Abstract

The wrench capability analysis of an aerial parallel robot named flying parallel robot (FPR), which involves multiple unmanned aerial vehicles (UAVs) cooperatively supporting a moving platform with rigid links, is investigated in this article. The concept of the available thrust set (ATS) associated with a quadrotor system is introduced, which allows to determine the admissible range of thrust forces generated by a quadrotor actuator given its actuation limits. Under the quasi-static equilibrium condition, the available wrench set (AWS) of the platform is calculated, through the derivation of a wrench matrix that relates the thrust force vectors to the wrench exerted on the platform. A quantitative metric, referred to as capacity margin, is adopted to evaluate the wrench capability of the system with certain robot configurations. The detailed analysis is showcased through several case studies and validated in both ROS simulations and experiments conducted on a real robot.

Issue Section:
Research Papers
Keywords:
mechanism synthesis and analysis, mechanisms and robots, multirobot systems, parallel robots, aerial systems
Topics:
Equilibrium (Physics), Robots, Thrust, Simulation

References

1.
Gouttefarde
,
M.
,
Daney
,
D.
, and
Merlet
,
J. P.
,
2011
, “
Interval-Analysis-Based Determination of the Wrench-Feasible Workspace of Parallel Cable-Driven Robots
,”
IEEE Trans. Robot.
,
27
(
1
), pp.
1
–
13
.
Google Scholar
Crossref
Search ADS
 
2.
Bouchard
,
S.
,
Gosselin
,
C.
, and
Moore
,
B.
,
2010
, “
On the Ability of a Cable-Driven Robot to Generate a Prescribed Set of Wrenches
,”
ASME J. Mech. Rob.
,
2
(
1
), p.
011010
.
Google Scholar
Crossref
Search ADS
 
3.
Carpentier
,
J.
,
Budhiraja
,
R.
, and
Mansard
,
N.
,
2017
, “
Learning Feasibility Constraints for Multi-Contact Locomotion of Legged Robots
,” 2
017 Robotics: Science and Systems (RSS)
,
Cambridge, MA
, July, Vol. 13.
4.
Fernbach
,
P.
,
Tonneau
,
S.
, and
Taix
,
M.
,
2018
, “
CROC: Convex Resolution of Centroidal Dynamics Trajectories to Provide a Feasibility Criterion for the Multi Contact Planning Problem
,”
2018 IEEE International Conference on Intelligent Robots and Systems (IROS)
,
Madrid, Spain
, pp.
8367
–
8373
.
5.
Orsolino
,
R.
,
Focchi
,
M.
,
Mastalli
,
C.
,
Dai
,
H.
,
Caldwell
,
D. G.
, and
Semini
,
C.
,
2018
, “
Application of Wrench-Based Feasibility Analysis to the Online Trajectory Optimization of Legged Robots
,”
IEEE Robot. Automat. Lett.
,
3
(
4
), pp.
3363
–
3370
.
Google Scholar
Crossref
Search ADS
 
6.
Carpentier
,
J.
, and
Mansard
,
N.
,
2018
, “
Multi-Contact Locomotion of Legged Robots
,”
IEEE Trans. Robot.
,
34
(
6
), pp.
1441
–
1460
.
Google Scholar
Crossref
Search ADS
 
7.
Aceituno-Cabezas
,
B.
,
Mastalli
,
C.
,
Dai
,
H.
,
Focchi
,
M.
,
Radulescu
,
A.
,
Caldwell
,
D. G.
,
Cappelletto
,
J.
,
Grieco
,
J. C.
,
Fernández-López
,
G.
, and
Semini
,
C.
,
2018
, “
Simultaneous Contact, Gait, and Motion Planning for Robust Multilegged Locomotion via Mixed-Integer Convex Optimization
,”
IEEE Robot. Automat. Lett.
,
3
(
3
), pp.
2531
–
2538
.
Google Scholar
Crossref
Search ADS
 
8.
Orsolino
,
R.
,
Focchi
,
M.
,
Caron
,
S.
,
Raiola
,
G.
,
Barasuol
,
V.
, and
Semini
,
C.
,
2020
, “
Feasible Region: An Actuation-Aware Extension of the Support Region
,”
IEEE Trans. Robot.
,
36
(
4
), pp.
1239
–
1255
.
Google Scholar
Crossref
Search ADS
 
9.
Miller
,
A. T.
, and
Allen
,
P. K.
,
2004
, “
Grasp It! A Versatile Simulator for Robotic Grasping
,”
IEEE Robot. Automat. Mag.
,
11
(
4
), pp.
110
–
122
.
Google Scholar
Crossref
Search ADS
 
10.
Borst
,
C.
,
Fischer
,
M.
, and
Hirzinger
,
G.
,
2004
, “
Grasp Planning: How to Choose a Suitable Task Wrench Space
,”
2004 IEEE International Conference on Robotics and Automation (ICRA)
,
New Orleans, LA
, Vol. 1, pp.
319
–
325
.
11.
Krug
,
R.
,
Lilienthal
,
A. J.
,
Kragic
,
D.
, and
Bekiroglu
,
Y.
,
2016
, “
Analytic Grasp Success Prediction With Tactile Feedback
,”
2016 IEEE International Conference on Robotics and Automation (ICRA)
,
Stockholm, Sweden
,
IEEE
, pp.
165
–
171
.
12.
Michael
,
N.
,
Fink
,
J.
, and
Kumar
,
V.
,
2010
, “Cooperative Manipulation and Transportation With Aerial Robots,”
Robotics: Science and Systems V
,
The MIT Press
, pp.
73
–
86
.
13.
Erskine
,
J.
,
Chriette
,
A.
, and
Caro
,
S.
,
2019
, “
Wrench Analysis of Cable-Suspended Parallel Robots Actuated by Quadrotors UAVs
,”
ASME J. Mech. Rob.
,
11
(
2
), p.
020909
.
Google Scholar
Crossref
Search ADS
 
14.
Sanalitro
,
D.
,
Savino
,
H. J.
,
Tognon
,
M.
,
Cortés
,
J.
, and
Franchi
,
A.
,
2020
, “
Full-Pose Manipulation Control of a Cable-Suspended Load With Multiple UAVs Under Uncertainties
,”
IEEE Robot. Autom. Lett.
,
5
(
2
), pp.
2185
–
2191
.
Google Scholar
Crossref
Search ADS
 
15.
Nguyen
,
H. N.
,
Park
,
S.
,
Park
,
J.
, and
Lee
,
D.
,
2018
, “
A Novel Robotic Platform for Aerial Manipulation Using Quadrotors as Rotating Thrust Generators
,”
IEEE Trans. Robot.
,
34
(
2
), pp.
353
–
369
.
Google Scholar
Crossref
Search ADS
 
16.
Li
,
Z.
,
Bégoc
,
V.
,
Chriette
,
A.
, and
Fantoni
,
I.
,
2022
, “
Wrench Capability Analysis and Control Allocation of a Collaborative Multi-Drone Grasping Robot
,”
ASME J. Mech. Rob.
,
15
(
2
), p.
021003
.
Google Scholar
Crossref
Search ADS
 
17.
Six
,
D.
,
Briot
,
S.
,
Chriette
,
A.
, and
Martinet
,
P.
,
2018
, “
The Kinematics, Dynamics and Control of a Flying Parallel Robot With Three Quadrotors
,”
IEEE Robot. Autom. Lett.
,
3
(
1
), pp.
559
–
566
.
Google Scholar
Crossref
Search ADS
 
18.
Liu
,
S.
,
Erskine
,
J.
,
Chriette
,
A.
, and
Fantoni
,
I.
,
2021
, “
Decentralized Control and Teleoperation of a Multi-UAV Parallel Robot Based on Intrinsic Measurements
,”
2021 IEEE International Conference on Intelligent Robots and Systems (IROS)
,
Prague, Czech Republic
, pp.
6329
–
6355
.
19.
Liu
,
S.
,
Fantoni
,
I.
,
Chriette
,
A.
, and
Six
,
D.
,
2022
, “
Wrench Estimation and Impedance-Based Control Applied to a Flying Parallel Robot Interacting With the Environment
,”
IFAC-PapersOnLine
,
55
(
14
), pp.
151
–
157
.
Google Scholar
Crossref
Search ADS
 
20.
Liu
,
S.
,
Fantoni
,
I.
, and
Chriette
,
A.
,
2024
, “
Decentralized Control and State Estimation of a Flying Parallel Robot Interacting With the Environment
,”
Control. Eng. Pract.
,
144
, p.
105817
.
Google Scholar
Crossref
Search ADS
 
21.
Rasheed
,
T.
,
Long
,
P.
, and
Caro
,
S.
,
2020
, “
Workspace of Mobile Cable-Driven Parallel Robots
,”
ASME J. Mech. Rob.
,
12
(
3
), p.
031009
.
Google Scholar
Crossref
Search ADS
 
22.
Gouttefarde
,
M.
, and
Krut
,
S.
,
2010
, “Characterization of Parallel Manipulator Available Wrench Set Facets,”
Advances in Robot Kinematics: Motion in Man and Machine
,
J.
Lenarcic
 and
M. M.
Stanisic
, eds.,
Springer
,
Netherlands
, pp.
475
–
482
.
23.
Herceg
,
M.
,
Kvasnica
,
M.
,
Jones
,
C. N.
, and
Morari
,
M.
,
2013
, “
Multi-Parametric Toolbox 3.0
,”
2013 European Control Conference (ECC)
,
Zurich, Switzerland
, pp.
502
–
510
.
24.
Guay
,
F.
,
Cardou
,
P.
,
Cruz Ruiz
,
A. L.
, and
Caro
,
S.
,
2014
, “Measuring How Well a Structure Supports Varying External Wrenches,”
New Advances in Mechanisms, Transmissions and Applications Mechanisms and Machine Science
,
V.
Petuya
,
C.
Pinto
, and
E.-C.
Lovasz
, eds., Vol. 17,
Springer
,
Dordrecht
, pp.
385
–
392
.
Google Scholar
Crossref
Search ADS
 
25.
PX4
, “PX4-Autopilot Simulation Package Web Page (PX4-Autopilot),” https://docs.px4.io/v1.12/en/simulation/gazebo, Accessed June 2021.
Copyright © 2025 by ASME
You do not currently have access to this content.