Andrei Ardentov
Publications:
Ardentov A. A.
Extremals in the Markov – Dubins Problem with Control on a Triangle
2024, Vol. 20, no. 1, pp. 2742
Abstract
We formulate a timeoptimal problem for a differential drive robot with bounded positive
velocities of the driving wheels. This problem is equivalent to a generalization of the classical
Markov – Dubins problem with an extended domain of control. We classify all extremal controls
via the Pontryagin maximum principle. Some optimality conditions are obtained; therefore, the
optimal synthesis is reduced to the enumeration of a finite number of possible solutions.

Ardentov A. A.
Hidden Maxwell Stratum in Euler's Elastic Problem
2019, Vol. 15, no. 4, pp. 409414
Abstract
This investigation continues the study of the classical problem of stationary configurations
of an elastic rod on a plane. The length of the rod, the ends of the rod and the directions at the
ends are fixed. The problem was first studied by Leonard Euler in 1744 and the optimal synthesis
problem is still an open problem. Euler described a family of geodesics containing the solutions,
which are called Euler elasticae. It is known that sufficiently small pieces of Euler elasticae
are optimal, i.e., they have a minimum of the potential energy. In theory, the point where an
optimal curve loses its optimality is called a cut point. Usually several optimal curves arrive at
such points, so the points have multiplicity more than 1 and are called Maxwell points. The aim
of this work is to describe numerically Maxwell points where two nonsymmetric elasticae come
with the same length and energy value.
