# Mathematical Research Seminar

Mathematical research seminar is organized by the departments of Mathematics of two members of the University - UP FAMNIT and Andrej Marušič Institute (UP IAM), every Monday from October to June.

You are cordially invited to attend the lectures.

**Datum in ura**/ Date and time: 27.3.23

**Predavalnica**/ Location: FAMNIT-MP1

**Predavatelj**/ Lecturer: Petar Pavešić (University of Ljubljana, Slovenia)

**Naslov**/ Title: How to Get Where You Want to Go (Topological complexity of motion planning)

**Vsebina**/ Abstract:

Motion planning is among the core problems in robotics, see for example LaValle, Planning Algorithms for a nice overview of the subject.

Mathematically, one can consider all possible positions of a robot, view it as a topological space and try to find a continuous path ('*motion plan*') in that space from a given initial position to a required final position of the robot. A further refinement arises if we require that the motion plan is __predictable__ in the sense that the chosen path depends continuously on the input and output data (think of motion plans for self-driving cars).

It turns out that predictable motion planning has inherent instabilities, which are caused by the global topology of the space of all robot positions.__Topological complexity__ was introduced some twenty years ago by Michael Farber as a measure for these instabilities. We will present some basic results of the theory and describe some applications and open problems.

Mark your calendar and join us for what promises to be an unforgettable experience.

Feel free to invite any friends or colleagues who may be interested.

We look forward to sharing the passion for math with you!