
34.
Li
,
H. Y.
,
Qi
,
C. K.
,
Gao
,
F.
,
Chen
,
X. B.
,
Zhao
,
Y.
, and
Chen
,
Z. J.
,
2022
, “
Mechanism Design and Workspace Analysis of a Hexapod Robot
,”
Mech. Mach. Theory
,
174
, p.
104917
.
35.
Rudin
,
N.
,
Kolvenbach
,
H.
,
Tsounis
,
V.
, and
Hutter
,
M.
,
2022
, “
Cat-Like Jumping and Landing of Legged Robots in Low Gravity Using Deep Reinforcement Learning
,”
IEEE Trans. Rob.
,
38
(
1
), pp.
317
328
.
36.
Kenneally
,
G.
,
De
,
A.
, and
Koditschek
,
D. E.
,
2016
, “
Design Principles for a Family of Direct-Drive Legged Robots
,”
IEEE Robot. Autom. Lett.
,
1
(
2
), pp.
900
907
.
37.
Chen
,
T.
,
Li
,
Y. B.
,
Rong
,
X. W.
,
Zhang
,
G. T.
,
Chai
,
H.
,
Bi
,
J.
, and
Wang
,
Q. S.
,
2021
, “
Design and Control of A Novel Leg-Arm Multiplexing Mobile Operational Hexapod Robot
,”
IEEE Robot. Autom. Lett.
,
7
(
1
), pp.
382
389
.
38.
Li
,
H. Y.
,
Qi
,
C. K.
,
Mao
,
L. H.
,
Zhao
,
Y.
,
Chen
,
X. B.
, and
Gao
,
F.
,
2021
, “
Staircase-Climbing Capability-Based Dimension Design of a Hexapod Robot
,”
Mech. Mach. Theory
,
164
, p.
104400
.
You do not currently have access to this content.