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2019 | OriginalPaper | Buchkapitel

6. Kinematics of the \(\text {S}_\text {n}\)-2UPS Spherical Robot

verfasst von : Patrick Grosch, Federico Thomas

Erschienen in: Parallel Robots With Unconventional Joints

Verlag: Springer International Publishing

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Abstract

In this chapter, we analize the kinetostatics of a non-holonomic parallel spherical robot which can maneuver to reach any orientation for its moving platform. We show how by properly locating the actuators, and by representing the platform orientation using Euler parameters, the analysis admits a simple bilinear formulation after introducing a local feedback transformation. Interestingly enough, the singularities introduced by this transformation coincide with the singularities of the robot Jacobian. Thus, from the practical point of view, no extra singularities are added. A complete description of the robot’s workspace, which also takes into account the limits of all joints, is presented. Part of this work has previously been published in [4].

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Literatur
1.
Zurück zum Zitat J. Angeles, Fundamentals of Robotic Mechanical Systems: Theory, Methods, and Algorithms, Mechanical Engineering Series (2003) J. Angeles, Fundamentals of Robotic Mechanical Systems: Theory, Methods, and Algorithms, Mechanical Engineering Series (2003)
2.
Zurück zum Zitat A. De Luca, G. Oriolo, Modelling and control of nonholonomic mechanical systems, in CISM International Centre for Mechanical Sciences (Chapter 7), vol. 360 (1995), pp. 277–342 A. De Luca, G. Oriolo, Modelling and control of nonholonomic mechanical systems, in CISM International Centre for Mechanical Sciences (Chapter 7), vol. 360 (1995), pp. 277–342
3.
Zurück zum Zitat R. Di Gregorio, Position analysis and path planning of the S-(nS)\(\underline{\rm P}\)U-S\(\underline{\rm P}\)U and S-(nS)PU-2S\(\underline{\rm P}\)U underactuated wrists. J. Mech. Robot. 4(2) (2012) R. Di Gregorio, Position analysis and path planning of the S-(nS)\(\underline{\rm P}\)U-S\(\underline{\rm P}\)U and S-(nS)PU-2S\(\underline{\rm P}\)U underactuated wrists. J. Mech. Robot. 4(2) (2012)
4.
Zurück zum Zitat P. Grosch, F. Thomas, A bilinear formulation for the motion planning of non-holonomic parallel orienting platforms, in Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, Tokyo, Japan (2013), pp. 953–958 P. Grosch, F. Thomas, A bilinear formulation for the motion planning of non-holonomic parallel orienting platforms, in Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, Tokyo, Japan (2013), pp. 953–958
5.
Zurück zum Zitat P. Grosch, R. Di Gregorio, F. Thomas, Generation of under-actuated manipulators with non-holonomic articulations from ordinary manipulators. J. Mech. Robot. 2(1), 11005–11012 (2010)CrossRef P. Grosch, R. Di Gregorio, F. Thomas, Generation of under-actuated manipulators with non-holonomic articulations from ordinary manipulators. J. Mech. Robot. 2(1), 11005–11012 (2010)CrossRef
6.
Zurück zum Zitat H. Hermes, Distributions and the Lie algebras their bases can generate. Proc. Am. Math. Soc. 106(2), 555–565 (1989)MathSciNetCrossRef H. Hermes, Distributions and the Lie algebras their bases can generate. Proc. Am. Math. Soc. 106(2), 555–565 (1989)MathSciNetCrossRef
7.
Zurück zum Zitat C. Innocenti, V. Parenti-Castelli, Echelon form solution of direct kinematics for the general fully-parallel spherical wrist. Mech. Mach. Theory 28(4), 553–561 (1993)CrossRef C. Innocenti, V. Parenti-Castelli, Echelon form solution of direct kinematics for the general fully-parallel spherical wrist. Mech. Mach. Theory 28(4), 553–561 (1993)CrossRef
8.
Zurück zum Zitat G. Lafferriere, A general strategy for computing steering controls of systems without drift, in IEEE Conference on Decision and Control, Brighton, UK (1991), pp. 1115–1120 G. Lafferriere, A general strategy for computing steering controls of systems without drift, in IEEE Conference on Decision and Control, Brighton, UK (1991), pp. 1115–1120
9.
Zurück zum Zitat R.M. Murray, Control of nonholonomic systems using chained forms. Fields Inst. Commun. Dyn. Control Mech. Syst. 1, 219–245 (1993)MathSciNetMATH R.M. Murray, Control of nonholonomic systems using chained forms. Fields Inst. Commun. Dyn. Control Mech. Syst. 1, 219–245 (1993)MathSciNetMATH
10.
Zurück zum Zitat R.M. Murray, Nilpotent bases for a class of nonintegrable distributions with applications to trajectory generation for nonholonomic systems. Math. Control Signals Syst. 7(1), 58–75 (1994)MathSciNetCrossRef R.M. Murray, Nilpotent bases for a class of nonintegrable distributions with applications to trajectory generation for nonholonomic systems. Math. Control Signals Syst. 7(1), 58–75 (1994)MathSciNetCrossRef
11.
Zurück zum Zitat R.M. Murray, S.S. Sastry, Nonholonomic motion planning: steering using sinusoids. IEEE Trans. Autom. Control 38(5), 700–716 (1993)MathSciNetCrossRef R.M. Murray, S.S. Sastry, Nonholonomic motion planning: steering using sinusoids. IEEE Trans. Autom. Control 38(5), 700–716 (1993)MathSciNetCrossRef
12.
Zurück zum Zitat P.E. Nikravesh, O.K. Kwon, R.A. Wehage, Euler parameters in computational kinematics and dynamics, Part 2. ASME J. Mech. Transm. Autom. Des. 107(3), 366–369 (1985)CrossRef P.E. Nikravesh, O.K. Kwon, R.A. Wehage, Euler parameters in computational kinematics and dynamics, Part 2. ASME J. Mech. Transm. Autom. Des. 107(3), 366–369 (1985)CrossRef
13.
Zurück zum Zitat P.E. Nikravesh, O.K. Kwon, R.A. Wehage, Euler Parameters in Computational Kinematics and Dynamics, Part 1. ASME J. Mech. Transm. Autom. Des. 107(3), 358–365 (1985)CrossRef P.E. Nikravesh, O.K. Kwon, R.A. Wehage, Euler Parameters in Computational Kinematics and Dynamics, Part 1. ASME J. Mech. Transm. Autom. Des. 107(3), 358–365 (1985)CrossRef
14.
Zurück zum Zitat C.W. Stammers, P.H. Prest, C.G. Mobley, A friction drive robot wrist: electronic and control requirements. Mechatronics 2(4), 391–401 (1992)CrossRef C.W. Stammers, P.H. Prest, C.G. Mobley, A friction drive robot wrist: electronic and control requirements. Mechatronics 2(4), 391–401 (1992)CrossRef
15.
Zurück zum Zitat F. Thomas, Approaching dual quaternions from matrix algebra. IEEE Trans. Robot. 30(5), 1037–1048 (2014)CrossRef F. Thomas, Approaching dual quaternions from matrix algebra. IEEE Trans. Robot. 30(5), 1037–1048 (2014)CrossRef
16.
Zurück zum Zitat D. Tilbury, R.M. Murray, S.S. Sastry, Trajectory generation for the n-trailer problem, using Goursat normal form. IEEE Trans. Autom. Control 40(5), 802–819 (1995)MathSciNetCrossRef D. Tilbury, R.M. Murray, S.S. Sastry, Trajectory generation for the n-trailer problem, using Goursat normal form. IEEE Trans. Autom. Control 40(5), 802–819 (1995)MathSciNetCrossRef
17.
Zurück zum Zitat K. Wohlhart, Displacement analysis of the general spherical Stewart platform. Mech. Mach. Theory 29(4), 581–589 (1994)CrossRef K. Wohlhart, Displacement analysis of the general spherical Stewart platform. Mech. Mach. Theory 29(4), 581–589 (1994)CrossRef
Metadaten
Titel
Kinematics of the -2UPS Spherical Robot
verfasst von
Patrick Grosch
Federico Thomas
Copyright-Jahr
2019
DOI
https://doi.org/10.1007/978-3-030-11304-9_6

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