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

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.

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 A New Direct Method for Solving Nonlinear Volterra-Fredholm-Hammerstein Integral Equations via Optimal Control Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
M. A. El-Ameen ◽  
M. El-Kady
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Integral Equations ◽  
Simple Form ◽  
Existence And Uniqueness ◽  
Direct Method ◽  
New Method ◽  
Fredholm Integral Equations ◽  
Hammerstein Integral Equations

A new method for solving nonlinear Volterra-Fredholm-Hammerstein (VFH) integral equations is presented. This method is based on reformulation of VFH to the simple form of Fredholm integral equations and hence converts it to optimal control problem. The existence and uniqueness of proposed method are achieved. Numerical results are given at the end of this paper.

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.

REDUCED MODEL OF PLASMA DISCHARGE CONTROL IN TOKAMAK WITH IRON CORE

2020 ◽  
Vol 7 (3) ◽  
pp. 11-22
Author(s):  
VALERY ANDREEV ◽  
◽  
ALEXANDER POPOV
Keyword(s):  
Optimal Control ◽  
Inverse Problem ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Nonlinear Behavior ◽  
Plasma Discharge ◽  
Reduced Model ◽  
Iron Core ◽  
Power Sources ◽  
Real Power

A reduced model has been developed to describe the time evolution of a discharge in an iron core tokamak, taking into account the nonlinear behavior of the ferromagnetic during the discharge. The calculation of the discharge scenario and program regime in the tokamak is formulated as an inverse problem - the optimal control problem. The methods for solving the problem are compared and the analysis of the correctness and stability of the control problem is carried out. A model of “quasi-optimal” control is proposed, which allows one to take into account real power sources. The discharge scenarios are calculated for the T-15 tokamak with an iron core.

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