scholarly journals Applications of optimal control of a nonconvex sweeping process to optimization of the planar crowd motion model

2019 ◽  
Vol 24 (8) ◽  
pp. 4191-4216
Author(s):  
Tan H. Cao ◽  
◽  
Boris S. Mordukhovich ◽  
◽  
Keyword(s):  
Optimal Control ◽  
Sweeping Process ◽  
Motion Model ◽  
Crowd Motion

scholarly journals Modeling Pedestrian Motion in Crowded Scenes Based on the Shortest Path Principle

2021 ◽  
Vol 12 (1) ◽  
pp. 381
Author(s):  
Yi Zou ◽  
Yuncai Liu
Keyword(s):  
Shortest Path ◽  
State Of The Art ◽  
Meaningful Work ◽  
Movement Behavior ◽  
Motion Model ◽  
Human Dynamics ◽  
Motion Trajectories ◽  
Crowd Motion ◽  
Crowded Scenes ◽  
Part Motion

In the computer vision field, understanding human dynamics is not only a great challenge but also very meaningful work, which plays an indispensable role in public safety. Despite the complexity of human dynamics, physicists have found that pedestrian motion in a crowd is governed by some internal rules, which can be formulated as a motion model, and an effective model is of great importance for understanding and reconstructing human dynamics in various scenes. In this paper, we revisit the related research in social psychology and propose a two-part motion model based on the shortest path principle. One part of the model seeks the origin and destination of a pedestrian, and the other part generates the movement path of the pedestrian. With the proposed motion model, we simulated the movement behavior of pedestrians and classified them into various patterns. We next reconstructed the crowd motions in a real-world scene. In addition, to evaluate the effectiveness of the model in crowd motion simulations, we created a new indicator to quantitatively measure the correlation between two groups of crowd motion trajectories. The experimental results show that our motion model outperformed the state-of-the-art model in the above applications.

A mathematical framework for a crowd motion model

2008 ◽  
Vol 346 (23-24) ◽  
pp. 1245-1250 ◽  
Author(s):  
Bertrand Maury ◽  
Juliette Venel
Keyword(s):  
Mathematical Framework ◽  
Motion Model ◽  
Crowd Motion

UAV Active SLAM Trajectory Programming Based on Optimal Control

2013 ◽  
Vol 765-767 ◽  
pp. 1932-1935
Author(s):  
Zeng Xiang Yang ◽  
Sai Jin
Keyword(s):  
Optimal Control ◽  
Optimization Problem ◽  
Simultaneous Localization And Mapping ◽  
Plane Motion ◽  
Programming Algorithm ◽  
Motion Model ◽  
Unknown Environment ◽  
Localization And Mapping ◽  
Simulation Results ◽  
Slam Algorithm

To decrease the uncertainty of simultaneous localization and mapping of UAV, and at the same time, to increase the speed of searching the unknown environment at which UAV locates, an active SLAM trajectory programming algorithm is proposed based on optimal control. Therefore, UAV SLAM is tackled as a combined optimization problem, considering the precision of UAV location and mapping integrity. Based on the simplified UAV plane motion model, this algorithm is simulated and tested by comparing with the random SLAM algorithm. Simulation results show that this algorithm is effective.

scholarly journals Optimal control of a nonconvex perturbed sweeping process

2019 ◽  
Vol 266 (2-3) ◽  
pp. 1003-1050 ◽  
Author(s):  
Tan H. Cao ◽  
B.S. Mordukhovich
Keyword(s):  
Optimal Control ◽  
Sweeping Process

scholarly journals Optimal control of the sweeping process over polyhedral controlled sets

2016 ◽  
Vol 260 (4) ◽  
pp. 3397-3447 ◽  
Author(s):  
G. Colombo ◽  
R. Henrion ◽  
D. Hoang Nguyen ◽  
B.S. Mordukhovich
Keyword(s):  
Optimal Control ◽  
Sweeping Process

scholarly journals A MACROSCOPIC CROWD MOTION MODEL OF GRADIENT FLOW TYPE

2010 ◽  
Vol 20 (10) ◽  
pp. 1787-1821 ◽  
Author(s):  
BERTRAND MAURY ◽  
AUDE ROUDNEFF-CHUPIN ◽  
FILIPPO SANTAMBROGIO
Keyword(s):  
Ad Hoc ◽  
Gradient Flow ◽  
Emergency Evacuation ◽  
Probability Measures ◽  
Motion Model ◽  
Exit Door ◽  
Incompressibility Constraint ◽  
Macroscopic Approach ◽  
Crowd Motion ◽  
Wasserstein Space

A simple model to handle the flow of people in emergency evacuation situations is considered: at every point x, the velocity U (x) that individuals at x would like to realize is given. Yet, the incompressibility constraint prevents this velocity field to be realized and the actual velocity is the projection of the desired one onto the set of admissible velocities. Instead of looking at a microscopic setting (where individuals are represented by rigid discs), here the macroscopic approach is investigated, where the unknown is a density ρ(t,x). If a gradient structure is given, say U = -∇D where D is, for instance, the distance to the exit door, the problem is presented as a Gradient Flow in the Wasserstein space of probability measures. The functional which gives the Gradient Flow is neither finitely valued (since it takes into account the constraints on the density), nor geodesically convex, which requires for an ad hoc study of the convergence of a discrete scheme.

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