scholarly journals Parametric Approach to Trajectory Tracking Control of Robot Manipulators

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Shijie Zhang ◽  
Yi Ning
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Trajectory Tracking ◽  
Tracking Control ◽  
Optimal Trajectory ◽  
Open Loop ◽  
Parametric Approach ◽  
Trajectory Tracking Control ◽  
Loop Control

The mathematic description of the trajectory of robot manipulators with the optimal trajectory tracking problem is formulated as an optimal control problem, and a parametric approach is proposed for the optimal trajectory tracking control problem. The optimal control problem is first solved as an open loop optimal control problem by using a time scaling transform and the control parameterization method. Then, by virtue of the relationship between the optimal open loop control and the optimal closed loop control along the optimal trajectory, a practical method is presented to calculate an approximate optimal feedback gain matrix, without having to solve an optimal control problem involving the complex Riccati-like matrix differential equation coupled with the original system dynamics. Simulation results of 2-link robot manipulator are presented to show the effectiveness of the proposed method.

Robust Tracking Control of Autonomous Underwater Vehicles in the Presence of Disturbance Inputs

2009 ◽  
Author(s):  
S. Singh ◽  
A. Sanyal ◽  
R. Smith ◽  
N. Nordkvist ◽  
M. Chyba
Keyword(s):  
Feedback Control ◽  
Trajectory Tracking ◽  
Tracking Control ◽  
Autonomous Underwater Vehicle ◽  
Autonomous Underwater Vehicles ◽  
Open Loop ◽  
Robust Tracking Control ◽  
Trajectory Tracking Control ◽  
Loop Control ◽  
Control Scheme

An autonomous underwater vehicle (AUV) is expected to operate in an ocean in the presence of poorly known disturbance forces and moments. The uncertainties of the environment makes it difficult to apply open-loop control scheme for the motion planning of the vehicle. The objective of this paper is to develop a robust feedback trajectory tracking control scheme for an AUV that can track a prescribed trajectory amidst such disturbances. We solve a general problem of feedback trajectory tracking of an AUV in SE (3). The feedback control scheme is derived using Lyapunov-type analysis. The results obtained from numerical simulations confirm the asymptotic tracking properties of the feedback control law. We apply the feedback control scheme to different mission scenarios, with the disturbances being initial errors in the state of the AUV.

scholarly journals Existence and uniqueness of constrained globally optimal feedback controls in a linear-quadratic framework

2006 ◽  
Vol 2006 ◽  
pp. 1-22 ◽  
Author(s):  
Yashan Xu
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Existence And Uniqueness ◽  
Closed Loop ◽  
Synthesis Method ◽  
Open Loop ◽  
Linear Quadratic ◽  
Feedback Controls ◽  
Loop Control

A constrained closed-loop optimal control problem is considered in a linear-quadratic framework. To solve the problem, a special type open-loop optimal control problem and a standard open-loop optimal control problem are introduced and carefully studied, via which the existence and uniqueness of the globally optimal closed-loop control is established by a synthesis method.

Adjoint-Based Optimization Procedure for Active Vibration Control of Nonlinear Mechanical Systems

2017 ◽  
Vol 139 (8) ◽  
Author(s):  
Carmine M. Pappalardo ◽  
Domenico Guida
Keyword(s):  
Optimal Control ◽  
Control Theory ◽  
Control Problem ◽  
Numerical Solution ◽  
Optimal Control Theory ◽  
Numerical Procedure ◽  
Nonlinear Optimal Control ◽  
Open Loop ◽  
Adjoint Equations ◽  
Loop Control

In this paper, a new computational algorithm for the numerical solution of the adjoint equations for the nonlinear optimal control problem is introduced. To this end, the main features of the optimal control theory are briefly reviewed and effectively employed to derive the adjoint equations for the active control of a mechanical system forced by external excitations. A general nonlinear formulation of the cost functional is assumed, and a feedforward (open-loop) control scheme is considered in the analytical structure of the control architecture. By doing so, the adjoint equations resulting from the optimal control theory enter into the formulation of a nonlinear differential-algebraic two-point boundary value problem, which mathematically describes the solution of the motion control problem under consideration. For the numerical solution of the problem at hand, an adjoint-based control optimization computational procedure is developed in this work to effectively and efficiently compute a nonlinear optimal control policy. A numerical example is provided in the paper to show the principal analytical aspects of the adjoint method. In particular, the feasibility and the effectiveness of the proposed adjoint-based numerical procedure are demonstrated for the reduction of the mechanical vibrations of a nonlinear two degrees-of-freedom dynamical system.

Experimental Study on Optimal Tracking Control of a Micro Ground Vehicle

2017 ◽  
Vol 29 (4) ◽  
pp. 757-765 ◽  
Author(s):  
Soichiro Watanabe ◽  
◽  
Masanori Harada
Keyword(s):  
Experimental Study ◽  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Predictive Control ◽  
Tracking Control ◽  
Reference Trajectory ◽  
Ground Vehicle ◽  
Optimal Tracking ◽  
Tracking Controller

This paper investigates the application of optimal control to a micro ground vehicle (MGV) experimentally. The model predictive control (MPC) technique is used for the overall tracking controller during the maneuver. The reference trajectory for MPC is preliminarily obtained by numerical computation of the optimal control problem, which is prescribed as a minimum-time maneuver. The results provide nominal tracking performance and validate the feasibility of the approach.

Sign in / Sign up

Export Citation Format

Share Document