Lyapunov-like methodology for robot tracking control synthesis

1990 ◽  
Vol 51 (3) ◽  
pp. 567-583 ◽  
Author(s):  
ZORAN R. NOVAKOVIC
Keyword(s):  
Tracking Control ◽  
Control Synthesis ◽  
Robot Tracking

scholarly journals Online Optimal Control of Robotic Systems with Single Critic NN-Based Reinforcement Learning

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Xiaoyi Long ◽  
Zheng He ◽  
Zhongyuan Wang
Keyword(s):  
Optimal Control ◽  
Reinforcement Learning ◽  
Tracking Control ◽  
Learning Algorithm ◽  
Tracking Error ◽  
Adaptive Dynamic Programming ◽  
Robotic Systems ◽  
Control Synthesis ◽  
Optimal Tracking ◽  
Optimal Tracking Control

This paper suggests an online solution for the optimal tracking control of robotic systems based on a single critic neural network (NN)-based reinforcement learning (RL) method. To this end, we rewrite the robotic system model as a state-space form, which will facilitate the realization of optimal tracking control synthesis. To maintain the tracking response, a steady-state control is designed, and then an adaptive optimal tracking control is used to ensure that the tracking error can achieve convergence in an optimal sense. To solve the obtained optimal control via the framework of adaptive dynamic programming (ADP), the command trajectory to be tracked and the modified tracking Hamilton-Jacobi-Bellman (HJB) are all formulated. An online RL algorithm is the developed to address the HJB equation using a critic NN with online learning algorithm. Simulation results are given to verify the effectiveness of the proposed method.

scholarly journals Decentralized Suboptimal State Feedback Integral Tracking Control Design for Coupled Linear Time-Varying Systems

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Mohamed Sadok Attia ◽  
Mohamed Karim Bouafoura ◽  
Naceur Benhadj Braiek
Keyword(s):  
Tracking Control ◽  
State Feedback ◽  
Linear Time ◽  
Least Square ◽  
Control Synthesis ◽  
Operational Matrices ◽  
Control Input ◽  
Time Varying ◽  
State Equations ◽  
Integral Control

In this paper, a suboptimal state feedback integral decentralized tracking control synthesis for interconnected linear time-variant systems is proposed by using orthogonal polynomials. Particularly, the use of operational matrices allows, by expanding the subsystem input states and outputs over a shifted Legendre polynomial basis, the conversion of time-varying parameter differential state equations to a set of time-independent algebraic ones. Hence, optimal open-loop state and control input coefficients are forwardly determined. These data are used to formulate a least-square problem, allowing the synthesis of decentralized state feedback integral control gains. Closed-loop asymptotic stability LMI conditions are given. The proposed approach effectiveness is proved by solving a nonconstant reference tracking problem for coupled inverted pendulums.

An Algorithm for Robust Tracking Control of Robots

Robotica ◽  
1991 ◽  
Vol 9 (1) ◽  
pp. 53-62 ◽  
Author(s):  
Zoran R. Novaković ◽  
Leon Z˘lajpah
Keyword(s):  
Tracking Control ◽  
Error Control ◽  
Sliding Mode ◽  
Tracking Error ◽  
Lyapunov Theory ◽  
Control Synthesis ◽  
Robust Tracking ◽  
Robust Tracking Control ◽  
Time Simulation ◽  
Inverse Kinematics Problem

SUMMARYBased on the Lyapunov theory, a new principle was developed for synthesizing robot tracking control in the presence of model uncertainties. First, a general Lyapunov-like robust tracking concept is presented. It is then used as a basis for the control algorithm derived via a quadratic Lyapunov function constructed using a sliding mode function (based on the output error). Control synthesis is made in task-space, without any need for solving the inverse kinematics problem, i.e. one does not need to inver the Jacobian matrix. It is also shown that the tracking error becomes close to zero in a settling time which is less than a prescribed finite time. Simulation results are incorporated.

Wheeled Mobile Robot Tracking Control without Velocity Measurement

2013 ◽  
Vol 373-375 ◽  
pp. 231-237 ◽  
Author(s):  
Qiang Wang ◽  
Guang Tong ◽  
Xin Xing
Keyword(s):  
Mobile Robot ◽  
Mobile Robots ◽  
Velocity Measurement ◽  
Tracking Control ◽  
Wheeled Mobile Robot ◽  
Design Parameters ◽  
Wheeled Mobile Robots ◽  
Trajectory Tracking Control ◽  
Robot Tracking ◽  
Control Scheme

In this paper, a new robust trajectory tracking control scheme for wheeled mobile robots without velocity measurement is proposed. In the proposed controller, the velocity observer is used to estimate the velocity of wheeled mobile robot. The dynamics of wheeled mobile robot is considered to develop the controller. The proposed controller has the following features: i) The proposed controller has good robustness performance; ii) It is easy to improve tracking performance by setting only one design parameters.

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