Geometric Control Theory And Applications For A Class Of Generalized Nonholonomic Chained Systems

It is well known that the nonholonomic systems represent a large class of mechanical systems. For the applications and theoretical importance, it has been received more and more increasing interests in controllers dealing with the stabilization and tracking problems. In this thesis, the controller designs are discussed for a class of generalized nonholonomic chained form systems.Firstly. the feedback stabilization problem of a standard nonholonomic chained system about the tractor with one trailer is discussed,.This model is a nonholonomic control system without driftless term, also called a tractor-trailer mobile robot. A states-inputs coordinate transformation can change the system into the chained form which was diffeomorphic to the original system. A discontinuous controller and a smooth time-varying controller are derived to stabilize the nonholonomic chained system respectively.The numerical simulation results perfectly show that the two controllers also can make the car configuration converge to the origin exponentially.Secondly, the stabilization problem for a generalized nonholonomic chained system is studied It is discussed for the one-legged hopping robot with a nonzero initial angular momentum in flight phase.The robot pose can be stabilized to the desired pose. Nonzero initial angular momentum results in the drift term for the original nonholonomic system. The model can’t be converted into a common standard chained form,but,it is a so called generalized chained system which is diffeomorphic with the original system.The time-varying controller makes the error of the robot pose exponentially converge to the origin, such that the robot pose converges to the desired pose, The effectiveness of the proposed control law is verified by the simulation.