Error Analysis Of Trajectory Tracking And Formation Of Robots With Positioning Noise

With the development of society and economy,the cost of labor in the whole world has been increasing gradually.The replacement of the labor of human by machine is conducted in the way from traditional mechanization and automation into diversification and intelligence.Especially,the related scientific research in the field of robot has attracted a lot of attention with the widespread applications of the robot technique recently.As the control of wheeled robots,among all kinds of their controls,is nonlinear and nonholonomic constrained,it becomes one of the focus of many researchers.A standardized trajectory control method of wheeled robots was proposed by Kanayama about from 1998 to 1990 firstly.According to this method,the error coordinate system is applied to achieve the control and such a method has become a base of wheeled robot control problem in many cases.Up to now,many methods for the control of wheeled robots based on the error coordinate system have been developed by the researchers worldwide.While,as the studies on the error analysis of wheeled robots with positioning noise is not sufficient,a novel trajectory tracking method based on the inverse trajectory on the local coordinate is proposed and the error analysis of the tracking and formation control of wheeled robots with positioning noise is studied in this dissertation.Also,it is proved that the task of tracking can be completed by this method.Meanwhile,the dynamical error analysis can be achieved.On the study of the error analysis of the formation of robots,the increases of the errors delivering among the robots are investigated and the relationship of these increases is pointed out.In addition,a sufficient condition is summarized,which limits the unlimited growth of the errors in the formation control.At last,an adjusted Actor-Critic method is used to solve the optimal control problem of the parameters in this system.The main contents of this dissertation can be summarized as follows.(1)In view of the lack of effective dynamical error analysis methods for stochastic systems with additive noise,the probability boundary problem of stochastic differential equations with additive noise is studied.By using It?o formula,martingale analysis,inequalities of probability,etc,the dynamic boundary of the error of this stochastic differential equation under probability,is obtained,which is named probability boundary.Based on this,on the one hand,a method to evaluate the dynamical error is designed and the probability inequality of dynamical error is obtained.On the other hand,the influence of the noise with non-normal distribution added in these systems is studied and the dynamical compression boundary index of probability boundary and the optimal control model of the time-varying parameters are obtained for the dynamical parameters in systems.(2)As the lack of error analysis method of the trajectory control of the wheeled robot with positioning errors,the control method of wheeled robot based on local coordinate system is studied.By introducing a virtual robot,local coordinate systems are constructed and corresponding kinematic models are established.By analyzing the effects of the kinematic model near the equilibrium point,a stochastic differential equation model containing additive noise is established,demonstrating sufficient conditions for the existence of probabilistic boundaries.Considering the influence of the perturbation of the actuator on the probability boundary and the control error,we map the state error of the system to the global coordinate system to realize the error analysis of the wheeled robot trajectory control.(3)Because the research on the error analysis of trajectory tracking and formation caused by position errors is insufficient,a kind of trajectory tracking method and the corresponding formation with their error analysis are studied.With the method of the inverse trajectory,the wheeled robot trajectory tracking task and the error analysis process can be realized under the environment of positioning noise.Then,aiming at the transmission of positioning noise and control error in formation,with the studies on the influence of the noise with non-normal distribution,the increase of the errors from robot to robot is investigated and the relationship of these increases is pointed out.In addition,a sufficient condition is summarized,which limits the unlimited growth of the errors in the formation control.As the time series is used as the parameters in the controller,an adjusted Actor-Critic method is used to solve the optimal control model of the parameters of this systems.Finally,numerical experiments verify the conclusions of this dissertation.