【作者】 王虎；

【导师】 陈虹；

【作者基本信息】 吉林大学 ， 控制理论与控制工程， 2007， 硕士

【摘要】 轮式移动机器人(Wheeled Mobile Robot, WMR)是非完整非线性系统的一个典型代表,它为这类系统控制理论研究提供了一个优秀的应用实例。本文主要研究基于滚动优化的机器人系统H_∞轨迹跟踪控制方法,其主要思想是利用预测控制“与时俱进”的特点处理机器人行进过程中性能与约束(稳定性)等矛盾,使得当外界干扰较大,控制量接近其约束边界时适当降低系统性能以保证满足时域硬约束(稳定性);当干扰较小时尽可能提高系统性能。而该思想是通过沿着目标轨迹线性化实现的,即将整个非线性跟踪控制过程分解为多个线性控制子过程,在每个采样时刻(实际运行轨迹的每个采样点)都将求解一个约束H_∞控制问题,并且此问题的求解是基于此刻更新的线性子系统和状态。同时为了避免选择加权函数,采样时刻的约束H_∞控制问题将采用线性矩阵不等式(LMI)工具进行描述。这种跟踪控制方法综合了预测控制、H_∞控制的优点,很好地实现了系统性能与输入约束(稳定性)之间的折中。LMI技术的应用使得在线优化切实可行。文中首先建立了轮式移动机器人的动力学方程,并讨论了其主要运动性质与控制性质;之后针对该系统提出了基于滚动优化的H_∞跟踪控制方法,同时分析了算法的可行性及闭环系统性质,并给出了仿真结果及相关分析。更多还原

【Abstract】 The increasing of people’s requirement and the developing of technologiesmakes the wheeled mobile robots (WMR) more and more widely used in everyaspect of the society. From the common serving robots and the self-determiningvehicles to the rovers used for space exploration, each of them can be considered asa special kind of WMR. These practical requirements motivate the study to WMRto be much deeper and particular. In many cases, we need to make the robot movealong a specified trajectory, and actually, this task can be theoretically describedas a control problem consist of planning and tracking in the presence of disturbanceand uncertainties. From the theory point of view, it is the most di?cult to atten-uate the disturbance and uncertainties while satisfying the control constraints (forexample the motor attaching to the driving wheel can only provide limited torque).This is a multi-object problem which is not easy to solve, since good performancealways needs large control actions, and thus a good controller should have theability to obtain a satisfied tradeo? between good performance and satisfying con-trol constraints. Though for tracking problem, various control methods have beensuggested, few of them have explicitly solve the tradeo? problem and for whichthere are two most popular methods. One is to cut the control input to its boundwhen it goes beyond the limit, and the disadvantage of this method is that theperformance or even the stability cannot be guaranteed. The other method is totranslate the multi-object optimization problem into a single-object optimizationproblem by weighting, but to choose suitable weighting functions which can giveattention to both performance and control constraints is not a trivial task. Themain job of this thesis is to propose a feasible and tractable method for trackingcontrol of WMR, our object is to make the WMR asymptotically track the giventrajectory and obtain a tradeo? between performance and control constraints. Wefirst present the mathematic model of WMR, and give a detailed analysis about itskinematical properties and control properties. Based on the analysis, we propose acontrol scheme, in which the controller design is separated to two parts, which arefeed forward part and feedback part. The responsibility of the feed forward part isto generate a feasible trajectory (including nominal state xd and nominal controlinput ud), and this can be completed by di?erential ?atness technique. What ismore di?cult is how to design the feed back controller which is used to correctthe errors caused by disturbances and uncertainties, and simultaneously obtain atradeo? between performance and control constraints. Given the desired trajectoryxd, note that we just have to make xe = x ? xd→0 in order to let x→xd. So wecan linearize the system along the desired trajectory to get the error system withxe = x ? xd as its state. By design the feedback controller of the error system, wewill get ue, then the closed-loop control can be obtained by u = ud + ue.For the design of feedback control ue, we suggest a moving horizon H∞trackingmethod in LMIscheme by combining the idea of predict control and robust control.This method have some properties and advantages as follows:1 The error system is time variable since the desired trajectory is time variable.2 The error model at every sampling time is taken as the predict model, so theinitial state and the predict model will be refreshed at each sampling time.3 In the LMIscheme,di?erent control object and performance requirementcan be independently described, which allows us to consider the control con-straints in a explicit way.4 We get a su?cient condition for the satisfying of control constraints by usingthe ellipsoid theory; we can obtain the tradeo? between performance andcontrol constraints by on-line adjusting the ellipsoid.5 The closed-loop dissipation can be guaranteed by introducing the dissipationconstraint.6 The online optimization algorithm is always feasible under some trivial con-ditions.We have precisely deduced the algorithm and had deeply analysis about thefeasibility of the algorithm and the closed-loop properties. Both of the theoreticalanalysis and the results of the simulation verifies that the proposed method canon-line adjust the performance according to the real-time information, i.e. relaxthe performance when the control inputs reach there bounds and improve theperformance when the control inputs are far away from there bound.There is also some problem which is not solved in this thesis, such as how tospeed the on line calculation and how to solve the trajectory planning and trackingsimultaneously.更多还原