5.

LITERARTURE SURVEY

Many

works have been done in the area of reducing the computational time of MPC

among which A.G Wills, Dale Bates, Andrew J Fleming, Brett Ninness, and S.O. R

Moheimani 3 suggests the use of explicit controller. It has good results at

high sampling rate. Depending on the longitudinal dynamics operating region of

lateral dynamics varies. Explicit control law defined for a specific

longitudinal state, here longitudinal velocity, may not be valid for other

regions. This problem could be addressed by exploring the state space and finding

set of explicit control laws.

A, Bicycle Model

Velocity at each wheel is in the direction of the

wheel at higher vehicle speeds, that the can no longer be made. In this case,

instead of a kinematic model, a dynamic model for lateral vehicle motion must

be developed. A “bicycle” model of the vehicle with two degrees of

freedom is considered. A method for

electronic stability control (ESC) based on model predictive control (MPC)

using the bicycle model with lagged tire force to reflect the lagged characteristics

of lateral tire forces on the prediction model of the MPC problem for better

description of the vehicle behavior 2. To avoid the computational burden in

finding the optimal solution of the MPC problem using the constrained optimal

control theory, the desired states and inputs as references are generated since

the solution of the MPC problem can be easily obtained in a closed form without

using numeric solvers using these reference values. The suggested method controls

the vehicle to follow the generated reference values to maintain the vehicle

yaw stability while the vehicle turns as the driver intended. The superiority

of the proposed method is verified through comparisons with an ESC method based

on ordinary MPC in the simulation environments on both high- and low-? surfaces

using the vehicle dynamics. Design

and implementation of a stabilization algorithm for a car like robot performing

high speed turns require control of such a kind of system 5. It is rather

difficult because of the complexity of the physical wheel soil interaction

model. In this paper, it is planned to analyze the complex dynamic model of

this process to elaborate a stabilization algorithm only based on the measurement

of the system yaw rate. Finally, simulation is performed to evaluate the

efficiency of this designed stabilization algorithm

B, Model Predictive Control

Symmetry in Linear Model Predictive Control (MPC) and defines a symmetry

for model predictive control laws and for model predictive control problems.

Properties of MPC symmetries are studied by using a group theory formalism

suggested by Claus Danielson, Francesco Borrelli 1. It show

how to efficiently compute MPC symmetries by transforming the search of MPC

symmetry generators into a graph automorphism problem. MPC symmetries are then

used to design model predictive control algorithms with reduced complexity. The

effectiveness of the proposed approach is shown through a simple large-scale

MPC problem whose explicit solution can only be found with the method

A new

approach of employing model predictive control (MPC) where the difficulties

imposed by actuator limitations in a range of active vibration and noise

control problems are well recognized by Adrain G Wills and Dale Bates. MPC permits limitations on allowable control action to be explicitly

included in the computation of an optimal control action. Such techniques have

been widely and successfully applied in many other areas. However, due to the

relatively high computational requirements of MPC, existing applications have

been limited to systems with slow dynamics. It illustrates that MPC can be

implemented on inexpensive hardware at high sampling rates using traditional

online quadratic programming methods for nontrivial models and with significant

control performance dividends. The problem of steering a non holonomic mobile robot

to a desired position and orientation is discussed by Karl

Worthmann, Mohamed W. A Model Predictive Control

(MPC) scheme based on tailored non quadratic stage cost is proposed to fulfill

this control task. We rigorously prove asymptotic stability while neither

stabilizing constraints nor costs are used. To this end, we first design

suitable maneuvers to construct bounds on the value function. Second, these

bounds are exploited to determine a prediction horizon length such that the

asymptotic stability of the MPC closed loop is guaranteed. Finally, numerical

simulations are conducted to explain the necessity of having non quadratic

running costs.

C. Trajectory Tracking

.

Based on the kinematic equations of the mobile robot, a tracking error model is

obtained by LIN Fengda1, LIN Zijian 4.

This nonlinear model is linearized around origin. Based on local linearized

model, an optimal controller is designed for the trajectory tracking problem by

using optimal linear quadratic (LQ) design approach. The simulation shows the

effectiveness of optimal LQR (linear quadratic regulator) controller for the

cases where the robot tracks both straight and curve trajectories.