Welcome to Peter Donelan's webpage

Research interests

• Singularity theory, algebraic geometry, invariant theory: applications to robotics, robot manipulators and mechanisms
• Mathematics and Poetry

Curriculum vitae

• CV pdf

Publications

• S. Amirinezhad and P. Donelan, Input and output singularities for parallel manipulators, in Proc. IFToMM World Congress, Springer (2019) (10pp), (to appear)

• S. Amirinezhad, P. Donelan and A. Müller, Transversality and its applications in kinematics, in Advances in Robot Kinematics, Bologna, Italy 2018, eds J. Lenarčič and V. Parenti-Castelli, Springer, (2018) 221-229

• S. Amirinezhad and P. Donelan, Kinematic constraint maps and C-space singularities for planar mechanisms with prismatic joints, in Advances in Robot Kinematics, Bologna, Italy 2018, eds J. Lenarčič and V. Parenti-Castelli, Springer, (2018) 212-220

• S. Amirinezhad and P. Donelan, Kinematic singularities of a 3-dof planar geared robot manipulator, in Advances in Robot Kinematics, Grasse, France, 2016, eds J. Lenarčič and J.-P. Merlet, Springer, (2018) 441-449

• P. Donelan and A. Müller, Towards a unified notion of kinematic singularities for robot arms and non-holonomic platforms, in Advances in Robot Kinematics, Grasse, France, 2016, eds J. Lenarčič and J.-P. Merlet, Springer, (2018) 393-401

• P. Donelan and J. M. Selig, Hyperbolic pseudoinverses for kinematics in the Euclidean group, SIAM J. Matrix Analysis and Applications, 37 (2017) 1541-1559

• S. Amirinezhad and P. Donelan, Kinematic constraint maps, C-space singularities and generalised Grashof conditions, in Proc. ASME 2017 IDETC/CIE Conf., ASME (2017) V05BT08A071 (10pp)

• L. Kempthorne and P. Donelan, Barbilian-Barbu - a case study in mathematico-poetic translation, Signata - Annals of Semiotics, 7 (2016) 337-360

• M. Daher and P. Donelan, Invariant properties of the Denavit-Hartenberg parameters, in Interdisciplinary Applications of Kinematics, Mechanisms and Machine Science Vol. 26, eds A. Kecskemethy and F. Geu Flores, Springer (2015) 43-51

• M. Daher and P. Donelan, Invariants of the k-fold adjoint action of the Euclidean isometry group, J. Geometry, 107 (2015) 169-185

• P. Donelan and A. Müller, General formulation of the singularity locus for a 3-dof regional manipulator, in Proc. Int. Conf. Robotics and Automation, Shanghai, 2011, IEEE, Piscataway NJ, (2011) 3958-3963

• P. Donelan and A. Müller, Singularities of regional manipulators revisited, in Advances in Robot Kinematics, Portoroz, 2010, eds J. Lenarčič and M. Stanišič, Springer, Dordrecht (2010) 509-519

• P. S. Donelan, Kinematic singularities of robot manipulators, in Advances in Robot Manipulators, ed A. Lazinica, In-Tech, Vienna, Austria (2010) 401-416

• P. Donelan, Genericity conditions for serial manipulators, in Advances in Robot Kinematics, Batz-sur-Mer, 2008, eds J. Lenarčič and P. Wenger, Springer, Dordrecht (2008) 185-192

• J. M. Selig and P. Donelan, A screw syzygy with application to robot singularity computation, in Advances in Robot Kinematics, Batz-sur-Mer, 2008, eds J. Lenarčič and P. Wenger, Springer, Dordrecht (2008) 147-154

• P. S. Donelan, Singularities of robot manipulators, in Singularity Theory, Proc. 2005 Marseille Singularity School and Conference, eds D. Chéniot et al, World Scientific, Singapore (2007) 189-218

• P. S. Donelan, Singularity-theoretic methods in robot kinematics, Robotica, 25 (2007) 641-659

• J.-P. Merlet and P. Donelan, On the regularity of the inverse Jacobian of parallel robots, in Advances in Robot Kinematics, Ljubljana, 2006, eds J. Lenarčič and B. Roth, Springer, Dordrecht (2006) 41-48

• M. Cocke, P. S. Donelan and C. G. Gibson, Trajectory singularities for a class of parallel motions, in Real and Complex Singularities, São Carlos Workshop, Marseille, 2004, eds J.-P. Brasselet and M. A. Soares Ruas, Birkhäuser (2006) 53-70

• M. Cocke, P. S. Donelan and C. G. Gibson, Screw Systems, Singular Trajectories and Darboux-Type Motions, in Proc. Symp. Life, Works, and Legacy of Sir Robert Ball on the Centenary of Treatise on Theory of Screws, Cambridge, 2000, (2000) 29pp

• M. Cocke, P. S. Donelan and C. G. Gibson, Instantaneous singular sets associated to spatial motions, in Real and Complex Singularities, São Carlos Workshop, 1998, eds. F. Tari and J. W. Bruce, Res. Notes Math., 412 Chapman and Hall/CRC, Boca Raton, (2000) 147-163

• P. S. Donelan and C. G. Gibson, Singular phenomena in kinematics, in Singularity Theory, Proc. European Singularities Conf., Liverpool, 1996, London Math. Soc. Lecture Notes 263, Cambridge UP (1999) 379-402

• P. S. Donelan, C. G. Gibson and W. Hawes, Trajectory singularities of general planar motions, Proc. Royal Soc. Edinburgh, 129A (1999) 37-55

• P. S. Donelan and C. P. Scott, Real inflections of four--bar coupler curves, Mechanism and Machine Theory, 30 (1995) 1179-1191

• P. S. Donelan and C. G. Gibson, On the hierarchy of screw systems, Acta Applicandae Mathematicae, 32 (1993) 267-296

• P. S. Donelan, On the geometry of planar motions, Quarterly J. Math. Oxford, 44 (1993) 165-184

• P. S. Donelan and C. G. Gibson, First-order invariants of Euclidean motions, Acta Applicandae Mathematicae, 24 (1991) 233-251

• P. S. Donelan, Generic properties in Euclidean kinematics, Acta Applicandae Mathematicae, 12 (1988) 265-286

Websites

• (with J. Azzato) Singularities in Robot Kinematics - A Publications Database (2007)

• (with A. Heyes, S. Shep and M. Sonzogni) A Timeline of Mathematics and Poetry (2017)

Other research outputs

• P. Donelan, Dan Barbilian/Ion Barbu: mathematician and poet, NZ Mathematics Colloquium, Canterbury, 2015

• D. Crook and P. Donelan, Polynomial invariants and SAGBI bases for multi-screws (2012) 12pp

• P Donelan and J Selig, Polynomial invariants of screws and screw systems, (2006) 12pp

• P. Donelan, Singularities of robot manipulators: Lie groups and exponential products, Singularities in Geometry and Applications, Bedlewo, 2011, (2000) 16pp, [Slides]

PhD and MSc students

• Seyedvahid Amirinezhad (PhD, 2019): A Constraint-Based Approach to Manipulator Kinematics and Singularities

• Loveday Kempthorne (PhD, joint with Translation Studies, 2015): Relations between Modern Mathematics and Poetry: Czesław Miłosz; Zbigniew Herbert; Ion Barbu/Dan Barbilian

• Amani Ahmed Otaif (MSc, 2013): Constraint Equations for a Planar Parallel Platform

• Mohammed Daher (PhD, 2013): Dual Numbers and Invariant Theory of the Euclidean Group with Applications to Robotics

• Deborah Crook (MSc, 2009): Polynomial Invariants of the Euclidean Group Action on Multiple Screws

• Sandra Chapman (MSc, 1995): The Geometry of the Point-Path Generated by Rigid Body Motion in Two and Three Dimensions

• Christopher Scott (MSc, 1992): Real Inflexions of the Four-Bar Coupler Curve

Summer scholarship projects

• Thomas Berry, Dual quaternions and their applications in robot kinematics, 2019