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MPC的线性优化

更新时间：2019-08-19 23:27:28 大小：296K 上传用户：JC丶查看TA发布的资源 标签：MPC 下载积分：5分 评价赚积分 （如何评价?） 打赏 收藏 评论(0) 举报

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Model predictive control of a mobile robot using linearization。MPC的线性优化


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Model Predictive Control of a Mobile Robot Using  
Linearization  
Felipe Ku¨hne  
Walter Fetter Lages  
Federal University of Rio Grande do Sul  
Electrical Engineering Department  
Av. Oswaldo Aranha, 103  
Joa˜o Manoel Gomes da Silva Jr.  
Porto Alegre, RS 90035-190 Brazil  
Email: kuhne,fetter,jmgomes @eletro.ufrgs.br  
Abstract— This paper presents an optimal control scheme for a predictions, an objective function is minimized with respect to  
wheeled mobile robot (WMR) with nonholonomic constraints. It  
is well known that a WMR with nonholonomic constraints can  
not be feedback stabilized through continuously differentiable,  
time-invariant control laws. By using model predictive control  
the future sequence of inputs, thus requiring the solution of a  
constrained optimization problem for each sampling interval.  
Although prediction and optimization are performed over a  
future horizon, only the values of the inputs for the current  
(MPC), a discontinuous control law is naturally obtained. One  
of the main advantages of MPC is the ability to handle constraints sampling interval are used and the same procedure is repeated  
(due to state or input limitations) in a straightforward way.  
Quadratic programming (QP) is used to solve a linear MPC  
by successive linearization of an error model of the WMR.  
at the next sampling time. This mechanism is known as moving  
or receding horizon strategy, in reference to the way in which  
the time window shifts forward from one sampling time to the  
next one.  
I. INTRODUCTION  
For complex, constrained, multivariable control problems,  
The field of mobile robot control has been the focus of  
active research in the past decades. Despite the apparent  
simplicity of the kinematic model of a wheeled mobile robot  
(WMR), the existence of nonholonomic constraints turns the  
design of stabilizing control laws for those systems in a  
considerable challenge. Due to Brockett conditions [1], a  
continuously differentiable, time-invariant stabilizing feedback  
control law can not be obtained. To overcome these limita-  
tions most works uses non-smooth and time-varying control  
laws [2]–[6]. Recent works dealing with robust and adaptive  
control of WMRs can be found in [7], [8].  
However, in realistic implementations it is difficult to obtain  
good performance, due to the constraints on inputs or states  
that naturally arise. None of the previously cited works have  
taken those constraints into account. This can be done in a  
straightforward way by using model predictive control (MPC)  
schemes. For a WMR this is an important issue, since the  
position of the robot can be restricted to belong to a safe  
region of operation. By considering input constraints, control  
actions that respect actuators limits can be generated.  
MPC has become an accepted standard in the process indus-  
tries [9]. It is used in many cases, where plants being con-  
trolled are sufficiently slow to allow its implementation [10].  
However, for systems with fast and/or nonlinear dynamics,  
the implementation of such technique remains fundamentally  
limited in applicability, due to large amount of on-line com-  
putation required [11].  
The model of a WMR is nonlinear. Although nonlin-  
ear model predictive control (NMPC) has been well devel-  
oped [10], [12], [13], the computational effort necessary is  
much higher than the linear version. In NMPC there is a  
nonlinear programming problem to be solved on-line, which  
is nonconvex, has a larger number of decision variables and  
a global minimum is in general impossible to find [14]. In  
this paper, we propose a strategy to overcome at least part  
of these problems. The fundamental idea consists in using a  
successive linearization approach, as briefly outlined in [14],  
yielding a linear, time-varying description of the system beeing  
solved through linear MPC. Then, considering the control  
inputs as the decision variables, it is possible to transform  
the optimization problem in a Quadratic programming (QP)  
problem. Since this is a convex problem, QP problems can  
be solved by numerically robust solvers which lead to global  
optimal solutions. It is then shown that even a real-time  
implementation is possible. Although MPC is not a new  
control method, works dealing with MPC of WMRs are recent  
Furthermore, coordinate transformations of the dynamic  
system to chained or power forms [2] are not necessary  
anymore, which turns the choice of tuning parameters for the  
MPC more intuitive. Regarding the nonholonomic features of  
the WMR, a piecewise-continuous (non-smooth) control law  
is implicitly generated by MPC.  
Model predictive control is an optimal control strategy and sparse [15]–[17].  
that uses the model of the system to obtain an optimal  
The remainder of this paper is organized as follows: in the  
control sequence by minimizing an objective function. At each next section the kinematic model of the WMR is shown. The  
sampling interval, the model is used to predict the behavior MPC algorithm is depicted in section III. Simulation results  
of the system over a prediction horizon. Based on these in MATLAB are shown in section IV. Section V presents some  

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