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Research Papers

Control and Motion Planning of a Nonholonomic Parallel Orienting Platform

[+] Author and Article Information
Janusz Jakubiak

Chair of Cybernetics and Robotics
Wrocław University of Technology,
ul. Janiszewskiego 11/17,
Wrocław 50-372, Poland
e-mail: janusz.jakubiak@pwr.edu.pl

Władyslaw Magiera

Chair of Signal Processing Systems
Wrocław University of Technology,
ul. Janiszewskiego 11/17,
Wrocław 50-372, Poland
e-mail: wladyslaw.magiera@pwr.edu.pl

Krzysztof Tchoń

Chair of Cybernetics and Robotics
Wrocław University of Technology,
ul. Janiszewskiego 11/17,
Wrocław 50-372, Poland
e-mail: krzysztof.tchon@pwr.edu.pl

Manuscript received August 14, 2014; final manuscript received February 17, 2015; published online April 6, 2015. Assoc. Editor: Federico Thomas.

J. Mechanisms Robotics 7(4), 041019 (Nov 01, 2015) (11 pages) Paper No: JMR-14-1210; doi: 10.1115/1.4029891 History: Received August 14, 2014; Revised February 17, 2015; Online April 06, 2015

An orienting platform is a mechanism which allows rotation of a spatial object without translational motion of that object. In this work, we study a parallel platform with one passive nonholonomic spherical joint and two series of spherical, actuated prismatic and universal joints (the platform is also known in literature as an (nS)-2SPU wrist). To solve the control and motion planning problems, an analytic approach is used. The design of practical stabilization and tracking algorithm is based on transverse functions and a method for motion planning respecting mechanical singularities is derived from endogenous configuration space approach. It is shown that the system is controllable and locally equivalent to the chained form system. Then, the stabilization, tracking, and motion planning algorithms are proposed. Results are verified with computer simulations. A combination of the open-loop motion planning algorithm and the closed-loop tracking provide a tool for designing a motion planning algorithm respecting mechanical singularities and robust to input disturbances.

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References

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Figures

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Fig. 1

Nonholonomic parallel orienting platform from CSIS-UPC [9]: overall design and the nS joint

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Fig. 2

Nonholonomic parallel orienting platform: schematic (adapted from Ref. [9])

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Fig. 3

Mechanical singularity locus

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Fig. 4

Stabilization problem, ɛ=0.3: controls, error, singularity function

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Fig. 5

Stabilization problem, ɛ=0.1: controls, error, singularity function

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Fig. 6

Stabilization problem, ɛ=0.05: controls, error, singularity function

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Fig. 7

Motion planning: controls in original and transformed systems, singularity function, convergence

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Fig. 10

Tracking of disturbed system with ɛ=0.01: controls, error, singularity function

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Fig. 8

Tracking of disturbed system with ɛ=0.3: controls, error, singularity function

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Fig. 9

Tracking of disturbed system with ɛ=0.05: controls, error, singularity function

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