On the Trajectory Generation of the Hydrodynamic Chaplygin Sleigh

In this letter we consider the asymptotic behaviour and the trajectory generation problem for the Chaplygin sleigh interacting with a potential fluid. We investigate which trajectories can be obtained, at least asymptotically as t tents to infinity, by controlling some of the coordinates (shape-control variables) and using the theory of reconstruction. Moreover we support our conclusions via numerical simulations

Global Formulation and Control of a Class of Nonholonomic Systems

This thesis study motion of a class of non-holonomic systems using geometric mechanics, that provide us an efficient way to formulate and analyze the dynamics and their temporal evolution on the configuration manifold. The kinematics equations of the system, viewed as a rigid body, are constrained by the requirement that the system maintain contact with the surface. They describe the constrained translation of the point of contact on the surface. In this thesis, we have considered three different examples with nonholonomic constraint i-e knife edge or pizza cutter, a circular disk rolling without slipping, and rolling sphere. For each example, the kinematics equations of the system are defined without the use of local coordinates, such that the model is globally defined on the manifold without singularities or ambiguities. Simulation results are included that show effectiveness of the proposed control laws