Every manipulator contact task that begins with a transition from free motion to constraint motion may exhibit impacts that could drive the system unstable. Stabilization of manipulators during this transition is, therefore, an important issue in contact task control design. This paper presents a discontinuous controller to regulate the transition mode in hydraulic actuators. The controller, upon sensing a nonzero force, positions the actuator at the location where the force was sensed, thus, exerting minimal force on a nonmoving environment. The scheme does not require force or velocity feedback as they are difficult to measure throughout the short transition phase. Also, no knowledge about the environment or hydraulic parameters is required for control action. Due to the discontinuity of the control law, the control system is nonsmooth. First, the existence, continuation and uniqueness of Filippov’s solution to the system are proven. Next, the extension of Lyapunov stability theory to nonsmooth systems is employed to guarantee the global asymptotic convergence of the entire system’s state towards the equilibrium point. Complete dynamic characteristics of hydraulic functions and Hertz-type contact model are included in the stability analysis. Experiments are conducted to verify the practicality and effectiveness of the proposed controller. They include actuator collisions with hard and soft environments and with various approach velocities.

1.
Payandeh
,
S.
, 1996, “
A method for controlling robotic contact tasks
,”
Robotica
0263-5747,
14
, pp.
281
288
.
2.
Volpe
,
R.
, and
Khosla
,
P.
, 1993, “
A theoretical and experimental investigation of impact control for manipulators
,”
Int. J. Robot. Res.
0278-3649,
12
, pp.
351
365
.
3.
Brogliato
,
B.
, and
Orhant
,
P.
, 1998, “
Contact stability analysis of a one degree-of-freedom robot
,”
Dyn. Control
0925-4668,
8
, pp.
37
53
.
4.
Tornambe
,
A.
, 1999, “
Modeling and control of impact in mechanical systems: Theory and experimental results
,”
IEEE Trans. Autom. Control
0018-9286,
44
, pp.
294
309
.
5.
Pagilla
,
P. R.
, and
Yu
,
B.
, 2001, “
A stable transition controller for constrained robots
,”
IEEE/ASME Trans. Mechatron.
1083-4435,
6
, pp.
65
74
.
6.
Xu
,
W. L.
,
Han
,
J. D.
, and
Tso
,
S. K.
, 2000, “
Experimental study of contact transition control incorporating joint acceleration feedback
,”
IEEE/ASME Trans. Mechatron.
1083-4435,
5
, pp.
292
301
.
7.
Tarn
,
T. J.
,
Wu
,
Y.
,
Xi
,
N.
, and
Isidori
,
A.
, 1996, “
Force regulation and contact transition control
,”
IEEE Control Syst.
1066-033X,
16
, pp.
32
40
.
8.
Heinrichs
,
B.
,
Sepehri
,
N.
, and
Thornton-Trump
,
A. B.
, 1997, “
Position-based impedance control of an industrial hydraulic manipulator
,”
IEEE Control Syst.
1066-033X,
17
, pp.
46
52
.
9.
Bilodeau
,
G.
, and
Papadopoulos
,
E.
, 1998, “
A model-based impedance control scheme for high-performance hydraulic joints
,”
Proc. IEEE∕RSJ Int. Conf. Intelligent Robots and Systems
, pp.
1308
1313
.
10.
Ha
,
Q. P.
,
Nguyen
,
Q. H.
,
Rye
,
D. C.
, and
Durrant-Whyte
,
H. F.
, 2000, “
Impedance control of a hydraulically actuated robotic excavator
,”
Autom. Constr.
0926-5805,
9
, pp.
421
435
.
11.
Clegg
,
A. C.
,
Dunnigan
,
M. W.
, and
Lane
,
D. M.
, 2001, “
Self-tuning position and force control of an underwater hydraulic manipulator
,”
Proc. IEEE Int. Conf. Robotics and Automation
, pp.
3226
3231
.
12.
Seraji
,
H.
,
Lim
,
D.
, and
Steele
,
R.
, 1996, “
Experiments in contact control
,”
J. Rob. Syst.
0741-2223,
13
, pp.
53
73
.
13.
Liu
,
R.
, and
Alleyne
,
A.
, 2000, “
Nonlinear Force∕Pressure Tracking of an Electro-Hydraulic Actuator
,”
ASME J. Dyn. Syst., Meas., Control
0022-0434,
122
, pp.
232
237
.
14.
Alleyne
,
A.
, 1996, “
Nonlinear force control of an electrohydraulic actuator
,”
Japan∕USA Symposium on Flexible Automation
, Boston, MA, pp.
193
200
.
15.
Wu
,
G.
,
Sepehri
,
N.
, and
Ziaei
,
K.
, 1998, “
Design of a hydraulic force control system using a generalized predictive control algorithm
,”
IEE Proc.: Control Theory Appl.
1350-2379,
145
, pp.
428
436
.
16.
Bluethmann
,
B.
,
Ananthakrishnan
,
S.
,
Scheerer
,
J.
,
Faddis
,
T. N.
, and
Greenway
,
R. B.
, 1995, “
Experiments in dexterous hybrid force and position control of a master–slave electrohydraulic manipulator
,”
Proc. IEEE International Conference on Intelligent Robots and Systems
, pp.
27
32
.
17.
Dunnigan
,
M. W.
,
Lane
,
D. M.
,
Clegg
,
A. C.
, and
Edwards
,
I.
, 1996, “
Hybrid position–force control of a hydraulic underwater manipulator
,”
IEE Proc.: Control Theory Appl.
1350-2379,
143
, pp.
145
151
.
18.
Niksefat
,
N.
,
Wu
,
C. Q.
, and
Sepehri
,
N.
, 2001, “
Design of a Lyapunov controller for an electro-hydraulic actuator during contact tasks
,”
ASME J. Dyn. Syst., Meas., Control
0022-0434,
123
, pp.
299
307
.
19.
Filippov
,
A. F.
, 1960, “
Differential equations with discontinuous right-hand side
,”
Am. Math. Soc. Transl.
0065-9290,
42
, pp.
199
231
.
20.
Filippov
,
A. F.
, 1979. “
Differential equations with second members discontinuous on intersecting surfaces
.”
Diff. Eq.
0012-2661,
15
, pp.
1292
1299
.
21.
Shevitz
,
D.
, and
Paden
,
B.
, 1994, “
Lyapunov stability theory of nonsmooth systems
,”
IEEE Trans. Autom. Control
0018-9286,
39
, pp.
1910
1914
.
22.
Fujita
,
T.
, and
Hattori
,
S.
, 1980, “
Periodic vibration and impact characteristics of a nonlinear system with collision
,”
Bull. JSME
0021-3764,
23
, pp.
409
418
.
23.
Timoshenko
,
S. P.
, and
Goodier
,
J. N.
, 1970,
Theory of elasticity
,
McGraw-Hill
, New York.
24.
Van Vliet
,
J.
,
Sharf
,
I.
, and
Ma
,
O.
, 2000, “
Experimental validation of contact dynamics simulation of constrained robotic tasks
,”
Int. J. Robot. Res.
0278-3649,
19
, pp.
1203
1217
.
25.
Mills
,
J. K.
, 1990, “
Manipulator transition to and from contact tasks: A discontinuous control approach
,”
Proc. IEEE Int. Conf. Robotics and Automation
, pp.
440
446
.
26.
Eppinger
,
S. D.
, and
Seering
,
W. P.
, 1987, “
Understanding bandwidth limitations in robot force control
,”
Proc. IEEE Int. Conf. Robotics and Automation
, pp.
904
909
.
27.
Mills
,
J. K.
, and
Nguyen
,
C. V.
, 1992, “
Robotic manipulator collisions: modelling and simulation
,”
ASME J. Dyn. Syst., Meas., Control
0022-0434,
114
, pp.
650
659
.
28.
Marhefka
,
D. W.
, and
Orin
,
D. E.
, 1996, “
Simulation of contact using a nonlinear damping model
,”
Proc. IEEE Int. Conf. Robotics and Automation
, pp.
1662
1668
.
29.
Merritt
,
H. E.
, 1967,
Hydraulic Control Systems
,
Wiley
, New York.
30.
Shoji
,
Y.
,
Inaba
,
M.
, and
Fukuda
,
T.
, 1991, “
Impact control of grasping
,”
IEEE Trans. Ind. Electron.
0278-0046,
38
, pp.
187
194
.
31.
Chiu
,
D.
, and
Lee
,
S.
, 1996, “
Design and experimentation of jump impact controller
,”
Proc. IEEE Int. Conf. Robotics and Automation
, pp.
1903
1908
.
32.
Tornambe
,
A.
, 1996, “
Global regulation of a planar robot arm striking a surface
,”
IEEE Trans. Autom. Control
0018-9286,
41
(
10
), pp.
1517
1521
.
33.
Kolmogorov
,
A. N.
, and
Fomin
,
S. V.
, 1957,
Element of the theory of functions and functional analysis (volume 1: metric and normal spaces)
,
Graylock
, New York.
You do not currently have access to this content.