Rapid advances in computer technology and robotics have resulted in the increasing use of robots in science, medicine, household and industry. However, many problems of great practical significance remain that require the application of modern mathematical and computational tools. In my talk, I will give examples from different mathematical disciplines (optimization, statistical learning, dynamical systems, algebraic topology) of a fruitful interaction between mathematicians and roboticists that lead to new questions for mathematics research. The focus will be on the dynamical systems approach to robotics that our group at the University of Minho follows. I will show how we use basic concepts like attractor state, stability and bifurcation to endow autonomous robots with higher-level cognitive functions for natural human-robot interactions. |