scholarly journals Optimal Stochastic Control Problem for General Linear Dynamical Systems in Neuroscience

2017 ◽  
Vol 2017 ◽  
pp. 1-7
Author(s):  
Yan Chen ◽  
Yingchun Deng ◽  
Shengjie Yue ◽  
Chao Deng
Keyword(s):  
Stochastic Control ◽  
Optimal Trajectory ◽  
Control Method ◽  
Dimensional Space ◽  
Target Position ◽  
Movement Trajectory ◽  
Linear Dynamical Systems ◽  
Reaching Movement ◽  
Optimal Velocity ◽  
Straight Line

This paper considers a d-dimensional stochastic optimization problem in neuroscience. Suppose the arm’s movement trajectory is modeled by high-order linear stochastic differential dynamic system in d-dimensional space, the optimal trajectory, velocity, and variance are explicitly obtained by using stochastic control method, which allows us to analytically establish exact relationships between various quantities. Moreover, the optimal trajectory is almost a straight line for a reaching movement; the optimal velocity bell-shaped and the optimal variance are consistent with the experimental Fitts law; that is, the longer the time of a reaching movement, the higher the accuracy of arriving at the target position, and the results can be directly applied to designing a reaching movement performed by a robotic arm in a more general environment.

Tracking control in x-y plane of an offshore container crane

2016 ◽  
Vol 23 (3) ◽  
pp. 469-483 ◽  
Author(s):  
Dongho Kim ◽  
Youngjin Park
Keyword(s):  
Tracking Control ◽  
Control Method ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Target Position ◽  
Container Ship ◽  
Scaled Model ◽  
Tracking Controller ◽  
Loading And Unloading ◽  
Linearized Model

A tracking controller is proposed for a crane attached to a mobile harbor (MH) equipped with a dual-stage trolley system, to dynamically position a container from the MH to the container ship or vice versa. Wave-induced motions of the MH and container ship occur during loading and unloading operations owing to external disturbances such as waves. However, a challenging task is to move a payload with unwanted swing motions accurately to the loading and unloading positions on a moving target vessel. To solve this problem, a dynamic MH crane model is derived in three-dimensional space, with roll, pitch, and heave motions caused by sea-wave disturbances. The MH crane model is then linearized to design a tracking controller and the parameters of the linearized model are obtained by carrying out the system identification process. A preview tracking control method that includes feedback and feed-forward control with the predicted target position in the x-y plane in the near future is utilized. Through numerical simulations and experiments with a scaled model, the tracking performance of the proposed dynamic positioning control system is considered when sinusoidal roll and pitch motions of the MH are generated to mimic the wavy sea environment.

The human-like trajectory planning for autonomous vehicles based on optimal control in a test track environment

2021 ◽  
pp. 095440702110090
Author(s):  
Xing Xu ◽  
Minglei Li ◽  
Feng Wang ◽  
Ju Xie ◽  
Xiaohan Wu ◽  
...  
Keyword(s):  
Optimal Control ◽  
Autonomous Vehicles ◽  
Optimal Trajectory ◽  
Control Method ◽  
Autonomous Vehicle ◽  
Trajectory Data ◽  
Test Track ◽  
Optimal Control Method ◽  
The Future ◽  
On The Road

A human-like trajectory could give a safe and comfortable feeling for the occupants in an autonomous vehicle especially in corners. The research of this paper focuses on planning a human-like trajectory along a section road on a test track using optimal control method that could reflect natural driving behaviour considering the sense of natural and comfortable for the passengers, which could improve the acceptability of driverless vehicles in the future. A mass point vehicle dynamic model is modelled in the curvilinear coordinate system, then an optimal trajectory is generated by using an optimal control method. The optimal control problem is formulated and then solved by using the Matlab tool GPOPS-II. Trials are carried out on a test track, and the tested data are collected and processed, then the trajectory data in different corners are obtained. Different TLCs calculations are derived and applied to different track sections. After that, the human driver’s trajectories and the optimal line are compared to see the correlation using TLC methods. The results show that the optimal trajectory shows a similar trend with human’s trajectories to some extent when driving through a corner although it is not so perfectly aligned with the tested trajectories, which could conform with people’s driving intuition and improve the occupants’ comfort when driving in a corner. This could improve the acceptability of AVs in the automotive market in the future. The driver tends to move to the outside of the lane gradually after passing the apex when driving in corners on the road with hard-lines on both sides.

scholarly journals An Improved Path-Generating Regulator for Two-Wheeled Robots to Track the Circle/Arc Passage

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Jun Dai ◽  
Naohiko Hanajima ◽  
Toshiharu Kazama ◽  
Akihiko Takashima
Keyword(s):  
Control Method ◽  
Convergence Property ◽  
Tangential Direction ◽  
Navigation Problem ◽  
Wheeled Robots ◽  
Robot Trajectory ◽  
Look Ahead ◽  
Straight Line ◽  
The Family ◽  
Straight Lines

The improved path-generating regulator (PGR) is proposed to path track the circle/arc passage for two-wheeled robots. The PGR, which is a control method for robots so as to orient its heading toward the tangential direction of one of the curves belonging to the family of path functions, is applied to navigation problem originally. Driving environments for robots are usually roads, streets, paths, passages, and ridges. These tracks can be seen as they consist of straight lines and arcs. In the case of small interval, arc can be regarded as straight line approximately; therefore we extended the PGR to drive the robot move along circle/arc passage based on the theory that PGR to track the straight passage. In addition, the adjustable look-ahead method is proposed to improve the robot trajectory convergence property to the target circle/arc. The effectiveness is proved through MATLAB simulations on both the comparisons with the PGR and the improved PGR with adjustable look-ahead method. The results of numerical simulations show that the adjustable look-ahead method has better convergence property and stronger capacity of resisting disturbance.

A self-organized reciprocal control method for multi-robot simultaneous coverage and tracking

2018 ◽  
Vol 38 (5) ◽  
pp. 689-698 ◽  
Author(s):  
Runfeng Chen ◽  
Jie Li ◽  
Lincheng Shen
Keyword(s):  
Control Method ◽  
Task Assignment ◽  
Decision Time ◽  
Velocity Space ◽  
Deadweight Loss ◽  
Traffic Surveillance ◽  
Content Type ◽  
Optimal Velocity ◽  
Service Environment ◽  
Self Organized

Purpose Multi-robots simultaneously coverage and tracking (SCAT) is the problem of simultaneously covering area and tracking targets, which is essential for many applications, such as delivery service, environment monitor, traffic surveillance, crime monitor, anti-terrorist mission and so on. The purpose of this paper is to improve the performance of detected target quantity, coverage rate and less deadweight loss by designing a self-organized method for multi-robots SCAT. Design/methodology/approach A self-organized reciprocal control method is proposed, coupling task assignment, tracking and covering, equipped with collision-avoiding ability naturally. First, SCAT problem is directly modeled as optimal reciprocal coverage velocity (ORCV) in velocity space. Second, the preferred velocity is generated by calculating the best velocity to the center of some robot detected targets. ORCV is given by adjusting the velocity relative to neighbor robots’ toward in optimal coverage velocity (OCV); it is proven that OCV is collision-free assembly. Third, some corresponding algorithms are designed for finding optimal velocity under two situations, such as no detected targets and empty ORCV. Findings The simulation results of two cases for security robots show that the proposed method has detected more targets with less deadweight loss and decision time and no collisions anytime. Originality/value In this paper, a self-organized reciprocal control method is proposed for multi-robots SCAT problem, which is modeled in velocity space directly, different to the traditional method modeling in configuration space. What is more, this method considers the reciprocal of robots that contributes to the better accomplishment of SCAT cooperatively.

Three-dimensional path planning for unmanned aerial vehicle based on linear programming

Robotica ◽  
2011 ◽  
Vol 30 (5) ◽  
pp. 773-781 ◽  
Author(s):  
Yang Chen ◽  
Jianda Han ◽  
Xingang Zhao
Keyword(s):  
Linear Programming ◽  
Path Planning ◽  
Real Time ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Linear Constraints ◽  
Flying Height ◽  
Ant Colony Optimization Algorithm ◽  
Optimal Velocity ◽  
Aerial Vehicle

SUMMARYIn this paper, an approach based on linear programming (LP) is proposed for path planning in three-dimensional space, in which an aerial vehicle is requested to pursue a target while avoiding static or dynamic obstacles. This problem is very meaningful for many aerial robots, such as unmanned aerial vehicles. First, the tasks of target-pursuit and obstacle-avoidance are modelled with linear constraints in relative coordination according to LP formulation. Then, two weighted cost functions, representing the optimal velocity resolution, are integrated into the final objective function. This resolution, defined to achieve the optimal velocity, deals with the optimization of a pair of orthogonal vectors. Some constraints, such as boundaries of the vehicle velocity, acceleration, sensor range, and flying height, are considered in this method. A number of simulations, under static and dynamic environments, are carried out to validate the performance of generating optimal trajectory in real time. Compared with ant colony optimization algorithm and genetic algorithm, our method has less parameters to tune and can achieve better performance in real-time application.

Use of Mechanisms Marking Centers of Simplexes in Their 2-Dimensional Projections as Axonographs of Multidimensional Spaces

2021 ◽  
Vol 8 (4) ◽  
pp. 13-23
Author(s):  
Sherzod Abdurahmanov
Keyword(s):  
Dimensional Space ◽  
Spatial Location ◽  
Straight Line Segment ◽  
Barycentric Coordinates ◽  
Parallel Projection ◽  
Problem Solution ◽  
Similarity Coefficients ◽  
Translational Movement ◽  
Straight Line ◽  
Multidimensional Objects

A brief historical excursion into the graphics of geometry of multidimensional spaces at the paper beginning clarifies the problem – the necessary to reduce the number of geometric actions performed when depicting multidimensional objects. The problem solution is based on the properties of geometric figures called N- simplexes, whose number of vertices is equal to N + 1, where N expresses their dimensionality. The barycenter (centroid) of the N-simplex is located at the point that divides the straight-line segment connecting the centroid of the (N–1)-simplex contained in it with the opposite vertex by 1: N. This property is preserved in the parallel projection (axonometry) of the simplex on the drawing plane, that allows the solution of the problem of determining the centroid of the simplex in its axonometry to be assigned to a mechanism which is a special Assembly of pantographs (the author's invention) with similarity coefficients 1:1, 1:2, 1:3, 1:4,...1:N. Next, it is established, that the spatial location of a point in N-dimensional space coincides with the centroid of the simplex, whose vertices are located on the point’s N-fold (barycentric) coordinates. In axonometry, the ends of both first pantograph’s links and the ends of only long links of the remaining ones are inserted into points indicating the projections of its barycentric coordinates and the mechanism node, which serves as a determinator, graphically marks the axonometric location of the point defined by its coordinates along the axes х1, х2, х3 … хN.. The translational movement of the support rods independently of each other can approximate or remote the barycentric coordinates of a point relative to the origin of coordinates, thereby assigning the corresponding axonometric places to the simplex barycenter, which changes its shape in accordance with its points’ occupied places in the coordinate axes. This is an axonograph of N-dimensional space, controlled by a numerical program. The last position indicates the possibility for using the equations of multidimensional spaces’ geometric objects given in the corresponding literature for automatic drawing when compiling such programs.

Development of Path Tracking Control Algorithm for a 4 DOF Spatial Manipulator Using PID Controller

2017 ◽  
pp. 314-327
Author(s):  
Pradeep Reddy Bonikila ◽  
Ravi Kumar Mandava ◽  
Pandu Ranga Vundavilli
Keyword(s):  
Pid Controller ◽  
Dynamic Models ◽  
Control Method ◽  
Robotic Manipulator ◽  
Industrial Applications ◽  
Path Tracking ◽  
End Effector ◽  
Straight Line ◽  
Feedback Control Method ◽  
Manipulator Arm

The path tracking phenomenon of a robotic manipulator arm plays an important role, when the manipulators are used in continuous path industrial applications, such as welding, machining and painting etc. Nowadays, robotic manipulators are extensively used in performing the said tasks in industry. Therefore, it is essential for the manipulator end effector to track the path designed to perform the task in an effective way. In this chapter, an attempt is made to develop a feedback control method for a 4-DOF spatial manipulator to track a path with the help of a PID controller. In order to design the said controller, the kinematic and dynamic models of the robotic manipulator are derived. Further, the concept of inverse kinematics has been used to track different paths, namely a straight line and parabolic paths continuously. The effectiveness of the developed algorithm is tested on a four degree of freedom manipulator arm in simulations.

The control method for the multi-phase traffic model

2016 ◽  
Vol 27 (10) ◽  
pp. 1650111
Author(s):  
Yi Liu ◽  
Rong-Jun Cheng ◽  
Yan-Qiang Ma ◽  
Hong-Xia Ge
Keyword(s):  
Traffic Control ◽  
Control Method ◽  
Turning Points ◽  
Control Signal ◽  
Two Phase ◽  
Optimal Velocity ◽  
Car Following Model ◽  
The Stability ◽  
Improved Model ◽  
Multi Phase

Based on multi-phase car-following model proposed by Nagatani, the control theory method is used to analyze the stability of the model. The optimal velocity function is improved to have more turning points. The original optimal velocity with one turning point shows two-phase traffic, while the improved model with [Formula: see text] turning points exhibits [Formula: see text] phase traffic. Control signal is added into the model. Numerical simulation is conducted to show the results for the stability of the model with and without control signal.

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