Integrating Path Integral Control With Backstepping Control to Regulate Stochastic System

Shinyoung Bae,Jong Min Lee,Tae Hoon Oh,Jong Woo Kim,Yeonsoo Kim 제어·로봇·시스템학회 2023 International Journal of Control, Automation, and Vol.21 No.7

Path integral control integrated with backstepping control is proposed to address the practical regulation problem, wherein the system dynamics are represented as stochastic differential equations. Path integral control requires the sampling of uncontrolled trajectories to calculate the optimal control input. However, the probability of generating a low-cost trajectory from uncontrolled dynamics is low. This implies that the path integral control requires an excessive number of trajectory samples to approximate the optimal control input appropriately. Therefore, we propose an integrated method of backstepping and path integral control to provide a systematic approach for sampling stabilized trajectories that are close to the optimal one. This proposed method requires a relatively small number of samples than that of the path integral control and uses the terminal set to further reduce the computational load. In simulation studies, the proposed method is applied to a single-input single-output example and a continuous stirred-tank reactor for demonstration. The results show the advantages of integrating the backstepping control and the path integral control.

LPV/H ∞ CONTROLLER DESIGN FOR PATH TRACKING OF AUTONOMOUS GROUND VEHICLES THROUGH FOUR-WHEEL STEERING AND DIRECT YAW-MOMENT CONTROL

Peng Hang,Xinbo Chen,Fengmei Luo 한국자동차공학회 2019 International journal of automotive technology Vol.20 No.4

This paper focuses on the path-tracking controller design for autonomous ground vehicles (AGVs) using fourwheel steering (4WS) and direct yaw-moment control (DYC) systems. In order to deal with the parametric uncertainties, a linear parameter-varying (LPV) H∞ controller is designed as the high-level controller to generate the front and rear wheel steering angles and external yaw moment based on linear matrix inequality (LMI) approach. The lower-level controller is designed for torque allocation between the left and right side wheels to yield the desired total longitudinal force and external yaw moment utilizing weighted least square (WLS) allocation algorithm. To test the performance of the proposed pathtracking controller, numerical simulations are carried out based on a high-fidelity and full-vehicle model constructed in CarSim. Simulation results show that the LPV/H∞ controller has better path-tracking performance than the fixed gain H∞ controller. To show the superiority of 4WS+DYC control system, the contrast simulation is performed based on LPV/H∞ controller. Simulation results indicate that 4WS+DYC control system has better path-tracking performance and handling stability than active front steering (AFS), AFS+DYC and 4WS control systems.

비행체 시간지연을 고려한 정밀경로추종 PID 제어기법

이인석(Ihnseok Rhee),박상혁(Sanghyuk Park),이경호(Kyoung-ho Lee) 한국항공우주학회 2011 韓國航空宇宙學會誌 Vol.39 No.7

무인항공기가 복잡한 지형이나 위험 지역에서 안전한 비행을 하기 위해서는 요구되는 경로를 정밀하게 추종할 수 있는 제어기법이 필요하다. 경로추종을 위해 사용되는 PID 제어기에서는 경로의 곡률을 앞먹임하여 추종성능을 개선할 수 있다. 한편 경로를 정밀 추종하기 위해서는 제어기의 이득을 크게 하는 것이 필요하나 비행체의 응답속도가 느린 경우 큰 경로 추종 이득을 사용할 경우 성능 저하 또는 불안정성이 발생할 수 있다. 여기서는 응답지연을 고려하여 앞먹임을 갖는 PID제어기의 설계방법을 고려하였다. 앞먹임에 필요한 경로정보를 간단히 얻기 위해 주어진 경로를 3차 스플라인 방법을 적용하여 3차 다항식으로 나타내었다. 설계한 제어기의 추종성능을 평가하기 위해 높은 고도에서 운용되는 느린 횡방향 동특성을 갖는 무인항공기에 대해 비선형 시뮬레이션을 수행하였다. 제어기에서는 횡방향 동특성을 1차 모델로 가정하여 반영하였다. 시뮬레이션을 통하여 동특성을 고려한 경우는 비행체가 주어진 경로를 매우 정밀하게 추종함을 확인하였다. In order to complete missions in a complicated terrain or highly dangerous area, an unmanned aerial vehicle(UAV) needs a fine controller to precisely follow the desired path. A PID controller used for the path following feeds forward path curvature information to the control input to improve the path following performance. High gain for PID controller is necessary to follow path tightly. However the high gain could cause instability or performance degradation when the vehicle has slow dynamics. We present PID controller design method which considers response delay of vehicle as well as path curvature. In order to obtain path curvature the desired path is described as a 3rd order polynomial by applying cubic spline interpolation. We apply the proposed controller to the path following of a UAV which is operated in high altitude and has very slow lateral dynamics. The lateral dynamics are modelled as a first order delayed system in the controller design. Nonlinear simulation shows the UAV with proposed controller follows an arbitrary path very tightly.

정밀경로추종을 위한 PID 제어기법

이인석,박상혁,이경호 한국항공우주학회 2011 한국항공우주학회 학술발표회 논문집 Vol.2011 No.4

무인항공기가 복잡한 지형이나 위험 지역에서 안전한 비행을 하기 위해서는 요구되는 경로를 정밀하게 추종할 수 있는 제어기법이 필요하다. 경로추종을 위해 일반적으로 다뤄지는 PID 제어기는 설계가 쉬운 반면에 복잡한 궤적을 정밀하게 추종하는데 적합하지 않다고 알려져 있다. 하지만 본 연구에서는 PID 제어기에 경로정보의 앞먹임을 추가함으로써 정밀한 경로추종이 가능하게 하였다. 앞먹임에 필요한 경로정보를 간단히 얻기 위해 주어진 경로를 3차 스플라인 방법을 적용하여 3차 다항식으로 나타내었다. 또한 무인항공기의 동특성을 1차 모델로 가정하여 제어기에 반영함으로써 무인항공기의 응답지연으로 인한 성능저하를 감소하고자 하였다. 마지막으로 설계된 제어기를 무인항공기 비선형 모델에 적용하여 그 성능을 확인하였다. In order to complete missions in the complicated terrain or highly dangerous area, an unmanned aerial vehicle(UAV) needs a fine controller to precisely follow the desired path. APID controller is widely used for the path following because a controller design is easy. But it is known as an unsuitable controller to a sophisticated path following. In this paper, a PID controller feeding path informations forward is suggested for following desired path tightly. In order to obtain path information the desired path is described as 3rd order polynomial by applying cubic spline interpolation. Moreover, the dynamic of UAV is modelled as a first order delayed system which degrade the performance of the path following. PD controller is designed by considering the delay to alleviate the degradation. Finally, designed controller is applied to the nonlinear model of UAV for confirmation of performance.

Spatial target path following and coordinated control of multiple UUVs

Qi, Xue,Xiang, Peng,Cai, Zhi-jun The Society of Naval Architects of Korea 2020 International Journal of Naval Architecture and Oc Vol.12 No.1

The coordination control of multiple Underactuated Underwater Vehicles (UUVs) moving in three dimensional space is investigated in this paper. The coordinated path following control task is decomposed into two sub tasks, that is, path following control and coordination control. In the spatial curve path following control task, path following error dynamics is build in the Serret-Frenet coordinate frame. The virtual reference object can be chosen freely on the desired spatial path. Considering the speed of the UUV, the line-of-sight navigation is introduced to help the path following errors quickly converge to zero. In the coordination control sub task, the communication topology of multiple UUVs is described by the graph theory. The speed of each UUV is adjusted to achieve the coordination. The path following system and the coordination control system are viewed as the feedback connection system. Input-to-state stable of the coordinated path following system can be proved by small gain theorem. The simulation experiments can further demonstrate the good performance of the control method.

Spatial target path following and coordinated control of multiple UUVs

Qi, Xue,Xiang, Peng,Cai, Zhi-jun The Society of Naval Architects of Korea 2020 International Journal of Naval Architecture and Oc Vol.12 No.-

The coordination control of multiple Underactuated Underwater Vehicles (UUVs) moving in three dimensional space is investigated in this paper. The coordinated path following control task is decomposed into two sub tasks, that is, path following control and coordination control. In the spatial curve path following control task, path following error dynamics is build in the Serret-Frenet coordinate frame. The virtual reference object can be chosen freely on the desired spatial path. Considering the speed of the UUV, the line-of-sight navigation is introduced to help the path following errors quickly converge to zero. In the coordination control sub task, the communication topology of multiple UUVs is described by the graph theory. The speed of each UUV is adjusted to achieve the coordination. The path following system and the coordination control system are viewed as the feedback connection system. Input-to-state stable of the coordinated path following system can be proved by small gain theorem. The simulation experiments can further demonstrate the good performance of the control method.

Design of Fuzzy-PID Controller for Path Tracking of Mobile Robot with Differential Drive

Do Khac Tiep,Kinam Lee,Dae-Yeong Im,Bongwoo Kwak,Young-Jae Ryoo 한국지능시스템학회 2018 INTERNATIONAL JOURNAL of FUZZY LOGIC and INTELLIGE Vol.18 No.3

In this paper, a design of a fuzzy-PID controller for path tracking of a mobile robot with differential drive is proposed. The fuzzy-PID controller consists of a PID controller and a fuzzy controller with two inputs and three outputs. When the system response has the error and the error rate, the fuzzy controller can tune the parameters of the PID controller. The model based on Lagrange dynamic approach for a robot with differential drive is described. The fuzzy-PID controller and the classical PID controller are compared by simulation. The path tracking of a mobile robot with differential drive was tested using MATLAB/Simulink. The simulation results show that the fuzzy-PID controller has a better performance than the classical PID controller. The proposed controller has better convergence rate in comparison with the classical PID controller for a mobile robot with any arbitrary initial state. It has the advantages of rapid respond, high stability, tracking accuracy and good anti-interference, so the fuzzy-PID controller is the appropriate choice for path tracking control of mobile robots with differential drive.

Path Tracking Control Coverage of a Mining Robot Based on Exhaustive Path Planning with Exact Cell Decomposition

Dae Hwan Kim,Giang Hoang,Min-Ji Bae,Jin Wook Kim,Suk Min Yoon,Tae-Kyeong Yeo,Hong Sup,Sang-Bong Kim 제어로봇시스템학회 2014 제어로봇시스템학회 국제학술대회 논문집 Vol.2014 No.10

This paper addresses exhaustive coverage path planning of a mining robot based on cellular decomposition in minable area. For this work, the followings are done. First, the map of minable area is decomposed into cells by exact cell decomposition. Second, the coverage path is generated using back-and-forth motion. Third, direction of coverage path and generating graph path using proposed special spanning tree is considered to get minimum distance of moving path. The exhaustive coverage path is obtained by combining coverage path and moving path. Fourth, a controller is designed for a two-wheeled robot to track the exhaustive coverage path generated by path planning method. Finally, simulation and experimental results can prove efficiency of the proposed exhaustive coverage path planning method.

Control as Anaphor Movement

이정식 한국생성문법학회 2009 생성문법연구 Vol.19 No.4

Whether the control module independently exists or not has been a hot theoretical issue in recent syntactic debates in generative grammar. In the standard theory (Chomsky 1981, Landau 2003), raising and control have been treated as distinct processes: Whereas raising involves movement, control involves a rule of construal relating PRO to its antecedent. Hornstein (1999) and Boeckx (2000), among others, have recently claimed that control is just an instance of raising. Despite some theoretical merits, the latter claim, called control-as-movement, can only thrive at the cost of the standard theta theory in that this claim is forced to allow the movement into a theta-position. This paper attempts to combine two approaches which are deficient on their own into a new proposal in which problems of these two can be reconciled. The major point of this middle path is that the obligatorily controlled PRO is a reflexive clitic similar to se in the Romance languages, and that it moves toward its antecedent, called control-as-anaphor-movement. As a consequence, this approach maintains the standard theta theory as it is and still captures the movement properties of control while eliminating the control module.

Speed-varying path tracking based on model predictive control for autonomous vehicles

Shuang Tang,Jun Li,Wei Zhou 한국자동차공학회 2024 International journal of automotive technology Vol.25 No.2

In order to improve autonomous vehicles path-tracking accuracy and stability, a lateral–longitudinal coordination pathtrackingcontrol method is proposed. The proposed coordination control consists of path-tracking control and speed trackingcontrol. First, the desired safety speed is planned according to the known road curvature and adhesion coeffi cient in orderto prevent the tire force saturation. Based on the three-degree-of-freedom (3DOF) vehicle dynamic model and the previewtracking error model, model predictive control (MPC) theory is adopted to design the speed-varying vehicle path-trackingcontroller. Then, the quadratic programming (QP) method is used to solve the objective function with constraints, whichcalculates the steering angle to control the vehicle track the reference path. In addition, a PID speed controller is designed tocalculate the torque of each wheel to track the desired speed. Finally, according to the yaw rate error and the vehicle slip angleerror, a yaw moment stability controller based on the fuzzy logic control theory is designed to balance the vehicle stabilityand motility. The simulation results based on a Matlab/Carsim platform show that the coordination path-tracking controlmethod proposed in this paper can eff ectively improve the vehicle tracking accuracy and the stability on diff erent roads.