Constrained Optimum Trajectories with Specified Range

1980 ◽  
Vol 3 (1) ◽  
pp. 78-85 ◽  
Author(s):  
Heinz Erzberger ◽  
Homer Lee
Keyword(s):  
Optimum Trajectories

Dynamic Cooperative Speed Optimization at Signalized Arterials with Various Platoons

2019 ◽  
Vol 2673 (5) ◽  
pp. 528-537 ◽  
Author(s):  
Xia Wu ◽  
Xiangmo Zhao ◽  
Qi Xin ◽  
Qiaoli Yang ◽  
Shaowei Yu ◽  
...  
Keyword(s):  
Traffic Signals ◽  
Programming Algorithm ◽  
Connected Vehicles ◽  
Driving Behaviors ◽  
Optimum Trajectories ◽  
Speed Optimization ◽  
The Status ◽  
Driving Model ◽  
Optimum Approach ◽  
Multiple Vehicles

Aggressive and inappropriate driving behaviors will lead to excessive fuel consumption. Both the Signal Phase and Timing (SPaT) and the status of preceding vehicles have significant impacts on driving behaviors. Drivers can obtain accurate SPaT information and the status of preceding vehicles via V2X communications. Many speed advisory strategies have been presented based on the consideration of this information. However, existing studies do not consider the cooperative optimization of multiple intersections and various platoons. Once connected vehicles travel through intersections with their own fuel-optimum trajectories, the following vehicles could be adversely affected by the preceding vehicles, leading to the following vehicles being stopped at the intersection. To address these problems, this paper presents an improved cooperative eco-driving model for when a vehicle passes two successive traffic signals during the green phase; a dynamic nonlinear programming algorithm is used to generate the optimal speed profile for various platoons considering the SPaT and the preceding vehicles’ status. Numerous simulations on VISSIM for uninformed and connected vehicles haves been conducted to make comparison analysis. It is apparent that the proposed eco-driving model produces a significant fuel saving. In addition, cooperative optimization for the various platoons and separate optimization of multiple vehicles were performed to seek the most effective solution. The results indicated that systematic optimization (cooperative optimization of the all vehicles) is identified as the fuel-optimum approach in comparison to the separate optimization.

Graphical Determination of Optimum Trajectories for Third-Order Systems

1970 ◽  
Vol 92 (2) ◽  
pp. 271-278
Author(s):  
Yousri M. Abd-El-Fattah
Keyword(s):  
Control Function ◽  
Maximum Error ◽  
Control Signal ◽  
Graphical Solution ◽  
Third Order ◽  
Two Phase ◽  
State Trajectory ◽  
Optimum Trajectories ◽  
Initial States

The present paper explains the use of two phase planes in the graphical determination of optimum trajectories for third-order systems, depending on the sign of a single control function. The control function is defined on these planes by means of different contours. Accordingly, the control signal is known at the different points on these planes. Once the control signal is found, the state trajectory is determined. Most of the arbitrary initial states are treated and, in particular, the cases of separate steps in each of the error and its first as well as second time derivatives. This work also explains the use of the graphical solution in obtaining the maximum error and switching times.

Optimum trajectories for spacecraft mission to asteroid Apophis with a return to the Earth

2013 ◽  
Vol 47 (4) ◽  
pp. 334-345 ◽  
Author(s):  
V. V. Ivashkin ◽  
I. V. Krylov ◽  
A. Lan
Keyword(s):  
The Earth ◽  
Optimum Trajectories ◽  
Spacecraft Mission

scholarly journals Fixed-Range Optimum Trajectories for Short-Haul Aircraft

1976 ◽  
Vol 13 (10) ◽  
pp. 748-754 ◽  
Author(s):  
John F. Barman ◽  
Heinz Erzberger
Keyword(s):  
Optimum Trajectories

scholarly journals A Simplest Differential Game on a Plane with Four Participants

2019 ◽  
pp. 40-50
Author(s):  
Viktor D. Shiryayev ◽  
Elena V. Shagilova
Keyword(s):  
Game Theory ◽  
Characteristic Function ◽  
Dynamic Stability ◽  
Differential Game ◽  
Cooperative Game ◽  
Cooperative Game Theory ◽  
Standard Procedures ◽  
Optimum Trajectories ◽  
Optimality Principles ◽  
Cooperative Differential Game

Introduction. The article presents a simplest differential game with four participants. The players move on a plane and can do simple movements. The game under considering comes down to a cooperative differential game. The dynamic stability of such optimality principles as the S-kernel and Shapley vector is shown. Materials and Methods. The standard procedures of the cooperative game theory are applied to the analysis and decision of a cooperative differential game. The conditional and optimum trajectories, along which the players move, are found using the Pontryagin’s maximum principle. When constructing the characteristic function, the minimax approach is used. Results. The optimum strategy of the players, conditional and optimum trajectories of their movements at various ways of formation of coalitions are written out explicitly. The characteristic function is constructed according to the accepted max-min principle; the S-kernel and Shapley vector are considered as a decision. The components of the Shapley vector are written out explicitly; the fact that the Shapley vector is an element of the S-kernel and nonemptiness of the S-kernel, when the players are moving along an optimum trajectory, are shown. Using the results of the static cooperative game theory for researching differential games, we face the problems, which are connected with specifics of the differential equations of the movement. As a priority, the problem of the dynamic stability of the optimality principles under consideration is identified. In the work, the dynamic stability of the Shapley vector and S-kernel is shown. Discussion and Conclusion. The results of the research show that the analysis of the dynamic stability of the optimality principles considered is relevant.

scholarly journals Optimum trajectories for an Earth–asteroid–Earth mission with a high thrust flight

2019 ◽  
Vol 484 (2) ◽  
pp. 161-166
Author(s):  
V. V. Ivashkin ◽  
Anqi Lang
Keyword(s):  
Space Mission ◽  
Conjugate Functions ◽  
Launch Vehicles ◽  
Earth Space ◽  
Earth Asteroid ◽  
Second Stage ◽  
The Earth ◽  
Optimum Trajectories ◽  
Upper Stage ◽  
High Thrust

The trajectories of a mission to an asteroid with the presence of a spacecraft (SC) near the asteroid for some time and including a return to the Earth have been studied. A two-stage method of constructing optimum (with respect to the maximum of the useful SC mass) interplanetary trajectories of an Earth–asteroid–Earth mission with high thrust engines has been developed: in the central Newtonian field of the Sun’s attraction at the first stage and with allowance for disturbances at the second stage. An algorithm of constructing conjugate functions for the case of maximizing the useful mass has been designed. The optimum trajectories for the Earth-Apophis-Earth mission have been constructed and analyzed. The possibility in principle of organizing the Earth-Apophis-Earth space mission based on the "Soyuz" and "Zenit" launch vehicles and "Fregat" upper stage for a flight has been demonstrated.

Time-Optimum Trajectories for Robots With Multiple End-Effectors

2003 ◽  
Author(s):  
Martin Hosek
Keyword(s):  
Flat Panel Display ◽  
Maximum Throughput ◽  
Throughput Performance ◽  
Straight Line ◽  
Optimum Trajectories ◽  
Manufacturing Applications ◽  
S Curve ◽  
End Effectors ◽  
Automated Tools ◽  
Motion Profile

Aggressive throughput performance of automated tools for semiconductor and flat-panel-display manufacturing applications have led to development of substrate-handling robots with multiple end-effectors. For maximum throughput levels, a method for calculating a time-optimum substrate transfer trajectory without causing any of the substrates carried by the robot to slide, and without violating other prescribed constraints, is required. This paper presents an algorithm which provides the required functionality with desirable computational efficiency and reliability. The key idea is to identify the set of fundamental trajectory shapes which cover all possible combinations of constraints for a given category of moves, e.g., moves along a straight line or along a circular arc, decompose the fundamental shapes into segments where a single constraint is active, and determine the time-optimum motion profiles in the segments. The fundamental shapes for each of the categories are found as simplified versions of the generic shape which corresponds to the case when all of the constraints are active. Each of the shapes has a set of conditions associated with it to determine whether the shape can be used for a particular move. An example comparison of a motion profile generated based on pre-defined time-optimum shapes with a conventional s-curve trajectory demonstrates that the present algorithm produces substantially faster motion, resulting in an improved throughput performance of the robot.

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