Class Of Second-order Nonholonomic Systems Research Articles

A discontinuous exponential stabilization law for an underactuated X4-AUV

In this paper, stabilization of a class of second-order nonholonomic systems for an underactuated X4-AUV is investigated. We present a model of the underactuated X4-AUV with six degrees of freedom (DOF) and four control inputs. Then, the system is written in a control-affine form by applying a partial linearization technique, and a dynamic controller based on Astolfi's discontinuous control is derived to stabilize all states of the system to the desired equilibrium point exponentially. The present approach does not necessitate the conversion of the system model into a "chained form", and thus does not rely on any special transformation techniques to obtain a canonical form. A simulation is conducted to demonstrate the effectiveness of the proposed controller.

Stabilization of second-order nonholonomic systems in canonical chained form

Stabilization of a class of second-order nonholonomic systems in canonical chained form is investigated in this paper. First, the models of two typical second-order nonholonomic systems, namely, a three-link planar manipulator with the third joint unactuated, and a kinematic redundant manipulator with all joints free and driven by forces/torques imposing on the end-effector, are presented and converted to second-order chained form by transformations of coordinate and input. A discontinuous control law is then proposed to stabilize all states of the system to the desired equilibrium point exponentially. Computer simulation is given to show the effectiveness of the proposed controller.

非ホロノミック機械系の平均化法による挙動解析と振幅変調制御 平面２Ｒ自由関節マニピュレータの位置制御

Manipulators with free joints fall in a class of second-order nonholonomic systems whose dynamical constraints are nonintegrable. Control of such systems is one of major research topics in robotics and control engineering. In the literature, the authors analyzed nonlinear behaviors of a two joint manipulator with a free joint in response to a periodic input. The manipulator showed chaotic behaviors for larger input-amplitudes. A control method to position both joints via modulation of the input-amplitude was also proposed. Although the strategy was effective, it sufferes from heuristics and difficulty for generalization. In this paper, behaviors of the free-joint manipulator with a periodic input are approximated via the 1st-order and 2nd-order averaging methods. The invariant manifolds of the averaged behavior are analyzed and identified by defining a “pseudo-Hamiltonian” on an “input-amplitude normalized phase plane”. A control method to reach a desired invariant manifold via modulation of the input-amplitude is also proposed and a termination control at the destination is formulated. The effectiveness of the proposed control methods is verified by computer simulations.