Control of underactuated mechanical systems via passive velocity field control: Application to snakeboard and 3D rigid body

Abstract In this paper we consider the application of a new formulation of passive velocity field control (PVFC) to the control problem of a class of underactuated mechanical systems (UAMS). In our previous report synthesizing the desired velocity vector fields for PVFC by the decoupling vector fields, we were able to prove that control torques may be successfully obtained and the solvability of the synthesizing problem of PVFC for the UAMS may be guaranteed. We newly develop this control design methodology and propose an explicit feedback solution to the control problems of the UAMS, such as snakeboard, underactuated 3D rigid bodies. Several simulations show the validity of the proposed control methodology.