# Some mathematical problems in robotics

Discussion paper

Selig, JM (2000).

*Some mathematical problems in robotics.*School of Computing, Information Systems and Mathematics, South Bank University, London.

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Selig, JM and Ding, X (2001). A screw theory of static beams.*IEEE International Conference on Intelligent Robots and Systems.*San Diego, CA, USA 29 Oct - 03 Nov 2001 London South Bank University. doi:10.1109/IROS.2001.973376

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Gallet, M, Nawratil, G, Schicho, J and Selig, JM (2017). Mobile Icosapods.*Advances in Applied Mathematics.*88 (July), pp. 1-25.

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Selig, JM (1986). Note on the Principle of Transference.*Design Engineering Technical Conference.*Columbus, Ohio London South Bank University.

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Wallace, R and Selig, JM (1995). Scaling Direct Drive Robots.*Robotics and Automation, 1995 IEEE International Conference on.*Nagoya, Japan 21 - 27 May 1995 Wallace.

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Selig, JM (2000). Spatial stiffness matrix from simple stretched springs.*IEEE International Conference on Robotics & Automation.*San Francisco Ca. USA 24 - 28 Apr 2000 London South Bank University. doi:10.1109/ROBOT.2000.845218

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Selig, JM and Ding, X (2001). Theory of vibrations in Stewart platforms.*IEEE International Conference on Intelligent Robots and Systems.*San Diego, CA USA London South Bank University. doi:10.1109/IROS.2001.976395

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##### Clifford algebra of points, lines and planes

Selig, JM (2000). Clifford algebra of points, lines and planes.*Robotica.*18 (5), pp. 545 - 556.

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Selig, JM (2007). Cayley maps for SE(3).*12th International Federation for the Promotion of Mechanism and Machine Science World Congress.*Besancon France London South Bank University. pp. ? - ? (6)

##### A geometric Newton-Raphson method for Gough-Stewart platforms

Selig, JM and Li, H (2009). A geometric Newton-Raphson method for Gough-Stewart platforms.*Fifth International Workshop on Computational Kinematics.*University of Duisburg-Essen, Germany 06 - 08 May 2009 London South Bank University. pp. 183 - 190 doi:10.1007/978-3-642-01947-0_23

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Selig, JM and Donelan, P (2008). A screw syzygy with applications to robot singularity computation. in: Advances in Robot Kinematics: Analysis and Design Netherlands Springer Science+Business Media B.V. pp. 147 - 154##### Dynamics of vibratory bowl feeders

Selig, JM and Dai, JS (2005). Dynamics of vibratory bowl feeders.*Proceedings of the 2005 IEEE International Conference on Robotics and Automation April 2005.*Barcelona, Spain Apr 2005 London South Bank University. doi:10.1109/ROBOT.2005.1570617

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Selig, JM (2006). Active versus passive transformations in robotics.*IEEE Robotics and Automation Magazine.*13 (1), pp. 79 - 84.

##### Structure of the spatial stiffness matrix

Selig, JM and Ding, X (2002). Structure of the spatial stiffness matrix.*International Journal of Robotics and Automation.*17 (1), pp. 1 - 16.

##### Diagonal spatial stiffness matrices

Selig, JM and Ding, X (2002). Diagonal spatial stiffness matrices.*International Journal of Robotics and Automation.*17 (2), pp. 100 - 106.

##### Three problems in robotics

Selig, JM (2002). Three problems in robotics.*Symposium Commemorating the Legacy, Works, and Life of Sir Robert Stawell Ball.*University of Cambridge 09 - 11 Jul 2000 London South Bank University. doi:10.1243/0954406021524927

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Selig, JM (2010). Exponential and cayley maps for dual quaternions.*Advances in Applied Clifford Algebras.*20 (3-4), pp. 923 - 936.

##### Half-turns and line symmetric motions

Selig, JM and Husty, M (2011). Half-turns and line symmetric motions.*Mechanism and Machine Theory.*46 (2), pp. 156 - 167.

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Selig, JM (2011). On the instantaneous acceleration of points in a rigid body.*Mechanism and Machine Theory.*46 (10), pp. 1522 - 1535.

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Selig, JM (2011). On the geometry of point-plane constraints on rigid-body displacements.*Acta Applicandae Mathematicae.*116 (2), pp. 133 - 155.

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Selig, JM (2013). Characterisation of Frenet-Serret and Bishop motions with applications to needle steering.*Robotica.*31 (6), pp. 981 - 992.

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Ding, X and Selig, JM (2004). On the compliance of coiled springs.*International Journal of Mechanical Sciences.*46 (5), pp. 703 - 727.

##### Curves of stationary acceleration in SE(3)

Selig, JM (2007). Curves of stationary acceleration in SE(3).*IMA Journal of Mathematical Control and Information.*24 (1), pp. 95 - 113.

##### A screw theory of Timoshenko beams

Selig, JM and Ding, X (2009). A screw theory of Timoshenko beams.*Journal of Applied Mechanics, Transactions ASME.*76 (3), pp. 1 - 7.

##### Rigid body dynamics using Clifford algebra

Selig, JM and Bayro-Corrochano, E (2010). Rigid body dynamics using Clifford algebra.*Advances in Applied Clifford Algebras.*20 (1), pp. 141 - 154.

##### On the geometry of the homogeneous representation for the group of proper rigid-body displacements

Selig, JM (2013). On the geometry of the homogeneous representation for the group of proper rigid-body displacements.*Romanian Journal of Technical Sciences - Applied Mechanics.*58 (1-2), pp. 5 - 28.

##### Rational interpolation of car motions

Selig, JM (2015). Rational interpolation of car motions.*Journal of Mechanisms and Robotics.*7 (3).

##### Quadratic constraints on rigid-body displacements

Selig, JM (2010). Quadratic constraints on rigid-body displacements.*Journal of Mechanisms and Robotics.*2 (4).

##### On the line geometry of rigid-body inertia

Selig, JM and Martins, D (2014). On the line geometry of rigid-body inertia.*Acta Mechanica.*225 (11), pp. 3073 - 3101.

##### A Class of Explicitly Solvable Vehicle Motion Problems

Selig, JM (2015). A Class of Explicitly Solvable Vehicle Motion Problems.*IEEE Transactions on Robotics.*31 (3), pp. 766 - 777 (11).

##### Persistent rigid-body motions and Study's "Ribaucour" problem

Selig, JM and Carricato, M (2016). Persistent rigid-body motions and Study's "Ribaucour" problem.*Journal of Geometry.*108 (1), pp. 149-169.

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Rudnev, M and Selig, JM (2016). On the use of the Klein quadric for geometric incidence problems in two dimensions.*Siam Journal on Discrete Mathematics.*30 (2), pp. 934 - 954 (21).