Project will be devoted to the investigation of novel concepts for the analysis and design of nonlinear controllers of flexible and chained mechanical systems to either compensate or control efficiently their oscillatory modes and limit cycles. The compensation of the oscillatory modes is motivated by the flexible robotic and crane applications, where standard linear methods fail either due to the strongly nonlinear dynamics or due to the limited controllability. Limit cycles control then aims to multiply chained and actuated robotic systems. Special attention is paid to the robotic walking, optimized with respect to the injected energy. Both these application directions are intrinsically related: while the former requires removing energy from the system during the periodic cycle, the latter requires the energy injection to maintain the stable cyclic movement. These mutually mirrored problems are analyzed and implemented using the nonlinear system transformations, virtual constraints, multi-dimensional system analysis, nonlinear Lyapunov redesign and theory of time delay systems.