A WAVELET COLLOCATION SCHEME FOR SOLVING SOME OPTIMAL PATH PLANNING PROBLEMS

2016 ◽  
Vol 57 (4) ◽  
pp. 461-481
Author(s):  
MARZIYEH MORTEZAEE ◽  
ALIREZA NAZEMI
Keyword(s):  
Optimal Control ◽  
Path Planning ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Operational Matrix ◽  
Optimal Path ◽  
Computational Method ◽  
Haar Wavelets ◽  
Optimal Path Planning ◽  
Planning Problems

We consider an approximation scheme using Haar wavelets for solving optimal path planning problems. The problem is first expressed as an optimal control problem. A computational method based on Haar wavelets in the time domain is then proposed for solving the obtained optimal control problem. A Haar wavelets integral operational matrix and a direct collocation method are used to find an approximate optimal trajectory of the original problem. Numerical results are also presented for several examples to demonstrate the applicability and efficiency of the proposed method.

Trajectory Planning of Quadrotor Systems for Various Objective Functions

Robotica ◽  
2020 ◽  
Vol 39 (1) ◽  
pp. 137-152
Author(s):  
Hamidreza Heidari ◽  
Martin Saska
Keyword(s):  
Optimal Control ◽  
Path Planning ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Trajectory Planning ◽  
Minimum Principle ◽  
Optimal Path ◽  
Necessary Condition ◽  
Objective Functions ◽  
Wide Range

SUMMARYQuadrotors are unmanned aerial vehicles with many potential applications ranging from mapping to supporting rescue operations. A key feature required for the use of these vehicles under complex conditions is a technique to analytically solve the problem of trajectory planning. Hence, this paper presents a heuristic approach for optimal path planning that the optimization strategy is based on the indirect solution of the open-loop optimal control problem. Firstly, an adequate dynamic system modeling is considered with respect to a configuration of a commercial quadrotor helicopter. The model predicts the effect of the thrust and torques induced by the four propellers on the quadrotor motion. Quadcopter dynamics is described by differential equations that have been derived by using the Newton–Euler method. Then, a path planning algorithm is developed to find the optimal trajectories that meet various objective functions, such as fuel efficiency, and guarantee the flight stability and high-speed operation. Typically, the necessary condition of optimality for a constrained optimal control problem is formulated as a standard form of a two-point boundary-value problem using Pontryagin’s minimum principle. One advantage of the proposed method can solve a wide range of optimal maneuvers for arbitrary initial and final states relevant to every considered cost function. In order to verify the effectiveness of the presented algorithm, several simulation and experiment studies are carried out for finding the optimal path between two points with different objective functions by using MATLAB software. The results clearly show the effect of the proposed approach on the quadrotor systems.

scholarly journals A New Method for the Optimal Control Problem of Path Planning for Unmanned Ground Systems

IEEE Access ◽  
2018 ◽  
Vol 6 ◽  
pp. 33251-33260 ◽  
Author(s):  
Jie Liu ◽  
Wei Han ◽  
Chun Liu ◽  
Haijun Peng
Keyword(s):  
Optimal Control ◽  
Path Planning ◽  
Optimal Control Problem ◽  
Control Problem ◽  
New Method ◽  
Ground Systems

New operational matrices approach for optimal control based on modified Chebyshev polynomials

2021 ◽  
Vol 2 (2) ◽  
pp. 68-78
Author(s):  
Anam Alwan Salih ◽  
Suha SHIHAB
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Chebyshev Polynomials ◽  
Optimization Technique ◽  
Computational Method ◽  
Operational Matrices ◽  
Algebraic Equations ◽  
Quadratic Optimal Control ◽  
Chebyshev Orthogonal Polynomial

The purpose of this paper is to introduce interesting modified Chebyshev orthogonal polynomial. Then, their new operational matrices of derivative and integration or modified Chebyshev polynomials of the first kind are introduced with explicit formulas. A direct computational method for solving a special class of optimal control problem, named, the quadratic optimal control problem is proposed using the obtained operational matrices. More precisely, this method is based on a state parameterization scheme, which gives an accurate approximation of the exact solution by utilizing a small number of unknown coefficients with the aid of modified Chebyshev polynomials. In addition, the constraint is reduced to some algebraic equations and the original optimal control problem reduces to optimization technique, which can be solved easily, and the approximate value of the performance index is calculated. Moreover, special attention is presented to discuss the convergence analysis and an upper bound of the error for the presented approximate solution is derived. Finally, some important illustrative examples of obtained results are shown and proved that powerful method in a simple way to get an optimal control of the considered.

Motorway Path Planning for Automated Road Vehicles Based on Optimal Control Methods

2018 ◽  
Vol 2672 (19) ◽  
pp. 112-123 ◽  
Author(s):  
Konstantinos Makantasis ◽  
Markos Papageorgiou
Keyword(s):  
Optimal Control ◽  
Path Planning ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Dynamic Programming Algorithm ◽  
Weighting Factor ◽  
Initial Guess ◽  
Programming Algorithm ◽  
Road Vehicles ◽  
Planning Algorithm

A path-planning algorithm for automated road vehicles on multi-lane motorways is derived from the opportune formulation of an optimal control problem. In this framework, the objective function to be minimized contains appropriate respective terms to reflect: the goals of the vehicle advancement; passenger comfort; prevailing traffic rules (e.g., overtaking only from left); and the avoidance of obstacles (other moving vehicles) and of the vehicle departing from the road. Each term is coupled with a weighting factor that reflects its comparative importance. For the numerical solution of the optimal control problem, a very efficient feasible direction algorithm is used. To avoid local minima, a simplified dynamic programming algorithm is also conceived to deliver the initial guess trajectory for the optimal control algorithm. With low computation times, the approach is readily executable within a model-predictive control frame. The performance of the proposed algorithm is illustrated using two typical driving scenarios.

scholarly journals OPTIMAL CONTROL OF SWITCHED IMPULSIVE SYSTEMS WITH TIME DELAY

2012 ◽  
Vol 53 (4) ◽  
pp. 292-307 ◽  
Author(s):  
K. H. WONG ◽  
W. M. TANG
Keyword(s):  
Optimal Control ◽  
Time Delay ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Time Instant ◽  
Computational Method ◽  
Impulsive Systems ◽  
Delay Differential ◽  
The Cost ◽  
System With Time Delay

AbstractWe develop a computational method for solving an optimal control problem governed by a switched impulsive dynamical system with time delay. At each time instant, only one subsystem is active. We propose a computational method for solving this optimal control problem where the time spent by the state in each subsystem is treated as a new parameter. These parameters and the jump strengths of the impulses are decision parameters to be optimized. The gradient formula of the cost function is derived in terms of solving a number of delay differential equations forward in time. Based on this, the optimal control problem can be solved as an optimization problem.

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