Trajectory planning and an efficient control scheme play a crucial role in improving the performance of pick-and-place robots. This paper introduces a novel method of trajectory planning with cycle time and path constraints. Assuming that a smooth trajectory is given, to be followed within a prescribed cycle time, the newly proposed method of trajectory planning removes the torque peaks of the actuators by a suitable scheduling of the velocity of the moving plate. Since pick-and-place robots are usually expected to meet the end poses in a certain time span, while disregarding the intermediate poses, the velocity can be tuned properly around the critical points of the trajectory by means of a time-scaling function. Moreover, the authors report the formulation of a linear quadratic regulator (LQR) controller with normalized variables to be used in conjunction with our trajectory-tracking control scheme for an in-house-developed Schönflies-motion generator. This parallel robot offers a functionally symmetric, single-loop architecture, with an isostatic kinematic chain, and virtually unlimited rotatability of its gripper. A comparison between two actuation systems developed by the authors is conducted via simulation results.

References

1.
Hervé
,
J. M.
,
1999
, “
The Lie Group of Rigid Body Displacements, a Fundamental Tool for Mechanism Design
,”
Mech. Mach. Theory
,
34
(
5
), pp.
719
730
.
2.
Brogårdh
,
T.
,
2001
, “
Device for Relative Movement of Two Elements
,” U.S. Patent No. 4,741,207.
3.
Angeles
,
J.
, and
Morozov
,
A.
,
2006
, “
Four-Degree-of-Freedom Parallel Manipulator for Producing Schönflies Motions
,” U.S. Patent No. 7,127,962.
4.
Gallardo-Alvarado
,
J.
,
Abedinnasab
,
M. H.
, and
Lichtblau
,
D.
,
2016
, “
Simplified Kinematics for a Parallel Manipulator Generator of the Schönflies Motion
,”
ASME J. Mech. Robot.
,
8
(
6
),
061020
.
5.
Corbel
,
D.
,
Gouttefarde
,
M.
,
Company
,
O.
, and
Pierrot
,
F.
,
2010
, “
Actuation Redundancy as a Way to Improve the Acceleration Capabilities of 3T and 3T1R Pick-and-Place Parallel Manipulators
,”
ASME J. Mech. Robot.
,
2
(
4
),
041002
.
6.
Altuzarra
,
O.
,
Zubizarreta
,
A.
,
Cabanes
,
I.
, and
Pinto
,
C.
,
2009
, “
Dynamics of a Four Degrees-of-Freedom Parallel Manipulator With Parallelogram Joints
,”
Mechatronics
,
19
(
8
), pp.
1269
1279
.
7.
Huang
,
T.
,
Bai
,
P.
,
Mei
,
J.
, and
Chetwynd
,
D. G.
,
2016
, “
Tolerance Design and Kinematic Calibration of a Four-Degrees-of-Freedom Pick-and-Place Parallel Robot
,”
ASME J. Mech. Robot.
,
8
(
Oct. 6
),
061018
.
8.
Clavel
,
R.
,
1990
, “
Device for the Movement and Positioning of an Element in Space
,” U.S. Patent No. 4,976,582.
9.
Pierrot
,
F.
,
Shibukawa
,
T.
, and
Morita
,
K.
,
2003
, “
Four-Degree-of-Freedom Parallel Robot
,” U.S. Patent No. 6,516,681.
10.
Brantmark
,
H.
, and
Hemmingson
,
E.
,
2001
, “
FlexPicker With PickMaster Revolutionizes Picking Operations
,”
Ind. Robot An Int. J.
,
28
(
5
), pp.
414
420
.
11.
Lee
,
C.
, and
Lee
,
P.
,
1990
,
Geometric Methods in Robotics and Mechanism Research: Theory and Applications
,
Y.
Lou
, and
Z.
Li
, eds.,
LAP Lambert Academic Publishing
,
Saarbrücken
, pp.
95
112
.
12.
Lee
,
P.-C.
, and
Lee
,
J.-J.
,
2012
, “
Singularity and Workspace Analysis of Three Isoconstrained Parallel Manipulators With Schoenflies Motion
,”
Front. Mech. Eng.
,
7
(
2
), pp.
163
187
.
13.
Harada
,
T.
, and
Angeles
,
J.
,
2014
, “
Kinematics and Singularity Analysis of a CRRHHRRC Parallel Schönflies Motion Generator
,”
Trans. Can. Soc. Mech. Eng.
,
38
(
2
), pp.
173
183
.
14.
Karimi Eskandary
,
P.
, and
Angeles
,
J.
,
2018
, “
The Dynamics of a Parallel Schönflies-Motion Generator
,”
Mech. Mach. Theory
,
119
, pp.
119
129
.
15.
Harada
,
T.
,
Friedlaender
,
T.
, and
Angeles
,
J.
,
2014
, “
The Development of an Innovative Two-DOF Cylindrical Drive: Design, Analysis and Preliminary Tests
,”
2014 EEE International Conference on Robotics and Automation
,
31 May–7 June 2014
, IEEE, pp.
6338
6344
.
16.
Karimi Eskandary
,
P.
, and
Angeles
,
J.
,
2018
, “
The Translating Π-Joint: Design and Applications
,”
Mech. Mach. Theory
,
122
, pp.
361
370
.
17.
Trentelman
,
H. L.
,
Stoorvogel
,
A.
, and
Hautus
,
M.
,
2001
,
Control Theory for Linear Systems
,
Springer
,
Dordrecht
.
18.
Kalman
,
R. E.
,
1960
, “
Contributions to the Theory of Optimal Control
,”
Bol. la Soc. Mat. Mex.
,
5
(
2
), pp.
102
119
.
19.
Wang
,
H.
,
Dong
,
H.
,
He
,
L.
,
Shi
,
Y.
, and
Zhang
,
Y.
,
2010
, “
Design and Simulation of LQR Controller With the Linear Inverted Pendulum
,”
2010 International Conference on Electrical and Control Engineering
,
Sept. 16–18
, IEEE, pp.
699
702
.
20.
Divelbiss
,
A. W.
, and
Wen
,
J. T.
,
1997
, “
Trajectory Tracking Control of a Car-Trailer System
,”
IEEE Trans. Control Syst. Technol.
,
5
(
3
), pp.
269
278
.
21.
Bourbonnais
,
F.
,
Bigras
,
P.
, and
Bonev
,
I. A.
,
2015
, “
Minimum-Time Trajectory Planning and Control of a Pick-and-Place Five-Bar Parallel Robot
,”
IEEE/ASME Trans. Mechatronics
,
20
(
2
), pp.
740
749
.
22.
Liu
,
H.
,
Lai
,
X.
, and
Wu
,
W.
,
2013
, “
Time-Optimal and Jerk-Continuous Trajectory Planning for Robot Manipulators With Kinematic Constraints
,”
Robot. Comput. Integr. Manuf.
,
29
(
Apr. 2
), pp.
309
317
.
23.
Perumaal
,
S. S.
, and
Jawahar
,
N.
,
2013
, “
Automated Trajectory Planner of Industrial Robot for Pick-and-Place Task
,”
Int. J. Adv. Robot. Syst.
,
10
(
2
), pp.
100
.
24.
Gasparetto
,
A.
,
Lanzutti
,
A.
,
Vidoni
,
R.
, and
Zanotto
,
V.
,
2011
, “
Validation of Minimum Time-Jerk Algorithms for Trajectory Planning of Industrial Robots
,”
ASME J. Mech. Robot.
,
3
(
3
),
031003
.
25.
Menon
,
M. S.
,
Ravi
,
V. C.
, and
Ghosal
,
A.
,
2017
, “
Trajectory Planning and Obstacle Avoidance for Hyper-Redundant Serial Robots
,”
ASME J. Mech. Robot.
,
9
(
4
),
041010
.
26.
Boscariol
,
P.
, and
Gasparetto
,
A.
,
2013
, “
Model-Based Trajectory Planning for Flexible-Link Mechanisms With Bounded Jerk
,”
Robot. Comput. Integr. Manuf.
,
29
(
4
), pp.
90
99
.
27.
Azizi
,
M. R.
, and
Naderi
,
D.
,
2013
, “
Dynamic Modeling and Trajectory Planning for a Mobile Spherical Robot With a 3DOF Inner Mechanism
,”
Mech. Mach. Theory
,
64
, pp.
251
261
.
28.
Zhang
,
N.
, and
Shang
,
W.
,
2016
, “
Dynamic Trajectory Planning of a 3-DOF Under-Constrained Cable-Driven Parallel Robot
,”
Mech. Mach. Theory
,
98
, pp.
21
35
.
29.
Gosselin
,
C.
, and
Foucault
,
S.
,
2014
, “
Dynamic Point-to-Point Trajectory Planning of a Two-DOF Cable-Suspended Parallel Robot
,”
IEEE Trans. Robot.
,
30
(
3
), pp.
728
736
.
30.
Jiang
,
X.
, and
Gosselin
,
C.
,
2016
, “
Dynamic Point-to-Point Trajectory Planning of a Three-DOF Cable-Suspended Parallel Robot
,”
IEEE Trans. Robot.
,
32
(
Dec. 6
), pp.
1550
1557
.
31.
Gauthier
,
J. F.
,
Angeles
,
J.
, and
Nokleby
,
S.
,
2008
, “Optimization of a Test Trajectory for SCARA Systems”.
Advances in Robot Kinematics: Analysis and Design
,
Springer Netherlands
,
Dordrecht
, pp.
225
234
.
32.
Kutt
,
H. R.
,
1975
, “
The Numerical Evaluation of Principal Value Integrals by Finite-Part Integration
,”
Numer. Math.
,
24
(
3
), pp.
205
210
.
33.
Saha
,
S. K.
, and
Angeles
,
J.
,
1991
, “
Dynamics of Nonholonomic Mechanical Systems Using a Natural Orthogonal Complement
,”
ASME J. Appl. Mech.
,
58
(
1
), pp.
238
.
34.
Nabat
,
V.
,
2005
, “
Par4: Very High Speed Parallel Robot for Pick-and-Place
,”
2005 IEEE/RSJ International Conference on Intelligent Robots and Systems
, IEEE, pp.
553
558
.
35.
Friedlaender
,
T.
,
2015
,
Ph.D. thesis
,
McGill University
,
Montreal
.
36.
Kailath
,
T.
,
1980
,
Linear Systems
,
Prentice-Hall
,
New Jersey
.
37.
Bryson
,
A.
, and
Luenberger
,
D.
,
1970
, “
The Synthesis of Regulator Logic Using State-Variable Concepts
,”
Proc. IEEE
,
58
(
11
), pp.
1803
1811
.
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