Adaptive Integral Sliding Mode Stabilization of Nonholonomic Drift-Free Systems

Abstract

This article presents adaptive integral sliding mode control algorithm for the stabilization of nonholonomic drift-free systems. First the system is transformed, by using input transform, into a special structure containing a nominal part and some unknown terms which are computed adaptively. The transformed system is then stabilized using adaptive integral sliding mode control. The stabilizing controller for the transformed system is constructed that consists of the nominal control plus a compensator control. The compensator control and the adaptive laws are derived on the basis of Lyapunov stability theory. The proposed control algorithm is applied to three different nonholonomic drift-free systems: the unicycle model, the front wheel car model, and the mobile robot with trailer model. The controllability Lie algebra of the unicycle model contains Lie brackets of depth one, the model of a front wheel car contains Lie brackets of depths one and two, and the model of a mobile robot with trailer contains Lie brackets of depths one, two, and three. The effectiveness of the proposed control algorithm is verified through numerical simulations.

Backstepping based nonlinear adaptive control for the extended nonholonomic double integrator

“…As in [1], system (3) will be referred to as the Extended Nonholonomic Double Integrator (ENDI). The ENDI system (3) satisfies the following properties:…”

“…The reason for this is primarily threefold: i) Mechanical systems such as wheeled mobile robots, robot manipulators, space robots and underwater vehicles have non integrable constraints; ii) the formation of control law for systems which cannot be easily transformable into linear control problem in a meaningful way is quiet challenging and iii) these systems cannot be stabilized by static time invariant state feedback laws as pointed out by Brockett [6]. Different control strategies have been presented for the stabilization of nonholnomic systems to overcome the limitations of the Brockett result like: discontinuous time-invariant stabilization [4,10,12,14], smooth time-varying stabilization [13,15], adaptive techniques [9,19] and sliding mode control [1,5,17].…”

“…In a number of published work [1,5,16], the authors have concentrated on the kinematic models of nonholonomic systems with their velocity as direct control inputs. Although this approach works well in many situation, the performance of some physical systems will degrade if their dynamics, like forces and torques which are the actual inputs, are neglected.…”

Robust Approach for Global Stabilization of a Class of Underactuated Mechanical Systems in Presence of Uncertainties

“…Further, the control is not robust to uncertainties and external disturbances; and hence, results in degraded system performance. A balancing control obtained from robust nonlinear control techniques like sliding mode control (SMC) [35][36][37][38][39] will not sufer from these drawbacks. Tis is the motivation behind this work.…”

Smooth super twisting sliding mode based steering control for nonholonomic systems transformable into chained form

“…In recent years, various control design techniques have been proposed for nonholonomic systems in chained form, and much effort has been devoted to the stabilization and tracking control, see [5,7,10,19,20]. Among the techniques mentioned in the literature, Sliding Mode Control (SMC) has attracted much attention of the researchers due to its simplicity, fast response, and robustness to external noise and parameter variation [1,11,21]. However, one major drawback of SMC is the presence of the chattering effect, caused by the switching frequency of the control.…”