doc. Mgr. Petr Vašík, Ph.D.
E-mail:   vasik@fme.vutbr.cz  Dept.:   Institute of Mathematics Position:   Director of Institute Room:   A1/1846 Dept.:   Institute of Mathematics Dept. of Algebra and Discrete Mathematics Position:   Associate Professor Room:   A1/1846

Supervised courses:

• Algebras of rotations and their applications (9ARA)
• Bachelor Project (UM) (6BM)
• Bachelor Seminar (B-MAI) (SES)
• Functions of a Complex Variable (9FKP)
• Geometrical Algorithms (0AV)
• Linear Algebra I (SLA)
• Selected Chapters from Mathematics (0KM)

Publications:

• NÁVRAT, A.; VAŠÍK, P.:
  On geometric control models of a robotic snake, Universita del Salento
  journal article in Web of Science
• HRDINA, J.; VAŠÍK, P.; NÁVRAT, A.; MATOUŠEK, R.:
  CGA-based robotic snake control, Springer Basel AG
  journal article in Web of Science
• HRDINA, J.; NÁVRAT, A.; VAŠÍK, P.; MATOUŠEK, R.:
  Geometric Control of the Trident Snake Robot Based on CGA, Springer Basel AG
  journal article in Web of Science
• HRDINA, J.; VAŠÍK, P.; HOLUB, M.:
  Dual numbers arithmentic in multiaxis machine error modeling, MM Science
  journal article in Scopus
• HRDINA, J.; VAŠÍK, P.; NÁVRAT, A.:
  Control of 3-Link Robotic Snake Based on Conformal Geometric Algebra, Springer Basel AG
  journal article in Web of Science
• HOLUB, M.; HRDINA, J.; VAŠÍK, P.; VETIŠKA, J.:
  Three-axes error modeling based on second order dual numbers, Springer-Verlag
  journal article in Web of Science
• HRDINA, J.; VAŠÍK, P.:
  Notes on differential kinematics in conformal geometric algebra approach,
  Mendel 2015, pp.363-374, ISBN 978-3-319-19824-8, (2015), Springer International Publishing
  conference paper
  akce: 21st International Conference on Soft Computing — MENDEL 2015, Brno University of Technology, 23.06.2015-25.06.2015
• HRDINA, J.; VAŠÍK, P.; MATOUŠEK, R.:
  Special orthogonal matrices over dual numbers and their applications
  journal article in Scopus
  akce: 21st International Conference on Soft Computing — MENDEL 2015, Brno University of Technology, 23.06.2015-25.06.2015
• HRDINA, J.; VAŠÍK, P.:
  Dual Numbers Approach in Multiaxis Machines Error Modeling, Hindawi
  journal article in Web of Science

List of publications at Portal BUT

Abstracts of most important papers:

• HRDINA, J.; VAŠÍK, P.; NÁVRAT, A.; MATOUŠEK, R.:
  CGA-based robotic snake control, Springer Basel AG
  journal article in Web of Science
  Local controllability of an n-link robotic snake with variable wheel positions is solved by means of the conformal geometric algebra, more precisely by the Clifford algebra of signature (3, 1). The non-holonomic kinematic equations are assembled, their role in the geometric control theory is discussed and the singular positions are elaborated. Within this paper, we present an alternative model description only, while all its kinematic properties remain.
• HRDINA, J.; VAŠÍK, P.; HOLUB, M.:
  Dual numbers arithmentic in multiaxis machine error modeling, MM Science
  journal article in Scopus
  When a kinematic chain of a multiaxis machine centre is assembled by means of homogeneous matrices, it is possible to include the error representing matrices within and neglect the error terms which do not affect the prescribed accuracy. Classically, such error terms are identified and neglected according to the system of given identities after the matrix multiplication. In our approach, the matrices itself are designed to form a ring that respects the desired arithmetic of error terms, particularly the ring of matrices over the dual numbers. On the other hand, to make this algebraically possible, several negligible terms remain.
• HRDINA, J.; VAŠÍK, P.; NÁVRAT, A.:
  Control of 3-Link Robotic Snake Based on Conformal Geometric Algebra, Springer Basel AG
  journal article in Web of Science
  Local controllability of a three link robotic snake is solved by means of 5D conformal geometric algebra. The non-holonomic kinematic equations are assembled, their role in the geometric control theory is discussed and the control solution is found. The functionality is demonstrated on a virtual model in CLUCalc programme. Finally, the snake robot dynamics is elaborated.
• HRDINA, J.; VAŠÍK, P.:
  Notes on differential kinematics in conformal geometric algebra approach,
  Mendel 2015, pp.363-374, ISBN 978-3-319-19824-8, (2015), Springer International Publishing
  conference paper
  akce: 21st International Conference on Soft Computing — MENDEL 2015, Brno University of Technology, 23.06.2015-25.06.2015
  We consider different elements of a 5D conformal geometric algebra (CGA) as moving geometric objects whose final position is given by a specific kinematic chain. We show the form of the differential kinematics equations for different CGA elements, in particular point pairs, spheres and their centres.