This paper presents a methodology for trajectory planning and tracking control of a tractor with a steerable trailer based on the system’s dynamic model. The theory of differential flatness is used as the basic approach in these developments. Flat outputs are found that linearize the system’s dynamic model using dynamic feedback linearization, a subclass of differential flatness. It is demonstrated that this property considerably simplifies motion planning and the development of controller. Simulation results are presented in the paper, which show that the developed controller has the desirable performance with exponential stability.

Issue Section:
Research Papers
Keywords:
asymptotic stability, mobile robots, nonlinear dynamical systems, path planning
Topics:
Control equipment, Dynamic models, Feedback, Path planning, Simulation results, Trajectories (Physics), Stability, Wheels, Mobile robots
1.
1998,
Robot Motion Planning and Control
(
Lecture Notes in Control and Information Sciences
), 1st ed.,
J.
Laumond
, ed.,
Springer
,
New York
, Chap. 4.
2.
Oriolo
,
G.
,
De Luca
,
A.
, and
Vendittelli
,
M.
, 2002, “
WMR Control via Dynamic Feedback Linearization: Design, Implementation, and Experimental Validation
,”
IEEE Trans. Control Syst. Technol.
1063-6536,
10
(
6
), pp.
835
–
852
.
Crossref
Search ADS
 
3.
Dixon
,
W.
,
Dawson
,
D.
,
Zergeroglu
,
E.
, and
Zhang
,
F.
, 2000, “
Robust Tracking and Regulation Control for Mobile Robots
,”
Int. J. Robust Nonlinear Control
1049-8923,
10
(
4
), pp.
199
–
216
.
Crossref
Search ADS
 
4.
Samson
,
C.
, and
Ait-Abderrahim
,
K.
, 1991, “
Feedback Control of a Nonholonomic Wheeled Cart in Cartesian Space
,”
Proceedings of the IEEE International Conference on Robotics and Automation
, pp.
1136
–
1141
.
5.
d’Andrea Novel
,
B.
,
Bastin
,
G.
, and
Campion
,
G.
, 1991, “
Modelling and Control of Non Holonomic Wheeled Mobile Robots
,”
Proceedings of the IEEE International Conference on Robotics and Automation
, pp.
1130
–
1135
.
6.
Samson
,
C.
, 1993, “
Time-Varying Feedback Stabilization of Car-Like Wheeled Mobile Robots
,”
Int. J. Robot. Res.
0278-3649,
12
(
1
), pp.
55
–
64
.
Crossref
Search ADS
 
7.
d’Andrea Novel
,
B.
,
Campion
,
G.
, and
Bastin
,
G.
, 1995, “
Control of Nonholonomic Wheeled Mobile Robots by State Feedback Linearization
,”
Int. J. Robot. Res.
0278-3649,
14
(
6
), pp.
543
–
559
.
Crossref
Search ADS
 
8.
Campion
,
G.
,
Bastin
,
G.
, and
d’Andrea Novel
,
B.
, 1996, “
Structural Properties and Classification of Kinematic and Dynamic Models of Wheeled Mobile Robots
,”
IEEE Trans. Rob. Autom.
1042-296X,
12
(
1
), pp.
47
–
61
.
Crossref
Search ADS
 
9.
Fierro
,
R.
, and
Lewis
,
F. L.
, 1997, “
Control of Nonholonomic Mobile Robot: Backstepping Kinematics Into Dynamics
,”
J. Rob. Syst.
0741-2223,
14
(
3
), pp.
149
–
163
.
Crossref
Search ADS
 
10.
Kim
,
B.
, and
Tsiotras
,
P.
, 2002, “
Controllers for Unicycle-Type Wheeled Robots: Theoretical Results and Experimental Validation
,”
IEEE Trans. Rob. Autom.
1042-296X,
18
(
3
), pp.
294
–
307
.
11.
Wang
,
D.
, and
Xu
,
G.
, 2003, “
Full-State Tracking and Internal Dynamics of Nonholonomic Wheeled Mobile Robots
,”
IEEE/ASME Trans. Mechatron.
1083-4435,
8
(
2
), pp.
203
–
214
.
Crossref
Search ADS
 
12.
Pathak
,
K.
, and
Agrawal
,
S.
, 2005, “
An Integrated Path-Planning and Control Approach for Nonholonomic Unicycles Using Switched Local Potentials
,”
IEEE Trans. Rob. Autom.
1042-296X,
21
(
6
), pp.
1201
–
1208
.
Crossref
Search ADS
 
13.
Murray
,
R.
, and
Sastry
,
S.
, 1991, “
Steering Nonholonomic Systems in Chained Form
,”
Proceedings of the IEEE Conference on Decision and Control
, pp.
1121
–
1126
.
14.
Rouchon
,
P.
,
Fliess
,
M.
,
Levine
,
J.
, and
Martin
,
P.
, 1993, “
Flatness and Motion Planning: The Car With n Trailers
,”
Proceedings of the European Control Conference
, pp.
1518
–
1522
.
15.
Jiang
,
B.
,
Liu
,
X.
,
Qi
,
X.
, and
Zhang
,
S.
, 1994, “
Nonlinear Feedback and Robust Tracking Control of Articulated Vehicles
,”
Proceedings of the IEEE Conference on Control Applications
, pp.
373
–
378
.
16.
DeSantis
,
R.
, 1994, “
Path-Tracking for a Tractor-Trailer-Like Robot
,”
Int. J. Robot. Res.
0278-3649,
13
(
6
), pp.
533
–
543
.
Crossref
Search ADS
 
17.
Bushnell
,
L.
,
Tilbury
,
D.
, and
Sastry
,
S.
, 1995, “
Steering Three-Input Nonholonomic Systems: The Fire Truck Example
,”
Int. J. Robot. Res.
0278-3649,
14
(
4
), pp.
366
–
381
.
Crossref
Search ADS
 
18.
Lamiraux
,
F.
, and
Laumond
,
J.
, 1998, “
A Practical Approach to Feedback Control for a Mobile Robot With Trailer
,”
Proceedings of the IEEE International Conference on Robotics and Automation
, Vol.
4
, pp.
3291
–
3296
.
19.
Hao
,
Y.
, and
Agrawal
,
S.
, 2005, “
Formation Planning and Control of UGVs With Trailers
,”
Auton. Rob.
0929-5593,
19
(
3
), pp.
257
–
270
.
Crossref
Search ADS
 
20.
Orosco-Guerrero
,
R.
,
Aranda-Bricaire
,
E.
, and
Velasco-Villa
,
M.
, 2002, “
Modeling and Dynamic Feedback Linearization of a Multi-Steered n-Trailer
,”
Proceedings of the 2002 IFAC, 15th Triennial Congress
,
Barcelona, Spain
.
21.
Fliess
,
M.
,
Levine
,
J.
,
Martin
,
P.
, and
Rouchon
,
P.
, 1995, “
Flatness and Defect of Non-Linear Systems: Introductory Theory and Examples
,”
Int. J. Control
0020-7179,
61
(
6
), pp.
1327
–
1361
.
Crossref
Search ADS
 
22.
Sira-Ramirez
,
H.
, and
Agrawal
,
S. K.
, 2004,
Differential Flat Systems
, 1st ed.,
Dekker
, New York.
23.
Ryu
,
J.-C.
,
Agrawal
,
S. K.
, and
Franch
,
J.
, 2007, “
Motion Planning and Control of a Tractor With a Steerable Trailer Using Differential Flatness
,”
Proceedings of the International Design Engineering Technical Conference (IDETC)
, Paper No. DETC2007-35288.
Copyright © 2008
 by American Society of Mechanical Engineers
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