Aircraft Trajectory Optimization for Collision Avoidance Using Stochastic Optimal Control

2018 ◽  
Vol 21 (5) ◽  
pp. 2308-2320 ◽  
Author(s):  
Wensheng Liu ◽  
Xuelin Liang ◽  
Yunzhu Ma ◽  
Weiyi Liu
Keyword(s):  
Optimal Control ◽  
Collision Avoidance ◽  
Stochastic Optimal Control ◽  
Trajectory Optimization ◽  
Aircraft Trajectory

scholarly journals Multiphase Mixed-Integer Optimal Control Approach to Aircraft Trajectory Optimization

2013 ◽  
Vol 36 (5) ◽  
pp. 1267-1277 ◽  
Author(s):  
Pierre Bonami ◽  
Alberto Olivares ◽  
Manuel Soler ◽  
Ernesto Staffetti
Keyword(s):  
Optimal Control ◽  
Trajectory Optimization ◽  
Mixed Integer ◽  
Control Approach ◽  
Aircraft Trajectory ◽  
Optimal Control Approach

scholarly journals On Entropy Regularized Path Integral Control for Trajectory Optimization

Entropy ◽  
2020 ◽  
Vol 22 (10) ◽  
pp. 1120
Author(s):  
Tom Lefebvre ◽  
Guillaume Crevecoeur
Keyword(s):  
Optimal Control ◽  
Path Integral ◽  
Stochastic Optimal Control ◽  
Trajectory Optimization ◽  
Optimization Problems ◽  
Search Methods ◽  
Integral Control ◽  
Policy Search ◽  
Optimal State ◽  
State Trajectory

In this article, we present a generalized view on Path Integral Control (PIC) methods. PIC refers to a particular class of policy search methods that are closely tied to the setting of Linearly Solvable Optimal Control (LSOC), a restricted subclass of nonlinear Stochastic Optimal Control (SOC) problems. This class is unique in the sense that it can be solved explicitly yielding a formal optimal state trajectory distribution. In this contribution, we first review the PIC theory and discuss related algorithms tailored to policy search in general. We are able to identify a generic design strategy that relies on the existence of an optimal state trajectory distribution and finds a parametric policy by minimizing the cross-entropy between the optimal and a state trajectory distribution parametrized by a parametric stochastic policy. Inspired by this observation, we then aim to formulate a SOC problem that shares traits with the LSOC setting yet that covers a less restrictive class of problem formulations. We refer to this SOC problem as Entropy Regularized Trajectory Optimization. The problem is closely related to the Entropy Regularized Stochastic Optimal Control setting which is often addressed lately by the Reinforcement Learning (RL) community. We analyze the theoretical convergence behavior of the theoretical state trajectory distribution sequence and draw connections with stochastic search methods tailored to classic optimization problems. Finally we derive explicit updates and compare the implied Entropy Regularized PIC with earlier work in the context of both PIC and RL for derivative-free trajectory optimization.

Safe Navigation With the Collision Avoidance of a Brownian Motion Obstacle

2017 ◽  
Author(s):  
Alexey A. Munishkin ◽  
Dejan Milutinović ◽  
David W. Casbeer
Keyword(s):  
Optimal Control ◽  
Brownian Motion ◽  
Numerical Simulations ◽  
Collision Avoidance ◽  
Stochastic Optimal Control ◽  
Time Optimal Control ◽  
Value Functions ◽  
Point Location ◽  
Safe Navigation ◽  
Time Optimal

This paper develops a control that combines deterministic and stochastic optimal control solutions to the problem of safe navigation around a spherical obstacle in order to reach a way-point location. The solution for navigation towards the way-point is based on the deterministic minimum time optimal control. Since the intent of the obstacle is unknown to the navigating vehicle, the vehicle anticipates this uncertainty and uses a stochastic optimal control for navigation around the obstacle. The two navigation solutions are combined based on their value functions. Results are illustrated by numerical simulations.

scholarly journals Research of Trajectory Optimization Approaches in Synthesized Optimal Control

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 336
Author(s):  
Askhat Diveev ◽  
Elizaveta Shmalko
Keyword(s):  
Optimal Control ◽  
Equilibrium Point ◽  
Trajectory Optimization ◽  
Stable Equilibrium ◽  
Equilibrium Points ◽  
Control Object ◽  
Symbolic Regression ◽  
Optimal Location ◽  
Stable Equilibrium Point ◽  
Stabilization System

This article presents a study devoted to the emerging method of synthesized optimal control. This is a new type of control based on changing the position of a stable equilibrium point. The object stabilization system forces the object to move towards the equilibrium point, and by changing its position over time, it is possible to bring the object to the desired terminal state with the optimal value of the quality criterion. The implementation of such control requires the construction of two control contours. The first contour ensures the stability of the control object relative to some point in the state space. Methods of symbolic regression are applied for numerical synthesis of a stabilization system. The second contour provides optimal control of the stable equilibrium point position. The present paper provides a study of various approaches to find the optimal location of equilibrium points. A new problem statement with the search of function for optimal location of the equilibrium points in the second stage of the synthesized optimal control approach is formulated. Symbolic regression methods of solving the stated problem are discussed. In the presented numerical example, a piece-wise linear function is applied to approximate the location of equilibrium points.

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