Andrei Ardentov

    Program Systems Institute of RAS


    Ardentov A. A.
    We formulate a time-optimal 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.
    Keywords: differential drive robot, Markov – Dubins problem, extremal trajectories, Pontryagin maximum principle
    Citation: Ardentov A. A.,  Extremals in the Markov – Dubins Problem with Control on a Triangle, Rus. J. Nonlin. Dyn., 2024, Vol. 20, no. 1, pp.  27-42
    Ardentov A. A.
    Hidden Maxwell Stratum in Euler's Elastic Problem
    2019, Vol. 15, no. 4, pp.  409-414
    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.
    Keywords: Euler elastica, Maxwell strata, optimal control
    Citation: Ardentov A. A.,  Hidden Maxwell Stratum in Euler's Elastic Problem, Rus. J. Nonlin. Dyn., 2019, Vol. 15, no. 4, pp.  409-414

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