Stabilization And Tracking Control For Nonholonomic And Underactuated Systems

There are many nonholonomic and underactuated systems in practical engineering,wheeled mobile robots is a typical class of nonholonomic system;bridge cranes,inverted pendulums and surface vessels are underactuated systems.Since these two kinds of systems are respec-tively subject to the velocity and acceleration nonholonomic constraints,it is very difficult to directly apply the conventional nonlinear control methods in their control designs.Therefore,research on nonholonomic and underactuated systems is of great significance both in theory and practice.Motivated by the existing results in the literature,the considered systems include nonholonomic systems with the one-order velocity constraints and underactuated crane,un-deractuated surface vessel(USV)systems with the second-order acceleration constraints.The stabilization and tracking control are studied for the aforementioned three classes of systems by using backstepping,cascade control method,differential-flatness-based approach,finite-time control technology,nonlinear time-varying method,etc.The main research contents can be summarized as follows:(1)The problem of modeling and trajectory tracking control is investigated for a class of stochastic nonholonomic systems in the presence of uncertain parameters.Prior to tracking controller design,the Lagrangian method is used to facilitate the rigorous derivation of the stochastic nonholonomic dynamic model.By reasonably introducing internal state vector,a reduced-order dynamic model is proposed.Then,an adaptive tracking controller is derived,guaranteeing that the closed-loop trajectory tracking error system is exponentially practically stable in mean square.The satisfactory control performance of the controller is demonstrat-ed by modeling and simulation for a mechanics system:a vertical mobile wheel in random vibration environment.(2)The problem of modeling and motion/force tracking is considered for a class of non-holonomic systems with affine constraints and external disturbances.The derivation process of the system dynamic model is briefly presented by using the Lagrangian modeling method.By introducing nonlinear state transformation,the system kinematic equation is injected into the system dynamic equation,then a reduced-order dynamic model,which possesses practical meaning,is developed.For this reduced-order system,the asymptotic stabilization and tra-jectory tracking control objectives are achieved by respectively using the cascade and filtering control theory.Meanwhile,in the control process,the tracking error of Lagrangian multiplier is bounded with a controllable bound.A practical simulation example is provided to show the efficiency of the proposed controller.(3)The finite-time positioning and anti-swing is studied for the underactuated crane system in 2-dimension space with either constant cable length or varying cable length.The differentially flat output is constructed to transform the crane system into linear system.The elegantly designed finite-time control algorithm can simultaneously regulate the trolley to the desired destination and eliminate the payload swing within a finite time.Considering cable length variation,after achieving the simultaneous positioning regulation and payload swing suppression and elimination within a finite time,a barrier-function-based tracking controller is designed such that the cable length can quickly track the desired trajectory.(4)The adaptive anti-swing control and positioning are simultaneously investigated for underactuated crane systems in the presence of multiple parallel payloads on the trolley and rail length limitation.The equations of motion for the crane system in question are established via the Lagrangian equation.An adaptive control strategy is proposed with the help of system energy function,energy shaping and barrier function.The Lyapunov method is used to present the stability analysis,which shows that under the designed adaptive controller,the payload swings can be suppressed ultimately and the trolley can be regulated to the destination while not exceeding the pre-specified boundaries.Simulation results illustrate the efficiency and robustness of the proposed control strategy.(5)The switching-based asymptotic stabilization controller is designed for a class of un-deractuated surface vessel possessing non-diagonal inertia and damping matrices.For the synthesis of controller,the investigated underactuated model is first converted into the cas-cade system with two subsystems using input and state transformations.It is shown that the transformed cascade system is globally asymptotically convergent if and only if its second subsystem is globally asymptotically convergent.By using the finite-time control technolo-gy,a finite-time switching control strategy is developed guaranteeing the globally asymptotic convergence of the original states to zero.Finally,the finite-time switching time,which is independent of the initial conditions,is also formulated in detail.(6)The smoothly time-varying stabilization and trajectory tracking problems are ad-dressed for underactuated ship with non-diagonal inertia and damping matrices.For stabiliza-tion control,a cascade system,which is equivalent to the original system,is derived,through state and input transformations.By virtue of backstepping and nonlinearly time-varying tech-nology,a smoothly time-varying stabilization controller is proposed such that the resulting closed-loop cascade system is globally uniformly convergent.For trajectory tracking control,the reference model is transformed via the similar state and input transformations,and then the cascade tracking error system can be constructed.By applying backstepping method,a trajectory tracking control algorithm is achieved to guarantee that the closed-loop trajectory tracking error system is globally exponentially convergent.Simulation results demonstrate the effectiveness and robustness of the proposed control methodologies.