Kostov, V. P.; Degtiariova-Kostova, E. V. The planar motion with bounded derivative of the curvature and its suboptimal paths. (English) Zbl 0877.49028 Acta Math. Univ. Comen., New Ser. 64, No. 2, 185-226 (1995). Summary: We describe the construction of suboptimal trajectories of the problem of a planar motion with bounded derivative of the curvature and we prove their suboptimality. ‘Suboptimal’ means longer than the optimal by no more than a constant depending only on the bound \(B\) for the curvature’s derivative. The initial and final coordinates, curvatures and tangent angles are given. The tangent angle and the curvature of the path are assumed to be continuous. The bound \(B\) and the distance \(d\) between the initial and final points satisfy an inequality of the kind \(d\gg 1/\sqrt B\). Cited in 5 Documents MSC: 49N70 Differential games and control 49N75 Pursuit and evasion games 93C85 Automated systems (robots, etc.) in control theory 49K15 Optimality conditions for problems involving ordinary differential equations Keywords:car-like robot; clothoid; Pontryagin maximum principle; suboptimal trajectories; planar motion PDFBibTeX XMLCite \textit{V. P. Kostov} and \textit{E. V. Degtiariova-Kostova}, Acta Math. Univ. Comen., New Ser. 64, No. 2, 185--226 (1995; Zbl 0877.49028) Full Text: EuDML EMIS