The Dubins traveling salesman problem (DTSP) has generated significant interest over the last decade due to its occurrence in several civil and military surveillance applications. This problem requires finding a curvature constrained shortest path for a vehicle visiting a set of target locations. Currently, there is no algorithm that can find an optimal solution to the DTSP. In addition, relaxing the motion constraints and solving the resulting Euclidean traveling salesman problem (ETSP) provide the only lower bound available for the DTSP. However, in many problem instances, the lower bound computed by solving the ETSP is far below the cost of the feasible solutions obtained by some well-known algorithms for the DTSP. This paper addresses this fundamental issue and presents the first systematic procedure for developing tight lower bounds for the DTSP.

Issue Section:
Research Papers
Keywords:
Autonomous systems, Motion controls, Robotics
Topics:
Algorithms, Vehicles, Turning angles

References

1.
Rathinam
,
S.
,
Sengupta
,
R.
, and
Darbha
,
S.
,
2007
, “
A Resource Allocation Algorithm for Multivehicle Systems With Nonholonomic Constraints
,”
IEEE Trans. Autom. Sci. Eng.
,
4
(
1
), pp.
98
–
104
.
Google Scholar
Crossref
Search ADS
 
2.
Le Ny
,
J.
,
Feron
,
E.
, and
Frazzoli
,
E.
,
2012
, “
On the Dubins Traveling Salesman Problem
,”
IEEE Trans. Autom. Control
,
57
(
1
), pp.
265
–
270
.
Google Scholar
Crossref
Search ADS
 
3.
Chandler
,
P.
, and
Pachter
,
M.
,
1998
, “
Research Issues in Autonomous Control of Tactical UAVS
,”
American Control Conference
(
ACC
), Philadelphia, PA, June 24–26, pp.
394
–
398
.
4.
Medeiros
,
A. C.
, and
Urrutia
,
S.
,
2010
, “
Discrete Optimization Methods to Determine Trajectories for Dubins' Vehicles
,”
Electron. Notes Discrete Math.
,
36
, pp.
17
–
24
.
Google Scholar
Crossref
Search ADS
 
5.
Macharet
,
D.
, and
Campos
,
M.
,
2014
, “
An Orientation Assignment Heuristic to the Dubins Traveling Salesman Problem
,”
Advances in Artificial Intelligence
—
IBERAMIA
2014, Santiago de Chile, Chile, Nov. 24–27, pp.
457
–
468
.
6.
Macharet
,
D. G.
,
Alves Neto
,
A.
,
da Camara Neto
,
V. F.
, and
Campos
,
M. F.
,
2013
, “
Efficient Target Visiting Path Planning for Multiple Vehicles With Bounded Curvature
,”
IEEE/RSJ International Conference on Intelligent Robots and Systems
(
IROS
), Tokyo, Japan, Nov. 3–7, pp.
3830
–
3836
.
7.
Macharet
,
D. G.
,
Neto
,
A. A.
,
da Camara Neto
,
V. F.
, and
Campos
,
M. F.
,
2012
, “
Data Gathering Tour Optimization for Dubins' Vehicles
,”
2012 IEEE Congress on Evolutionary Computation
(
CEC
), Brisbane, Australia, June 10–15, pp.
1
–
8
.
8.
Sujit
,
P.
,
Hudzietz
,
B.
, and
Saripalli
,
S.
,
2013
, “
Route Planning for Angle Constrained Terrain Mapping Using an Unmanned Aerial Vehicle
,”
J. Intell. Rob. Syst.
,
69
(
1–4
), pp.
273
–
283
.
Google Scholar
Crossref
Search ADS
 
9.
Kenefic
,
R. J.
,
2008
, “
Finding Good Dubins Tours for UAVS Using Particle Swarm Optimization
,”
J. Aerosp. Comput. Inf. Commun.
,
5
(
2
), pp.
47
–
56
.
Google Scholar
Crossref
Search ADS
 
10.
Macharet
,
D. G.
,
Neto
,
A. A.
,
da Camara Neto
,
V. F.
, and
Campos
,
M. F.
,
2011
, “
Nonholonomic Path Planning Optimization for Dubins' Vehicles
,”
IEEE International Conference on Robotics and Automation
(
ICRA
), Shanghai, China, May 9–13, pp.
4208
–
4213
.
11.
Tang
,
Z.
, and
Ozguner
,
U.
,
2005
, “
Motion Planning for Multitarget Surveillance With Mobile Sensor Agents
,”
IEEE Trans. Rob.
,
21
(
5
), pp.
898
–
908
.
Google Scholar
Crossref
Search ADS
 
12.
Savla
,
K.
,
Frazzoli
,
E.
, and
Bullo
,
F.
,
2008
, “
Traveling Salesperson Problems for the Dubins Vehicle
,”
IEEE Trans. Autom. Control
,
53
(
6
), pp.
1378
–
1391
.
Google Scholar
Crossref
Search ADS
 
13.
Epstein
,
C.
,
Cohen
,
I.
, and
Shima
,
T.
,
2017
, “On the Discretized Dubins Traveling Salesman Problem,”
IISE Trans.
,
49
(2), pp. 238–254.
14.
Ma
,
X.
, and
Castañón
,
D.
,
2006
, “
Receding Horizon Planning for Dubins Traveling Salesman Problems
,”
45th IEEE Conference on Decision and Control
(
CDC
), San Diego, CA, Dec. 13–15, pp.
5453
–
5458
.
15.
Isaacs
,
J. T.
, and
Hespanha
,
J. P.
,
2013
, “
Dubins Traveling Salesman Problem With Neighborhoods: A Graph-Based Approach
,”
Algorithms
,
6
(
1
), pp.
84
–
99
.
Google Scholar
Crossref
Search ADS
 
16.
Anderson
,
R. P.
, and
Milutinovic
,
D.
,
2014
, “
On the Construction of Minimum-Time Tours for a Dubins Vehicle in the Presence of Uncertainties
,”
ASME J. Dyn. Syst. Meas. Control
,
137
(
3
), p.
031001
.
Google Scholar
Crossref
Search ADS
 
17.
Isaiah
,
P.
, and
Shima
,
T.
,
2015
, “
Motion Planning Algorithms for the Dubins Travelling Salesperson Problem
,”
Automatica
,
53
, pp.
247
–
255
.
Google Scholar
Crossref
Search ADS
 
18.
Oberlin
,
P.
,
Rathinam
,
S.
, and
Darbha
,
S.
,
2010
, “
Today's Traveling Salesman Problem
,”
IEEE Rob. Autom. Mag.
,
17
(
4
), pp.
70
–
77
.
Google Scholar
Crossref
Search ADS
 
19.
Manyam
,
S. G.
,
Rathinam
,
S.
,
Darbha
,
S.
, and
Obermeyer
,
K. J.
,
2015
, “
Lower Bounds for a Vehicle Routing Problem With Motion Constraints
,”
Int. J. Rob. Autom.
,
30
(
3
).https://drive.google.com/file/d/0BxCsQMzYKbV9eFdaWXlPdVMxTGM/view
20.
Manyam
,
S. G.
,
Rathinam
,
S.
, and
Darbha
,
S.
,
2015
, “
Computation of Lower Bounds for a Multiple Depot, Multiple Vehicle Routing Problem With Motion Constraints
,”
ASME J. Dyn. Syst. Meas. Control
,
137
(
9
), p.
094501
.
Google Scholar
Crossref
Search ADS
 
21.
Manyam
,
S. G.
,
Rathinam
,
S.
,
Darbha
,
S.
, and
Obermeyer
,
K. J.
,
2012
, “Computation of a Lower Bound for a Vehicle Routing Problem With Motion Constraints,”
ASME
Paper No. DSCC2012-MOVIC2012-8713.
22.
Manyam
,
S. G.
,
Rathinam
,
S.
, and
Darbha
,
S.
,
2013
, “
Computation of Lower Bounds for a Multiple Depot, Multiple Vehicle Routing Problem With Motion Constraints
,”
IEEE 52nd Annual Conference on Decision and Control
(
CDC
), Florence, Italy, Dec. 10–13, pp.
2378
–
2383
.
23.
Dubins
,
L. E.
,
1957
, “
On Curves of Minimal Length With a Constraint on Average Curvature, and With Prescribed Initial and Terminal Positions and Tangents
,”
Am. J. Math.
,
79
(
3
), pp.
497
–
516
.
Google Scholar
Crossref
Search ADS
 
24.
Manyam
,
S. G.
,
Rathinam
,
S.
,
Casbeer
,
D.
, and
Garcia
,
E.
,
2017
, “
Tightly Bounding the Shortest Dubins Paths Through a Sequence of Points
,”
J. Intell. Rob. Syst.
,
88
(
2–4
), pp.
495
–
511
.
Google Scholar
Crossref
Search ADS
 
25.
Noon
,
C. E.
, and
Bean
,
J. C.
,
1991
, “
A Lagrangian Based Approach for the Asymmetric Generalized Traveling Salesman Problem
,”
Oper. Res.
,
39
(
4
), pp.
623
–
632
.
Google Scholar
Crossref
Search ADS
 
26.
Gutin
,
G.
, and
Punnen
,
A. P.
, eds.,
2002
,
The Traveling Salesman Problem and Its Variations
(Combinatorial Optimization),
Kluwer Academic
,
Dordrecht, The Netherlands
.
27.
Applegate
,
D. L.
,
Bixby
,
R. E.
,
Chvatal
,
V.
, and
Cook
,
W. J.
,
2007
,
The Traveling Salesman Problem: A Computational Study
(Princeton Series in Applied Mathematics),
Princeton University Press
,
Princeton, NJ
.
28.
Goaoc
,
X.
,
Kim
,
H.-S.
, and
Lazard
,
S.
,
2013
, “
Bounded-Curvature Shortest Paths Through a Sequence of Points Using Convex Optimization
,”
SIAM J. Comput.
,
42
(
2
), pp.
662
–
684
.
Google Scholar
Crossref
Search ADS
 
29.
Boissonnat
,
J.-D.
,
Crzo
,
A.
, and
Leblond
,
J.
,
1994
, “
Shortest Paths of Bounded Curvature in the Plane
,”
J. Intell. Rob. Syst.
,
11
(
1–2
), pp.
5
–
20
.
Google Scholar
Crossref
Search ADS
 
30.
Boissonnat
,
J.-D.
, and
Bui
,
X.-N.
,
1994
, “Accessibility Region for a Car That Only Moves Forwards Along Optimal Paths,” INRIA, Saclay, France, Research Report No.
2181
.https://hal.inria.fr/inria-00074491/document
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