5. through comparisons with an ESC method


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.

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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.