AProf Peter Donelan

AProf Peter Donelan profile picture

Associate Professor School of Mathematics and Statistics


Teaching in 2020

Research interests

Singularity theory, geometry, applications to robotics, robot manipulators and mechanisms


BSc Hons (Bristol), PhD (Southampton)

About me

My research has centred around singularity theory and its application in mathematical robotics, where there is a wide range of problems involving interesting geometry. Relevant language and tools come from algebraic geometry, especially the theory of invariants and Gröbner bases, differential geometry and Lie groups. I have taught graduate courses in all these topics and they feature in my published research.

From 2001-04 and 2013-18, I was head of school.  During those terms, I aimed to ensure students have the best possible education in the mathematical sciences, whether they enjoy the theoretical and abstract aspects or understanding how they can be used to solve problems in so many other fields. Both of these make mathematics and statistics students among the most sought after graduates in employment. I have worked with colleagues on the development of new programmes in actuarial science, applied statistics and data science, and developed close links with engineering and computer science as well as strong connections with schools and secondary teachers. The mathematical sciences have also maintained and grown a fine reputation as one of the university’s leading research centres, attracting funding both in New Zealand and internationally.


I am currently working on problems in singularities in parallel robot kinematics, invariant theory and the classification of mechanisms, and pseudoinverses for non-Riemannian metrics and their application. Loveday Kempthorne’s PhD thesis on mathematics and poetry, including the Romanian mathematician/poet Dan Barbilian/Ion Barbu, has sparked a separate avenue of research interest.

Supervision interest

I will supervise postgraduate projects in singularity theory, especially with application to kinematics, and other aspects of the geometry of motion using techniques of algebraic geometry and Lie theory.

Master’s and PhD 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

List of selected publications

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

S. Amirinezhad, P. Donelan and A. Müller, Transversality and its applications in kinematics, in Advances in Robot Kinematics, Bologna, 2018, Springer, (2018)  221-229

S. Amirinezhad and P. Donelan, Kinematic singularities of a 3-dof planar geared robot manipulator, in Advances in Robot Kinematics, Grasse, 2016, 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, 2016, 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, Invariants of the k-fold adjoint action of the Euclidean isometry group, J. Geometry, 107 (2015) 169-185

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

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. Lenarcic and M. Stanisic, 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. Lenarcic 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. Lenarcic and P. Wenger, Springer, Dordrecht (2008) 147-154

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

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

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. Lenarcic 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 SingularitiesSao Carlos Workshop, Marseille, 2004, eds J.-P. Brasselet and M. A. Soares Ruas, Birkhauser (2006) 53-70

M. Cocke, P. S. Donelan and C. G. Gibson, Instantaneous singular sets associated to spatial motions, in Real and Complex Singularities, Sao 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


Teaching in 2020