scholarly journals Deep Learning for Efficient and Optimal Motion Planning for AUVs with Disturbances

Sensors ◽  
2021 ◽  
Vol 21 (15) ◽  
pp. 5011
Author(s):  
Juan Parras ◽  
Patricia A. Apellániz ◽  
Santiago Zazo
Keyword(s):  
Optimal Control ◽  
Deep Learning ◽  
Motion Planning ◽  
Optimal Control Problems ◽  
Autonomous Vehicle ◽  
Control Problems ◽  
Planning Problem ◽  
Optimal Motion ◽  
Optimal Motion Planning ◽  
Hamilton Jacobi Bellman

We use the recent advances in Deep Learning to solve an underwater motion planning problem by making use of optimal control tools—namely, we propose using the Deep Galerkin Method (DGM) to approximate the Hamilton–Jacobi–Bellman PDE that can be used to solve continuous time and state optimal control problems. In order to make our approach more realistic, we consider that there are disturbances in the underwater medium that affect the trajectory of the autonomous vehicle. After adapting DGM by making use of a surrogate approach, our results show that our method is able to efficiently solve the proposed problem, providing large improvements over a baseline control in terms of costs, especially in the case in which the disturbances effects are more significant.

scholarly journals A bilevel optimal motion planning (BOMP) model with application to autonomous parking

2019 ◽  
Vol 3 (4) ◽  
pp. 370-382 ◽  
Author(s):  
Shenglei Shi ◽  
Youlun Xiong ◽  
Jiankui Chen ◽  
Caihua Xiong
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Motion Planning ◽  
Control Problem ◽  
Control Method ◽  
Significant Feature ◽  
Optimal Motion ◽  
Optimal Control Method ◽  
Optimal Motion Planning ◽  
Upper Level

Abstract In this paper, we present a bilevel optimal motion planning (BOMP) model for autonomous parking. The BOMP model treats motion planning as an optimal control problem, in which the upper level is designed for vehicle nonlinear dynamics, and the lower level is for geometry collision-free constraints. The significant feature of the BOMP model is that the lower level is a linear programming problem that serves as a constraint for the upper-level problem. That is, an optimal control problem contains an embedded optimization problem as constraints. Traditional optimal control methods cannot solve the BOMP problem directly. Therefore, the modified approximate Karush–Kuhn–Tucker theory is applied to generate a general nonlinear optimal control problem. Then the pseudospectral optimal control method solves the converted problem. Particularly, the lower level is the $$J_2$$J2-function that acts as a distance function between convex polyhedron objects. Polyhedrons can approximate objects in higher precision than spheres or ellipsoids. As a result, a fast high-precision BOMP algorithm for autonomous parking concerning dynamical feasibility and collision-free property is proposed. Simulation results and experiment on Turtlebot3 validate the BOMP model, and demonstrate that the computation speed increases almost two orders of magnitude compared with the area criterion based collision avoidance method.

Solving a class of fractional optimal control problems by the Hamilton–Jacobi–Bellman equation

2016 ◽  
Vol 24 (9) ◽  
pp. 1741-1756 ◽  
Author(s):  
Seyed Ali Rakhshan ◽  
Sohrab Effati ◽  
Ali Vahidian Kamyad
Keyword(s):  
Optimal Control ◽  
Fractional Derivative ◽  
Bellman Equation ◽  
Optimal Control Problems ◽  
Control Problems ◽  
Fractional Optimal Control ◽  
Solution Scheme ◽  
Hamilton Jacobi Bellman Equation ◽  
Fractional Optimal Control Problems ◽  
Hamilton Jacobi Bellman

The performance index of both the state and control variables with a constrained dynamic optimization problem of a fractional order system with fixed final Time have been considered here. This paper presents a general formulation and solution scheme of a class of fractional optimal control problems. The method is based upon finding the numerical solution of the Hamilton–Jacobi–Bellman equation, corresponding to this problem, by the Legendre–Gauss collocation method. The main reason for using this technique is its efficiency and simple application. Also, in this work, we use the fractional derivative in the Riemann–Liouville sense and explain our method for a fractional derivative of order of [Formula: see text]. Numerical examples are provided to show the effectiveness of the formulation and solution scheme.

scholarly journals Application of Optimal HAM for Finding Feedback Control of Optimal Control Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
H. Saberi Nik ◽  
Stanford Shateyi
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Convergent Series ◽  
Residual Error ◽  
Control Problems ◽  
Strong Nonlinearity ◽  
Control Parameters ◽  
Convergence Control ◽  
Hamilton Jacobi Bellman ◽  
Optimal Approach

An optimal homotopy-analysis approach is described for Hamilton-Jacobi-Bellman equation (HJB) arising in nonlinear optimal control problems. This optimal approach contains at most three convergence-control parameters and is computationally rather efficient. A kind of averaged residual error is defined. By minimizing the averaged residual error, the optimal convergence-control parameters can be obtained. This optimal approach has general meanings and can be used to get fast convergent series solutions of different types of equations with strong nonlinearity. The closed-loop optimal control is obtained using the Bellman dynamic programming. Numerical examples are considered aiming to demonstrate the validity and applicability of the proposed techniques and to compare with the existing results.

Energy-optimal motion planning of a biped pole-climbing robot with kinodynamic constraints

2018 ◽  
Vol 45 (3) ◽  
pp. 343-353 ◽  
Author(s):  
Xuefeng Zhou ◽  
Li Jiang ◽  
Yisheng Guan ◽  
Haifei Zhu ◽  
Dan Huang ◽  
...  
Keyword(s):  
Motion Planning ◽  
Optimal Path ◽  
Planning Method ◽  
Outdoor Environment ◽  
Planning Problem ◽  
Climbing Robot ◽  
Optimal Motion ◽  
Climbing Robots ◽  
Content Type ◽  
Optimal Motion Planning

Purpose Applications of robotic systems in agriculture, forestry and high-altitude work will enter a new and huge stage in the near future. For these application fields, climbing robots have attracted much attention and have become one central topic in robotic research. The purpose of this paper is to propose an energy-optimal motion planning method for climbing robots that are applied in an outdoor environment. Design/methodology/approach First, a self-designed climbing robot named Climbot is briefly introduced. Then, an energy-optimal motion planning method is proposed for Climbot with simultaneous consideration of kinematic constraints and dynamic constraints. To decrease computing complexity, an acceleration continuous trajectory planner and a path planner based on spatial continuous curve are designed. Simulation and experimental results indicate that this method can search an energy-optimal path effectively. Findings Climbot can evidently reduce energy consumption when it moves along the energy-optimal path derived by the method used in this paper. Research limitations/implications Only one step climbing motion planning is considered in this method. Practical implications With the proposed motion planning method, climbing robots applied in an outdoor environment can commit more missions with limit power supply. In addition, it is also proved that this motion planning method is effective in a complicated obstacle environment with collision-free constraint. Originality/value The main contribution of this paper is that it establishes a two-planner system to solve the complex motion planning problem with kinodynamic constraints.

Optimal Motion Planning for the Teaching Experimental Mobile Manipulator

2011 ◽  
Vol 138-139 ◽  
pp. 56-61
Author(s):  
Huai Ping Zhou ◽  
Ping Ge ◽  
Yong Fang
Keyword(s):  
Optimal Control ◽  
Motion Planning ◽  
Minimum Principle ◽  
Teaching Experiment ◽  
Mobile Manipulator ◽  
Optimal Motion ◽  
Control Scheme ◽  
Experimental Apparatus ◽  
Optimal Motion Planning ◽  
Optimal Control Scheme

An optimal motion planning based on minimum principle is presented to address the motion problem of the mobile manipulator in a sort of experimental system. In view of the characteristic of the practical experimental apparatus, the model of the manipulator is deduced based on the kinetic analysis and mathematic method. An optimal control scheme is then investigated to deal with the optimization problem of the motion planning for the manipulator, so as to guarantee the demand of the teaching experiment. Simulation verifies the control performance of the optimal control scheme for the optimal motion planning of the manipulator, and it helps improve the teaching experiment effect.

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