Nonlinear geometric control theory; optimal control; sub-Riemannian geometry; invariant control systems on Lie groups; applications in robotics; modelling of vision and image processing.
Main publications:
E.J. Bekkers, R. Duits, A. Mashtakov, G.R Sanguinetti, “A PDE Approach to Data-Driven Sub-Riemannian Geodesics in SE(2)”, Siam Journal on Imaging Sciences, 8:4 (2015), 2740-2770
A. P. Mashtakov, “Sub-Riemannian Geometry in Image Processing and Modeling of the Human Visual System”, Нелинейная динам., 15:4 (2019), 561–568
Alexey P. Mashtakov, Andrei A. Ardentov, Yuri L. Sachkov, “Parallel Algorithm and Software for Image Inpainting via Sub-Riemannian Minimizers on the Group of Rototranslations”, Numerical Mathematics: Theory, Methods and Applications, 6:1 (2013), 95–115
A. Mashtakov, R. Duits, Y. Sachkov, E.J. Bekkers, I. Beschastnyi, “Tracking of Lines in Spherical Images via Sub-Riemannian Geodesics in SO(3)”, Journal of Mathematical Imaging and Vision, 58:2 (2017), 239–264
A.P. Mashtakov, Yu.L. Sachkov, “Superintegrability of Left-Invariant Sub-Riemannian
Structures on Unimodular Three-Dimensional Lie
Groups”, Differential Equations, 51:11 (2015), 1482–1488
Alexey P. Mashtakov, Yuri L. Sachkov, “Extremal Trajectories in a Time-Optimal Problem on the Group of Motions of a Plane with Admissible Control in a Circular Sector”, Trudy Mat. Inst. Steklova, 321 (2023), 215–222; Proc. Steklov Inst. Math., 321 (2023), 200–207
A. P. Mashtakov, “Time minimization problem on the group of motions of a plane with admissible control in a half-disc”, Mat. Sb., 213:4 (2022), 100–122; Sb. Math., 213:4 (2022), 534–555
A. A. Ardentov, A. P. Mashtakov, “Control of a mobile robot with a trailer based on nilpotent approximation”, Avtomat. i Telemekh., 2021, no. 1, 95–118; Autom. Remote Control, 82:1 (2021), 73–92
A. P. Mashtakov, V. A. Yumaguzhin, V. N. Yumaguzhina, “On solutions to Fokker–Planck equations”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 178 (2020), 102–111
5.
A. P. Mashtakov, A. Yu. Popov, “Asymptotics of Extremal Controls in the Sub-Riemannian Problem on the Group of Motions of Euclidean Space”, Rus. J. Nonlin. Dyn., 16:1 (2020), 195–208
2019
6.
A. P. Mashtakov, “Sub-Riemannian Geometry in Image Processing and Modeling of the Human Visual System”, Rus. J. Nonlin. Dyn., 15:4 (2019), 561–568
A. P. Mashtakov, K. A. Putintseva, “Image processing toolkit inspired by mechanisms of human visual perception”, Program Systems: Theory and Applications, 10:4 (2019), 111–139
2018
8.
A. P. Mashtakov, “On the step-$2$ nilpotent $(n, n(n + 1)/2)$ sub-Riemannian structures”, Program Systems: Theory and Applications, 9:4 (2018), 319–360
2017
9.
V. Markasheva, A. Mashtakov, “Existence of global fundamental solution to a class of Fokker–Planck equations”, Program Systems: Theory and Applications, 8:4 (2017), 149–162
Alexey P. Mashtakov, A. Yu. Popov, “Extremal Controls in the Sub-Riemannian Problem on the Group of Motions of Euclidean Space”, Regul. Chaotic Dyn., 22:8 (2017), 949–954
A. Mashtakov, R. Duits, “A cortical based model for contour completion on the retinal sphere”, Program Systems: Theory and Applications, 7:4 (2016), 231–247
12.
Alexey Mashtakov, Andrei Ardentov, Yuri L. Sachkov, “Relation Between Euler’s Elasticae and Sub-Riemannian Geodesics on $SE(2)$”, Regul. Chaotic Dyn., 21:7-8 (2016), 832–839
A. A. Ardentov, I. Yu. Beschatny, A. P. Mashtakov, A. Yu. Popov, Yu. L. Sachkov, E. F. Sachkova, “Algorithms for evaluation position and orientation of UAV”, Program Systems: Theory and Applications, 3:3 (2012), 23–39
14.
A. P. Mashtakov, “Algorithms and Software Solving a Motion Planning Problem for Nonholonomic Five-dimensional Control Systems”, Program Systems: Theory and Applications, 3:1 (2012), 3–29
A. P. Mashtakov, “Asymptotics of extremal curves in the ball rolling problem on the plane”, CMFD, 42 (2011), 158–165; Journal of Mathematical Sciences, 199:6 (2014), 687–694
A. P. Mashtakov, Yu. L. Sachkov, “Extremal trajectories and the asymptotics of the Maxwell time in the problem of the optimal rolling of a sphere on a plane”, Mat. Sb., 202:9 (2011), 97–120; Sb. Math., 202:9 (2011), 1347–1371
Yu. L. Sachkov, A. A. Ardentov, A. P. Mashtakov, “Parallel algorithm and software for recovery of isophotes for corrupted images”, Program Systems: Theory and Applications, 1:1 (2010), 3–20
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