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DOI: 10.23952/cot.2022.23
Received November 21, 2021; Accepted September 17, 2022; Published November 11, 2022
Abstract. The Dubins car is a model of motion, in which the scalar control determines the instantaneous angular speed of rotation. The paper considers the symmetric variant of the constraints
, where
and
. We study the three-dimensional reachable set at a given instant
. An analytical description of two-dimensional sections of the set w.r.t. the angular coordinate
is given. The boundary of each
-section is formed with the help of a certain set of curves obtained using the Pontryagin maximum principle. This set includes circular arcs and circular involutes. The symmetry property of each
-section w.r.t. a certain straight line is established. Classification of possible types of the
-sections is proposed. The greatest difficulty is presented by analysis of the case with non-simply connected
-sections. The range of values
and
, at which the
-sections are non-simply connected, is indicated.
How to Cite this Article:
V. Patsko, A. Fedotov, Three-dimensional reachable set for the Dubins car: Foundation of analytical description, Commun. Optim. Theory 2022 (2022) 23.