Time minimization problem on the group of motions of a plane with admissible control in a half-disc

Abstract The time minimization problem with admissible control in a half-disc is considered on the group of motions plane. system under study provides model car plane that can move forwards or rotate place. Optimal trajectories such are used to detect salient curves image analysis. In particular, medical analysis for tracking vessels retinal images. independent interest geometric theory: it example when set values parameters contains zero at boundary. controllability and existence optimal studied. By analysing Hamiltonian Pontryagin maximum principle explicit form extremal controls found. Optimality extremals partially investigated. structure synthesis described. Bibliography: 33 titles.