Trajectory Optimization for Nonholonomic Vehicles on Non-Flat Terrains Using Shooting and Collocation Methods

2013 ◽  
Author(s):  
Dimitris M. Chatzigeorgiou
Keyword(s):  
Optimal Control ◽  
Mobile Robots ◽  
Performance Index ◽  
Trajectory Optimization ◽  
Optimization Problem ◽  
Control Policy ◽  
Collocation Methods ◽  
Governing Equations ◽  
Nonholonomic Mobile Robots ◽  
Nonholonomic Vehicles

In this paper we focus on the trajectory optimization problem for a specific family of robots; nonholonomic mobile robots. We study the particular case where such robots operate on smooth, non-flat terrains, i.e. terrains with large differences in elevation. Initially we present the governing equations of such robots and then study the trajectory optimization problem in order to solve for the optimal control policy. We test two different approaches for this problem, namely a shooting and a collocation method, for evaluating and optimizing a performance index.

Rapid trajectory optimization for hypersonic entry using a pseudospectral-convex algorithm

2019 ◽  
Vol 233 (14) ◽  
pp. 5227-5238 ◽  
Author(s):  
Jinbo Wang ◽  
Naigang Cui ◽  
Changzhu Wei
Keyword(s):  
Optimal Control ◽  
Optimal Control Theory ◽  
Trajectory Optimization ◽  
Numerical Experiments ◽  
Optimization Problem ◽  
Interior Point Methods ◽  
Pseudospectral Method ◽  
Trust Region ◽  
Convergence Properties ◽  
Dynamic Trust

Aiming at improving the autonomy of hypersonic entry vehicles, a rapid trajectory optimization algorithm, which has the potential to be implemented online and onboard, is proposed in this paper. The nonlinear and nonconvex hypersonic entry trajectory optimization problem is transformed into a series of convex subproblems through a proper combination of the pseudospectral method and an improved successive convexification method; thus, the high discretization accuracy of the pseudospectral method and the fast and deterministic convergence properties of the convex-optimization-based algorithm can be simultaneously exploited. The resulting subproblems can be solved efficiently by matured interior-point methods, and the solution converges rapidly by adopting a novel dynamic trust-region updating approach. The optimality of the solution is verified by the optimal control theory. The effectiveness of the algorithm is demonstrated by numerical experiments.

A new approach to optimal control of nonlinear vehicle suspension system with input constraint

2017 ◽  
Vol 24 (15) ◽  
pp. 3307-3320 ◽  
Author(s):  
Bahman Abdi ◽  
Mehdi Mirzaei ◽  
Reza Mojed Gharamaleki
Keyword(s):  
Optimal Control ◽  
Constrained Optimization ◽  
Performance Index ◽  
Optimization Problem ◽  
Suspension System ◽  
Vehicle Suspension ◽  
Control Force ◽  
Input Constraint ◽  
Constrained Optimization Problem ◽  
Vehicle Suspension System

The vehicle active suspension system is a multi-objective control system with the input constraint. In this paper, a new effective method is proposed for constrained optimal control of a vehicle suspension system including nonlinear characteristics for elasto-damping elements. In the proposed method, an equivalent constrained optimization problem is firstly formulated by performing a performance index which is defined as a weighted combination of predicted responses of nonlinear suspension system and control signal. Then, the constrained optimization problem is analytically solved by the Kerush–Kuhn–Tucker (KKT) theorem to find the control law. The proposed constrained controller is compared with the unconstrained optimal controller for which the limitation of control force is satisfied by regulation of its weighting factor in the performance index. Simulation studies are conducted to show the effectiveness of two controllers. The results indicate that the constrained controller utilizes the maximum capacity of external forces and consequently attains a better performance in the presence of force limitations.

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.

A Review on Tracking Control of Nonholonomic Mobile Robots

2018 ◽  
Author(s):  
Jiasheng Tao ◽  
Di Lu ◽  
Quan Wang ◽  
Yuping Qiu ◽  
Hua Chen ◽  
...  
Keyword(s):  
Mobile Robots ◽  
Tracking Control ◽  
Nonholonomic Mobile Robots
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