Iterative learning control with feedback using Fourier series with application to robot trajectory tracking

Robotica ◽  
1993 ◽  
Vol 11 (4) ◽  
pp. 291-298 ◽  
Author(s):  
Jong-Woon Lee ◽  
Hak-Sung Lee ◽  
Zeungnam Bien
Keyword(s):  
Fourier Series ◽  
Trajectory Tracking ◽  
Control Algorithm ◽  
Controller Design ◽  
Learning Control ◽  
Convergence Condition ◽  
Control Input ◽  
Robot Trajectory ◽  
Fourier Series Approximation ◽  
System States

SUMMARYThe Fourier series is employed to approximate the input/output (I/O) characteristics of a dynamic system and, based on the approximation, a new learning control algorithm is proposed in order to find iteratively the control input for tracking a desired trajectory. The use of the Fourier series approximation of I/O renders at least a couple of useful consequences: the frequency characteristics of the system can be used in the controller design and the reconstruction of the system states is not required. The convergence condition of the proposed algorithm is provided and the existence and uniqueness of the desired control input is discussed. The effectiveness of the proposed algorithm is illustrated by computer simulation for a robot trajectory tracking. It is shown that, by adding a feedback term in learning control algorithm, robustness and convergence speed can be improved.

scholarly journals Robust Iterative Learning Control for a Class of Linear Systems with Data Dropouts

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Wang Rui ◽  
Ma Xinghe ◽  
Bu Xuhui
Keyword(s):  
Iterative Learning Control ◽  
Control Algorithm ◽  
Contraction Mapping ◽  
Initial Conditions ◽  
Learning Control ◽  
Convergence Condition ◽  
Iterative Learning ◽  
Control Input ◽  
Initial Condition ◽  
Data Dropouts

A robust iterative learning control algorithm is proposed for a class of intermittent systems with disturbances and uncertain initial conditions. Based on the contraction mapping approach, the convergence condition for the proposed algorithm is first given, and then the bounds on control input and output trajectories can be obtained. It is shown that these bounds depend on bounds on the initial condition errors and disturbances, and the bounds are zero in the absence of these disturbances. A numerical example is also given to verify the theoretical result.

Mathematical modelling and model predictive controller design of a quad tiltrotor UAV

2020 ◽  
pp. 095440622097133
Author(s):  
Jingxian Liao ◽  
Xiaodong Song
Keyword(s):  
Mathematical Model ◽  
Model Predictive Control ◽  
Predictive Control ◽  
Trajectory Tracking ◽  
Controller Design ◽  
Control Input ◽  
Random Disturbance ◽  
Effect Analysis ◽  
Input Variables ◽  
Induced Velocity

A novel convertible unmanned aerial vehicle (UAV) with four tiltable rotors and a tandem-wing system has been developed. Considering the aerodynamic effect caused by the rotor-induced velocity, a mathematical model that contains the traditional free airstream analysis and rotor-induced effect analysis is proposed, from which the precise equilibrium point of the control inputs and states can be derived. Moreover, a control allocation algorithm is designed to provide the mapping relationship between traditional input variables and specific input variables of the UAV, so that the complicated mathematical model can be linearized for the design of model predictive control (MPC) system. In order to handle the control input constraints of the UAV system, an MPC system is applied for the trajectory tracking during the cruising phase. The simulation results demonstrate that the proposed model predictive control system has stability, accuracy without a random disturbance and quick response capabilities with a random disturbance during cruising trajectory tracking, which are in high demand for the quick UAV flight system.

scholarly journals Bridging Reinforcement Learning and Iterative Learning Control: Autonomous Reference Tracking for Unknown, Nonlinear Dynamics

2021 ◽  
Author(s):  
Michael Meindl ◽  
Dustin Lehmann ◽  
Thomas Seel
Keyword(s):  
Nonlinear Dynamics ◽  
Real World ◽  
Feedforward Control ◽  
Learning Control ◽  
Parameter Tuning ◽  
Control Input ◽  
Plug And Play ◽  
Reference Tracking ◽  
System States ◽  
Unknown Nonlinear Dynamics

<div>This work addresses the problem of reference tracking in autonomously learning agents with unknown, nonlinear dynamics. Existing solutions require model information or extensive parameter tuning, and have rarely been validated in real-world experiments. We propose a learning control scheme that learns to approximate the unknown dynamics by a Gaussian Process (GP), which is used to optimize and apply a feedforward control input on each trial. Unlike existing approaches, the proposed method neither requires knowledge of the system states and their dynamics nor knowledge of an effective feedback control structure. All algorithm parameters are chosen automatically, i.e. the learning method works plug and play. The proposed method is validated in extensive simulations and real-world experiments. In contrast to most existing work, we study learning dynamics for more than one motion task as well as the robustness of performance across a large range of learning parameters. The method’s plug and play applicability is demonstrated by experiments with a balancing robot, in which the proposed method rapidly learns to track the desired output. Due to its model-agnostic and plug and play properties, the proposed method is expected to have high potential for application to a large class of reference tracking problems in systems with unknown, nonlinear dynamics.</div>

PD Iterative Self-learning Control for 3R Plane Robot Trajectory Tracking

2013 ◽  
Vol 11 (10) ◽  
Author(s):  
Hongwei Gao ◽  
Kun Hong ◽  
Jinguo Liu ◽  
Yuquan Leng ◽  
Chuanyin Liu
Keyword(s):  
Trajectory Tracking ◽  
Learning Control ◽  
Robot Trajectory ◽  
Self Learning

scholarly journals Active Disturbance Rejection Based Robust Trajectory Tracking Controller Design in State Space

2019 ◽  
Vol 141 (6) ◽  
Author(s):  
Emre Sariyildiz ◽  
Rahim Mutlu ◽  
Chuanlin Zhang
Keyword(s):  
State Space ◽  
Trajectory Tracking ◽  
Disturbance Rejection ◽  
Position Control ◽  
Controller Design ◽  
Design Method ◽  
Control Input ◽  
Active Disturbance Rejection ◽  
Tracking Controller ◽  
Trajectory Tracking Controller

This paper proposes a new active disturbance rejection (ADR) based robust trajectory tracking controller design method in state space. It can compensate not only matched but also mismatched disturbances. Robust state and control input references are generated in terms of a fictitious design variable, namely differentially flat output, and the estimations of disturbances by using differential flatness (DF) and disturbance observer (DOb). Two different robust controller design techniques are proposed by using Brunovsky canonical form and polynomial matrix form approaches. The robust position control problem of a two mass-spring-damper system is studied to verify the proposed ADR controllers.

Study on Iterative Learning Control of Mobile Robot

2015 ◽  
Vol 775 ◽  
pp. 319-323
Author(s):  
Li Ping Qu ◽  
Yong Yin Qu ◽  
Hao Han Zhou
Keyword(s):  
Mobile Robot ◽  
Trajectory Tracking ◽  
Iterative Learning Control ◽  
Learning Control ◽  
Iterative Learning ◽  
Tracking Problem ◽  
Forgetting Factor ◽  
Robot Trajectory ◽  
Tracking Process

In order to solve the mobile robot trajectory tracking problem better, an iterative learning control (ILC) was applied. And the efficiency of mobile robot trajectory tracking was improved. From the simulation result, ILC with forgetting factor has very good performance for solving mobile robot trajectory tracking problem, and the smooth of trajectory tracking process also improved well.

scholarly journals Backstepping Approach for Autonomous Mobile Robot Trajectory Tracking

2016 ◽  
Vol 2 (3) ◽  
pp. 478 ◽  
Author(s):  
Ibari Benaoumeur ◽  
Benchikh Laredj ◽  
Hanifi Elhachimi Amar Reda ◽  
Ahmed-foitih Zoubir
Keyword(s):  
Mobile Robot ◽  
Trajectory Tracking ◽  
Controller Design ◽  
Tracking Errors ◽  
Robust Controller ◽  
Output Tracking ◽  
Robot Trajectory ◽  
Tracking Controller ◽  
Angular Velocities ◽  
The Given

This paper proposes a backstepping controller design for trajectory tracking of unicycle-type mobile robots. The main object of the control algorithms developed is to design a robust output tracking controller. The design of the controller is based on the lyapunov theorem, kinematic tracking controller of an unicycle-like mobile robot is used to provides the desired values of the linear and angular velocities for the given trajectory. A Lyapunov-based stability analysis is presented to guarantee the robot stability of the tracking errors. Simulation and experimental results show the effectiveness of the proposed robust controller in term of accuracy and stability under different load conditions.

Smooth adaptive fixed time convergent controller design for BTT missiles with uncertainties

2019 ◽  
Vol 124 (1273) ◽  
pp. 323-345
Author(s):  
Y. Yun ◽  
S. Tang ◽  
J. Guo ◽  
Y. Yun
Keyword(s):  
Control Algorithm ◽  
Performance Metrics ◽  
Controller Design ◽  
Sliding Mode ◽  
Fixed Time ◽  
Convergence Time ◽  
Control Input ◽  
Time Stability ◽  
Terminal Sliding Mode ◽  
Satisfactory Performance

ABSTRACTA smooth adaptive sliding-mode-based controller is developed for BTT missiles considering nonlinear couplings and aerodynamic uncertainties, wherein fixed-time stability theory is synthesised into sliding-mode control algorithm, such that control variables follow the desired command within fixed-bounded convergence time. Unlike other terminal sliding-mode-related works, the bound of settling time is independent of initial states, indicating that performance metrics, for instance the convergence rate, can be evaluated in advance. The control input is designed to be intrinsically smooth, based on adaptive estimations, and therefore the problem of singularity and chattering is effectively eliminated. Simulation results demonstrate the satisfactory performance and validate the effectiveness of the designed approach.

Trajectory tracking of wheeled mobile robot by adopting iterative learning control with predictive, current, and past learning items

Robotica ◽  
2014 ◽  
Vol 33 (7) ◽  
pp. 1393-1414 ◽  
Author(s):  
Chong Yu ◽  
Xiong Chen
Keyword(s):  
Mobile Robot ◽  
Trajectory Tracking ◽  
Iterative Learning Control ◽  
Control Algorithm ◽  
Mathematical Proof ◽  
Learning Control ◽  
Iterative Learning ◽  
Wheeled Mobile Robot ◽  
State Variables ◽  
Wheeled Mobile Robots

SUMMARYIn this paper, an iterative learning control algorithm is adopted to solve the high-precision trajectory tracking issue of a wheeled mobile robot with time-varying, nonlinear, and strong-coupling dynamics properties. The designed iterative learning control law adopts predictive, current and past learning items to drive the state variables, and input variables, and outputs variables converge to the bounded scope of their desired values. The algorithm can enhance the control performance, stability and robust characteristics. The rigorous mathematical proof of the convergence character of the proposed iterative learning control algorithm is given. The feasibility, effectiveness, and robustness of the proposed algorithm are illustrated by quantitative experiments and comparative analysis. The experimental results show that the proposed iterative learning control algorithm has an outstanding control effect on the trajectory tracking issue of wheeled mobile robots.

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