Adaptive/robust time‐varying stabilization of second‐order non‐holonomic chained form with input uncertainties

Abstract

SUMMARYAdaptive and robust time-varying control schemes are constructed to stabilize second-order nonholonomic chained form in the presence of input uncertainties. The proposed control schemes guarantee that all the state variables converge to zero asymptotically in spite of input uncertainties, and are applied to the stabilization of a planar rigid body driven by active force and torque with unknown inertia and geometric parameters. The basic idea of the proposed stabilization schemes is to first convert the nonholonomic system into a linear time-varying form by time-varying co-ordinate transformation, and then design control laws to stabilize the converted linear time-varying system.

An Improved Path‐Generating Regulator for Two‐Wheeled Robots to Track the Circle/Arc Passage

“…In general, the improved PGR with adjustable look-ahead method has better performance along circle/arc passage. Compared with the other research, like references [12][13][14][15][16][17][18][19], the improved PGR with the adjustable look-ahead method has not only the merits of convergence perfectly, but also the strong capacity of resisting disturbance. However, this method has the limitation in application that is just for circle/ arc passage problem.…”

Universal Practical Tracking Control of a Planar Underactuated Vehicle

“…It is assumed that the force F is acting on, and parallel to, the symmetric axis of vehicle. Then, the dynamic equation of vehicle can be written as with the second‐order nonholonomic constraint .…”

“…For nonholonomic systems, due to the nonexistence of static smooth time-invariant state feedback control laws achieving the asymptotic point stabilization [8], the control objectives are usually classified to two categories: fixed-point stabilization [9][10][11][12][13][14][15][16][17] and trajectory tracking Manuscript [4,[18][19][20][21]. The controllers developed for the two control objectives are effective in many practical situations, but usually not suitable for some complicated control goals, for example the docking of vehicles that consists of the both tasks.…”

Path-generating regulator along a straight passage for two-wheeled mobile robots

“…Although many methods focusing on the closed-loop control of nonholonomic systems have been proposed, most of the designed feedback control systems are in chained form which needs input transformation and coordinate transformation. For example, navigation utilizing chained system which is based on local coordinate transformation to the canonical form [3], feedback law based on time-variant analysis [4], [5], quasi-continuous exponential stabilization control [6], discontinuous state feedback control [7], [8], time-state control [9] and nonlinear optimal regulator [10]. A common characteristic of all these discontinuous controllers is that the converting variables can not be defined globally which brings out the result that the feedback control law can not be defined globally as well.…”