Abstract

In this work, we show that the differential kinematics of slider–pusher systems are differentially flat assuming quasi-static behavior and frictionless contact. Second, we demonstrate that the state trajectories are invariant to time-differential transformations of the path parametrizing coordinate. For one this property allows to impose arbitrary velocity profiles on the slider without impacting the geometry of the state trajectory. This property implies that certain path planning problems may be decomposed approximately into a strictly geometric path planning and an auxiliary throughput speed optimization problem. Building on these insights, we elaborate a numerical approach tailored to constrained time optimal collision free path planning and apply it to the slider–pusher system.

Issue Section:
Research Papers
Topics:
Collisions (Physics), Kinematics, Optimization, Path planning, Geometry, Trajectories (Physics)

References

1.
Yu
,
K.-T.
,
Bauza
,
M.
,
Fazeli
,
N.
, and
Rodriguez
,
A.
,
2016
, “
More Than a Million Ways to Be Pushed. A High-Fidelity Experimental Dataset of Planar Pushing
,”
IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)
, Daejeon, South Korea, Oct. 9–14, pp.
30
–
37
.
2.
Hogan
,
F. R.
, and
Rodriguez
,
A.
,
2020
, “
Feedback Control of the Pusher-Slider System: A Story of Hybrid and Underactuated Contact Dynamics
,”
Algorithmic Foundations of Robotics XII
,
Springer
,
Cham, Switzerland
, pp.
800
–
815
.
3.
Mason
,
M. T.
,
1986
, “
Mechanics and Planning of Manipulator Pushing Operations
,”
Int. J. Rob. Res.
,
5
(
3
), pp.
53
–
71
.10.1177/027836498600500303
4.
Goyal
,
S.
,
Ruina
,
A.
, and
Papadopoulos
,
J.
,
1991
, “
Planar Sliding With Dry Friction Part 1. Limit Surface and Moment Function
,”
Wear
,
143
(
2
), pp.
307
–
330
.10.1016/0043-1648(91)90104-3
5.
Goyal
,
S.
,
Ruina
,
A.
, and
Papadopoulos
,
J.
,
1991
, “
Planar Sliding With Dry Friction Part 2. Dynamics of Motion
,”
Wear
,
143
(
2
), pp.
331
–
352
.10.1016/0043-1648(91)90105-4
6.
Bauza
,
M.
, and
Rodriguez
,
A.
,
2017
, “
A Probabilistic Data-Driven Model for Planar Pushing
,” IEEE International Conference on Robotics and Automation (
ICRA
), Singapore, May 29–June 3, pp.
3008
–
3015
.10.1109/ICRA.2017.7989345
7.
Doshi
,
N.
,
Hogan
,
F. R.
, and
Rodriguez
,
A.
,
2020
, “
Hybrid Differential Dynamic Programming for Planar Manipulation Primitives
,” 2020 IEEE International Conference on Robotics and Automation (
ICRA
), Paris, France, May 31–Aug. 31, pp.
6759
–
6765
.10.1109/ICRA40945.2020.9197414
8.
Raghunathan
,
A. U.
,
Jha
,
D. K.
, and
Romeres
,
D.
,
2022
, “
PyROBOCOP: Python-Based Robotic Control & Optimization Package for Manipulation
,”
International Conference on Robotics and Automation
(
ICRA
), Philadelphia, PA,
May 23–27
, pp.
985
–
991
.10.1109/ICRA46639.2022.9812069
9.
Lynch
,
K. M.
,
Maekawa
,
H.
, and
Tanie
,
K.
,
1992
, “
Manipulation and Active Sensing by Pushing Using Tactile Feedback
,”
Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems
, Raleigh, NC, July 7–10, pp.
416
–
421
.10.1109/IROS.1992.587370
10.
Fliess
,
M.
,
Lévine
,
J.
,
Martin
,
P.
, and
Rouchon
,
P.
,
1995
, “
Flatness and Defect of Non-Linear Systems: Introductory Theory and Examples
,”
Int. J. Control
,
61
(
6
), pp.
1327
–
1361
.10.1080/00207179508921959
11.
Rigatos
,
G. G.
,
2015
, “
Differential Flatness Theory and Flatness-Based Control
,”
Nonlinear Control and Filtering Using Differential Flatness Approaches
,
Springer International Publishing
, Cham, Switzerland, pp.
47
–
101
.https://link.springer.com/chapter/10.1007/978-3-319-16420-5_2
12.
Stoican
,
F.
,
Prodan
,
I.
, and
Popescu
,
D.
,
2015
, “
Flat Trajectory Generation for Way-Points Relaxations and Obstacle Avoidance
,” 23rd Mediterranean Conference on Control and Automation (
MED
), Torremolinos, Spain, June 16–19, pp.
695
–
700
.10.1109/MED.2015.7158827
13.
Stoican
,
F.
,
Ivănuşcă
,
V.-M.
,
Prodan
,
I.
, and
Popescu
,
D.
,
2016
, “
Obstacle Avoidance Via B-Spline Parametrizations of Flat Trajectories
,” 24thMediterranean Conference on Control and Automation (
MED
), Athens, Greece, June 21–24, pp.
1002
–
1007
.10.1109/MED.2016.7536053
14.
Stoican
,
F.
,
Prodan
,
I.
,
Popescu
,
D.
, and
Ichim
,
L.
,
2017
, “
Constrained Trajectory Generation for UAV Systems Using a B-Spline Parametrization
,” 25th Mediterranean Conference on Control and Automation (
MED
), Valletta, Malta, July 3–6, pp.
613
–
618
.10.1109/MED.2017.7984185
15.
Greeff
,
M.
, and
Schoellig
,
A. P.
,
2018
, “
Flatness-Based Model Predictive Control for Quadrotor Trajectory Tracking
,” IEEE/RSJ International Conference on Intelligent Robots and Systems (
IROS
), Madrid, Spain, Oct. 1–5, pp.
6740
–
6745
.10.1109/IROS.2018.8594012
16.
Helling
,
S.
,
Lutz
,
M.
, and
Meurer
,
T.
,
2020
, “
Flatness-Based MPC for Underactuated Surface Vessels in Confined Areas
,”
IFAC-PapersOnLine
,
53
(
2
), pp.
14686
–
14691
.10.1016/j.ifacol.2020.12.1831
17.
Faessler
,
M.
,
Franchi
,
A.
, and
Scaramuzza
,
D.
,
2018
, “
Differential Flatness of Quadrotor Dynamics Subject to Rotor Drag for Accurate Tracking of High-Speed Trajectories
,”
IEEE Rob. Autom. Lett.
,
3
(
2
), pp.
620
–
626
.10.1109/LRA.2017.2776353
18.
Aguilar-Ibáñez
,
C.
,
Sira-Ramírez
,
H.
,
Suárez-Castañón
,
M. S.
,
Martínez-Navarro
,
E.
, and
Moreno-Armendariz
,
M. A.
,
2012
, “
The Trajectory Tracking Problem for an Unmanned Four-Rotor System: Flatness-Based Approach
,”
Int. J. Control
,
85
(
1
), pp.
69
–
77
.10.1080/00207179.2011.638328
19.
Thounthong
,
P.
,
Sikkabut
,
S.
,
Poonnoy
,
N.
,
Mungporn
,
P.
,
Yodwong
,
B.
,
Kumam
,
P.
,
Bizon
,
N.
,
Nahid-Mobarakeh
,
B.
, and
Pierfederici
,
S.
,
2018
, “
Nonlinear Differential Flatness-Based Speed/Torque Control With State-Observers of Permanent Magnet Synchronous Motor Drives
,”
IEEE Trans. Ind. Appl.
,
54
(
3
), pp.
2874
–
2884
.10.1109/TIA.2018.2800678
20.
Joševski
,
M.
, and
Abel
,
D.
,
2015
, “
Flatness-Based Model Predictive Control for the Fuel Optimization of Hybrid Electric Vehicles
,”
IFAC-PapersOnLine
,
48
(
23
), pp.
464
–
470
.10.1016/j.ifacol.2015.11.322
21.
Greeff
,
M.
, and
Schoellig
,
A. P.
,
2021
, “
Exploiting Differential Flatness for Robust Learning-Based Tracking Control Using Gaussian Processes
,”
IEEE Control Syst. Lett.
,
5
(
4
), pp.
1121
–
1126
.10.1109/LCSYS.2020.3009177
22.
Debrouwere
,
F.
,
Van Loock
,
W.
,
Pipeleers
,
G.
,
Diehl
,
M.
,
Swevers
,
J.
, and
De Schutter
,
J.
,
2013
, “
Convex Time-Optimal Robot Path Following With Cartesian Acceleration and Inertial Force and Torque Constraints
,”
Proc. Inst. Mech. Eng., Part I
,
227
(
10
), pp.
724
–
732
.10.1177/0959651813502644
23.
Verscheure
,
D.
,
Demeulenaere
,
B.
,
Swevers
,
J.
,
De Schutter
,
J.
, and
Diehl
,
M.
,
2009
, “
Time-Optimal Path Tracking for Robots: A Convex Optimization Approach
,”
IEEE Trans. Autom. Control
,
54
(
10
), pp.
2318
–
2327
.10.1109/TAC.2009.2028959
24.
Murphy
,
K. P.
,
2012
,
Machine Learning: A Probabilistic Perspective
,
MIT Press
, Cambridge, MA.
Copyright © 2023 by ASME
You do not currently have access to this content.