Research Papers

Time-Optimal Trajectory Planning of Cable-Driven Parallel Mechanisms for Fully Specified Paths With G1-Discontinuities

[+] Author and Article Information
Eric Barnett

Départment de Génie Mécanique,
Université Laval,
Québec, QC G1V 0A6, Canada
e-mail: eric.barnett.1@ulaval.ca

Clément Gosselin

Départment de Génie Mécanique,
Université Laval,
Québec, QC G1V 0A6, Canada
e-mail: gosselin@gmc.ulaval.ca

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received September 18, 2013; final manuscript received February 5, 2015; published online March 23, 2015. Assoc. Editor: Yongchun Fang.

J. Dyn. Sys., Meas., Control 137(7), 071007 (Jul 01, 2015) (12 pages) Paper No: DS-13-1388; doi: 10.1115/1.4029769 History: Received September 18, 2013; Revised February 05, 2015; Online March 23, 2015

Time-optimal trajectory planning (TOTP) is a well-studied problem in robotics and manufacturing, which involves the minimization of the time required for the operation point of a mechanism to follow a path, subject to a set of constraints. A TOTP technique, designed for fully specified paths that include abrupt changes in direction, was previously introduced by the first author of this paper: an incremental approach called minimum-time trajectory shaping (MTTS) was used. In the current paper, MTTS is converted to a dynamic technique and adapted for use with cable-driven parallel robots, which exhibit cable tension and motor torque constraints. For many applications, cable tensions along a path are verified after trajectory generation, rather than imposed during trajectory generation. For the technique proposed in this paper, the cable-tension constraints are imposed directly and fully integrated with MTTS, during trajectory generation, thus maintaining a time-optimal solution. MTTS is applied to a test system and path, and compared to the bang–bang technique. With the same constraints, the results obtained with both techniques are found to be very close. However, MTTS can be applied to a wider variety of paths, and accepts constraints on jerk and total acceleration that would be difficult to apply using the bang–bang approach.

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Fig. 1

Spatial 3DOF cable-suspended robot

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Fig. 2

The segment-to-segment angle, βi

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Fig. 4

Illustration of the ACON subalgorithm

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Fig. 3

Valid tension ranges for joint k along one path, during VCON

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Fig. 6

Tension constraints for joint k, imposed during ACON, for negative Δρk,b

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Fig. 5

Sweeping an acceleration curve for joint k

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Fig. 8

The JCON subalgorithm

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Fig. 7

The application of constraints to determine Δtb, during ACON

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Fig. 10

Test path: (a) 3D plot; (b) projection on the xy-plane; and (c) projection on the xz-plane

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Fig. 11

Steps of the MTTS algorithm, for the path shown in Fig. 10, with all constraints listed in Eq. (42) active

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Fig. 12

Trajectory parameters for the path shown in Fig. 10, using MTTS with all constraints listed in Eq. (42) active

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Fig. 9

The secondary technique applied during JCON

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Fig. 13

The bang–bang method, for the path shown in Fig. 10, with no constraints on jerk or acceleration

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Fig. 14

Trajectory parameters for the path shown in Fig. 10, using the bang–bang method, with no jerk or acceleration constraints

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Fig. 15

The bang–bang method compared to MTTS, for the path shown in Fig. 10, with no jerk or acceleration constraints: (a) s–s· plot, (b) cable tensions with the bang-bang method, and (c) cable tensions with MTTS



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