Input constraints are active in robot trajectory planning when a mobile robot traverses mobility challenges such as steep hills that limit the acceleration of the robot due to the torque constraints of the motor or engine or in manipulator lifting tasks when the load is sufficiently heavy that the torque constraints of the robot's motor prevent it from statically supporting the load in regions of the robot's workspace. This paper presents a general methodology for solving these planning tasks using a minimum-time cost function and applies it to the problem of a multiple degrees-of-freedom (DOF) manipulator lifting a heavy load. Planning for these types of problems requires use of the robot's dynamic model. Here, we plan using sampling-based model predictive optimization (SBMPO), which is only practical if the planning can be done quickly. Hence, substantial attention is given to efficient computations by: (1) using the dynamic model without integrating it, (2) using optimal control theory to develop an “optimistic A* estimate of cost-to-goal,” which is in this case a rigorous lower bound on the minimum time from a current state to a goal state, and (3) using prior experience to speed up the computation of a new trajectory. The methodology is experimentally verified for heavy lifting using a two-link manipulator.

References

References
1.
Chuy
,
O.
,
Collins
,
E.
,
Dunlap
,
D.
, and
Sharma
,
A.
,
2013
, “
Sampling-Based Direct Trajectory Generation Using the Minimum Time Cost Function
,”
Experimental Robotics
(Springer Tracts in Advanced Robotics, Vol.
88
),
J. P.
Desai
,
G.
Dudek
,
O.
Khatib
, and
V.
Kumar
, eds.,
Springer International Publishing
, Switzerland, pp.
651
666
.
2.
Dunlap
,
D.
,
Caldwell
,
C.
,
Collins
,
E.
, and
Chuy
,
O.
,
2011
,
Motion Planning for Mobile Robots Via Sampling-Based Model Predictive Optimization: Recent Advances in Mobile Robotics
,
InTech
,
Rijeka, Croatia
.
3.
Ordonez
,
C.
,
Gupta
,
N.
,
Chuy
,
O.
, and
Collins
,
E.
,
2013
, “
Momentum Based Traversal of Mobility Challenges for Autonomous Ground Vehicles
,”
IEEE
International Conference on Robotics and Automation
, May 6–10, pp.
752
759
.
4.
Dunlap
,
D.
,
Caldwell
,
C.
, and
Collins
,
E. G.
, Jr.
,
2010
, “
Nonlinear Model Predictive Control Using Sampling and Goal-Directed Optimization
,”
Multi-Conference on Systems and Control
, Sept. 8–10, pp.
1349
1356
.
5.
Dunlap
,
D.
,
2011
, “
Sampling Based Model Predictive Optimization With Application to Robot Kinodynamic Motion Planning
,” Ph.D. dissertation, Florida State University, Tallahassee, FL.
6.
Reese
,
B.
, and
Collins
,
E.
,
2016
, “
A Graph Search and Neural Network Approach to Adaptive Nonlinear Model Predictive Control
,”
Eng. Appl. Artif. Intell.
,
55
, pp.
250
268
.
7.
Sanchez
,
T. F. M.
,
2011
, “
Application of Sampling-Based Model Predictive Control to Motion Planning for Robotic Manipulators
,” Master's thesis, Florida State University, Tallahassee, FL.
8.
LaValle
,
S.
, and
Kuffner
,
J.
,
2001
, “
Randomized Kinodynamic Planning
,”
Int. J. Rob. Res.
,
20
(
5
), pp.
378
400
.
9.
Diankov
,
R.
, and
Kuffner
,
J.
,
2007
, “
Randomized Statistical Path Planning
,”
IEEE
International Conference on Intelligent Robots and Systems
, Oct. 29–Nov. 2.
10.
Karaman
,
S.
, and
Frazzoli
,
E.
,
2010
, “
Incremental Sampling-Based Optimal Motion Planning
,” Robotics: Science and Systems (RSS VI).
11.
Karaman
,
S.
, and
Frazzoli
,
E.
,
2010
, “
Optimal Kinodynamic Motion Planning Using Incremental Sampling-Based Method
,”
IEEE
Conference on Decision and Control
, Dec. 15–17, pp.
7681
7687
.
12.
Jetchev
,
N.
, and
Toussaint
,
M.
,
2013
, “
Fast Motion Planning From Experience: Trajectory Prediction for Speeding Up Movement Generation
,”
J. Auton. Rob.
,
34
(1), pp.
111
127
.
13.
Kavraki
,
L.
,
Kolountzakis
,
M.
, and
Latombe
,
J.
,
1998
, “
Analysis of Probabilistic Roadmaps for Path Planning
,”
IEEE Trans. Rob. Autom.
,
14
(1), pp.
166
171
.
14.
Kavraki
,
L.
,
Latombe
,
J.
, and
Oversmars
,
M.
,
1996
, “
Probabilistic Roadmaps for Path Planning in High-Dimensional Configuration Spaces
,”
IEEE Trans. Rob. Autom.
, 12(4), pp.
556
580
.
15.
Koenig
,
S.
, and
Likhachev
,
M.
,
2002
, “
D* Lite
,”
AAAI Conference
, pp.
476
483
.
16.
Stentz
,
A.
,
1995
, “
Focussed D* Algorithm for Real-Time Replanning
,”
International Joint Conference on Artificial Intelligence
(
IJCAI
), pp.1652–1659.
17.
Bobrow
,
J.
,
Dubowsky
,
S.
, and
Gibson
,
J.
,
1985
, “
Time-Optimal Control of Robotic Manipulators Along Specified Path
,”
Int. J. Rob. Res.
,
4
(
3
), pp.
3
17
.
18.
Shin
,
K.
, and
McKay
,
N.
,
1985
, “
Minimum-Time Control of Robotic Manipulators With Geometric Path Constraints
,”
IEEE Trans. Autom. Control
,
30
(6), pp.
531
541
.
19.
Wang
,
C. E.
,
Timoszyk
,
W. K.
, and
Bobrow
,
J. E.
,
2001
, “
Payload Maximization for Open Chained Manipulators: Finding Weightlifting Motions for a Puma 762 Robot
,”
IEEE Trans. Rob. Autom.
,
17
(2), pp.
218
224
.
20.
Spong
,
M.
,
1995
, “
The Swing Up Control Problem for the Acrobot
,”
IEEE Control Syst.
,
15
(
1
), pp.
49
55
.
21.
Fantoni
,
I.
,
Lozano
,
R.
, and
Spong
,
M.
,
2000
, “
Energy Based Control of the Pendubot
,”
IEEE Trans. Autom. Control
,
45
(
4
), pp.
725
729
.
22.
Dunlap
,
D.
,
Collins
,
E.
,
Yu
,
W.
, and
Charmane
,
C.
,
2011
, “
Motion Planning for Steep Hill Climbing
,”
IEEE
International Conference on Robotics and Automation
, May 9–13, pp.
707
714
.
23.
Sharma
,
A.
,
Ordonez
,
C.
, and
Collins
,
E.
,
2014
, “
Robust Sampling-Based Trajectory Tracking for Autonomous Vehicles
,”
IEEE
International Conference on Systems
, Man, and Cybernetics, Oct. 5–8, pp.
3446
3451
.
24.
Maciejowski
,
J. M.
,
2002
,
Predictive Control With Constraints
,
Prentice Hall
,
Haslow, UK
.
25.
Koenig
,
S.
,
Likhachev
,
M.
, and
Furcy
,
D.
,
2004
, “
Lifelong Planning A*
,”
Artif. Intell.
,
155
(
1–2
), pp.
93
146
.
26.
Halton
,
J. H.
,
1960
, “
On the Efficiency of Certain Quasi-Random Sequences of Points in Evaluating Multi-Dimensional Integrals
,”
Numer. Math.
,
2
(1), pp. 84–90.
27.
Ericson
,
C.
,
2005
,
Real-Time Collision Detection
,
Elsevier
,
New York
.
28.
Bryson
,
A.
, and
Ho
,
Y.
,
1975
,
Applied Optimal Control: Optimization, Estimation, and Control
,
Hemispher Publishing Corporation
,
New York
.
29.
Siciliano
,
B.
,
Sciavicco
,
L.
,
Villani
,
L.
, and
Oriolo
,
G.
,
2009
,
Robotics Modelling, Planning and Control
,
Springer
, London.
30.
Caldwell
,
C. V.
,
2011
, “
A Sampling-Based Model Predictive Control Approach to Motion Planning for Autonomous Underwater Vehicles
,”
Ph.D. thesis
, Florida State University, Tallahassee, FL.
31.
Unimation
,
1986
, “
Unimate PUMA Mark III Robot Equipment Manual 398Z1
,” Unimation, Incorporated, CT.
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