In this paper, we solve the motion planning problem for a class of underactuated multibodied planar mechanical systems. These systems interact with the environment via viscous frictional forces. The motion planning problem is solved by specifying the location of friction pads on the robot as well as by specifying the input of the actuated degrees of freedom. Moreover, through the proposed novel motion planning analysis, we identify the simplest planar swimming robot, the two-link swimmer.

References

References
1.
Laumond
,
J.-P.
,
1987
, “
Finding Collision-Free Smooth Trajectories for a Non-Holonomic Mobile Robot
,”
10th International Joint Conference on Artificial (IJCAI)
, pp.
1120
1123
.
2.
Laumond
,
J.-P.
,
Jacobs
,
P. E.
,
Taix
,
M.
, and
Murray
,
R. M.
,
1994
, “
A Motion Planner for Nonholonomic Mobile Robots
,”
IEEE Trans. Rob. Autom.
,
10
(
5
), pp.
577
593
.10.1109/70.326564
3.
Li
,
Z.
, and
Canny
,
J.
,
1990
, “
Motion of Two Rigid Bodies With Rolling Constraint
,”
IEEE Trans. Rob. Autom.
,
6
(
1
), pp.
62
72
.10.1109/70.88118
4.
Laumond
,
J.-P.
,
1986
, “
Feasible Trajectories for Mobile Robots With Kinematic and Environment Constraints
,”
Intelligent Autonomous Systems, International Conference
, North-Holland Publishing Co., Amsterdam, The Netherlands, pp.
346
354
.
5.
Murray
,
R. M.
, and
Sastry
,
S. S.
,
1993
, “
Nonholonomic Motion Planning: Steering Using Sinusoids
,”
IEEE Trans. Autom. Control
,
38
(
5
), pp.
700
716
.10.1109/9.277235
6.
Barraquand
,
J.
, and
Latombe
,
J.-C.
,
1991
, “
Robot Motion Planning: A Distributed Representation Approach
,”
Int. J. Rob. Res.
,
10
(
6
), pp.
628
649
.10.1177/027836499101000604
7.
Canny
,
J.
,
1988
,
The Complexity of Robot Motion Planning
,
MIT Press
, Cambridge, MA.
8.
Lafferriere
,
G.
, and
Sussmann
,
H. J.
,
1993
, “
A Differential Geometric Approach to Motion Planning
,”
Nonholonomic Motion Planning
,
Springer
, New York, pp.
235
270
.
9.
Bloch
,
A. M.
,
2003
,
Nonholonomic Mechanics and Control
, Vol.
24
,
Springer
, New York.10.1007/b97376
10.
Choset
,
H. M.
,
2005
,
Principles of Robot Motion: Theory, Algorithms, and Implementation
,
MIT Press
, Cambridge, MA.
11.
Bullo
,
F.
,
2005
,
Geometric Control of Mechanical Systems
, Vol.
49
,
Springer
, New York.10.1007/978-1-4899-7276-7
12.
Tsakiris
,
D. P.
,
1995
, “
Motion Control and Planning for Nonholonomic Kinematic Chains
,” DTIC Document, Maryland Univ., College Park Inst. for Systems Research, Technical Report No. ISR-PHD-95-4.
13.
Krishnaprasad
,
P.
, and
Tsakiris
,
D. P.
,
2001
, “
Oscillations, SE (2)-Snakes and Motion Control: A Study of the Roller Racer
,”
Dyn. Syst.: Int. J.
,
16
(
4
), pp.
347
397
.10.1080/14689360110090424
14.
Bloch
,
A. M.
,
Krishnaprasad
,
P.
,
Marsden
,
J. E.
, and
Murray
,
R. M.
,
1996
, “
Nonholonomic Mechanical Systems With Symmetry
,”
Arch. Ration. Mech. Anal.
,
136
(
1
), pp.
21
99
.10.1007/BF02199365
15.
Lafferriere
,
G.
, and
Sussmann
,
H.
,
1990
, “
Motion Planning for Controllable Systems Without Drift: A Preliminary Report
,” Rutgers University Systems and Control Center, Report No. SYCON-90-04.
16.
Sussmann
,
H. J.
,
1991
, “
Local Controllability and Motion Planning for Some Classes of Systems With Drift
,”
30th IEEE Conference
, Brighton, Dec. 11–13, pp.
1110
1114
.10.1109/CDC.1991.261504
17.
Ladd
,
A. M.
, and
Kavraki
,
L. E.
,
2005
, “
Motion Planning in the Presence of Drift, Underactuation and Discrete System Changes
,”
Robotics: Science and Systems
, pp.
233
240
.
18.
Mason
,
R.
, and
Burdick
,
J.
,
1999
, “
Propulsion and Control of Deformable Bodies in an Ideal Fluid
,”
IEEE International Conference on Robotics and Automation
, Detroit, MI, Vol.
1
, pp.
773
780
.10.1109/ROBOT.1999.770068
19.
Kanso
,
E.
,
Marsden
,
J. E.
,
Rowley
,
C. W.
, and
Melli-Huber
,
J.
,
2005
, “
Locomotion of Articulated Bodies in a Perfect Fluid
,”
J. Nonlinear Sci.
,
15
(
4
), pp.
255
289
.10.1007/s00332-004-0650-9
20.
Kanso
,
E.
, and
Marsden
,
J.
,
2005
, “
Optimal Motion of an Articulated Body in a Perfect Fluid
,” 44th IEEE Conference on Decision and Control, 2005 and 2005 European Control Conference (
CDC-ECC’05
), Dec. 12–15, pp.
2511
2516
.10.1109/CDC.2005.1582540
21.
Melli
,
J. B.
,
Rowley
,
C. W.
, and
Rufat
,
D. S.
,
2006
, “
Motion Planning for an Articulated Body in a Perfect Planar Fluid
,”
SIAM J. Appl. Dyn. Syst.
,
5
(
4
), pp.
650
669
.10.1137/060649884
22.
Melsaac
,
K.
, and
Ostrowski
,
J.
,
1999
, “
A Geometric Approach to Anguilliform Locomotion: Modelling of an Underwater Eel Robot
,”
IEEE International Conference on Robotics and Automation
, Vol.
4
, pp.
2843
2848
.
23.
Chernous’ko
,
F.
,
1999
, “
The Wavelike Motion of a Multilink System on a Horizontal Plane
,”
J. Appl. Math. Mech.
,
64
(
4
), pp.
497
508
.10.1016/S0021-8928(00)00075-7
24.
Chernous’ko
,
F.
,
2001
, “
Controllable Motions of a Two-Link Mechanism Along a Horizontal Plane
,”
J. Appl. Math. Mech.
,
65
(
4
), pp.
565
577
.10.1016/S0021-8928(01)00062-4
25.
Chernous’ko
,
F.
,
2005
, “
Modelling of Snake-Like Locomotion
,”
Appl. Math. Comput.
,
164
(2), pp.
415
434
.10.1016/j.amc.2004.06.057
26.
Chernous’ko
,
F.
, and
Shunderyuk
,
M. M.
,
2010
, “
The Influence of Friction Forces on the Dynamics of a Two-Link Mobile Robot
,”
Appl. Math. Comput.
,
74
, pp.
13
23
.
27.
Figurina
,
T.
,
2004
, “
Quasi-Static Motion of a Two-Link System Along a Horizontal Plane
,”
Multibody Syst. Dyn.
,
11
(
3
), pp.
251
272
.10.1023/B:MUBO.0000029391.77348.40
28.
Burton
,
L. J.
,
Hatton
,
R. L.
,
Choset
,
H.
, and
Hosoi
,
A. E.
,
2010
, “
Two Link Swimming Using Buoyant Orientation
,”
Phys. Fluids
,
22
(9), p.
091703
.10.1063/1.3481785
29.
Melli
,
J.
, and
Rowley
,
C.
,
2010
, “
Models and Control of Fish-Like Locomotion
,”
Exp. Mech.
,
50
(
9
), pp.
1355
1360
.10.1007/s11340-010-9349-z
30.
Babikian
,
S.
,
Shammas
,
E.
, and
Asmar
,
D.
,
2012
, “
Motion Planning for a Two-Link Planar Robot in a Viscous Environment
,”
IEEE International Conference on Intelligent Robots and Systems
(
IROS
), Vilamoura, Oct. 7–12, pp.
888
895
.10.1109/IROS.2012.6385610
31.
Greenwood
,
D.
,
1988
,
Principles of Dynamics
,
Prentice-Hall
, Upper Saddle River, NJ.
32.
Fiedler
,
M.
,
1986
,
Special Matrices and Their Applications in Numerical Mathematics
,
1st ed.
,
Springer
, New York.
33.
Bloch
,
A.
,
Krishnaprasad
,
P.
,
Marsden
,
J.
, and
Ratiu
,
T.
,
1996
, “
The Euler-Poincaré Equations and Double Bracket Dissipation
,”
Commun. Math. Phys.
,
175
(
1
), pp.
1
42
.10.1007/BF02101622
34.
Ostrowski
,
J.
,
1998
, “
Reduced Equations for Nonholonomic Mechanical Systems With Dissipative Forces
,”
Rep. Math. Phys.
,
42
(
1–2
), pp.
185
209
.10.1016/S0034-4877(98)80010-4
35.
Murray
,
R. N.
,
Li
,
Z.
, and
Sastry
,
S.
,
1994
,
A Mathematical Introduction to Robotics Manipulation
,
CRC Press
, Boca Raton, FL.
36.
Shammas
,
E. A.
,
2006
, “
Generalized Motion Planning for Underactuated Mechanical Systems
,” Ph.D. thesis, Carnegie Mellon University, Pittsburgh, PA.
37.
Shammas
,
E. A.
,
Choset
,
H.
, and
Rizzi
,
A. A.
,
2007
, “
Towards a Unified Approach to Motion Planning for Dynamic Underactuated Mechanical Systems With Non-Holonomic Constraints
,”
Int. J. Rob. Res.
,
26
(
10
), pp.
1075
1124
.10.1177/0278364907082098
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