Tracking Control Of Wheeled Mobile Robots Based On Moving Horizon Optimization

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 ? xdâ†'0 in order to let xâ†'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.