46,380 research outputs found
Kinetic description of optimal control problems and applications to opinion consensus
In this paper an optimal control problem for a large system of interacting
agents is considered using a kinetic perspective. As a prototype model we
analyze a microscopic model of opinion formation under constraints. For this
problem a Boltzmann-type equation based on a model predictive control
formulation is introduced and discussed. In particular, the receding horizon
strategy permits to embed the minimization of suitable cost functional into
binary particle interactions. The corresponding Fokker-Planck asymptotic limit
is also derived and explicit expressions of stationary solutions are given.
Several numerical results showing the robustness of the present approach are
finally reported.Comment: 25 pages, 18 figure
Modeling Cooperative Navigation in Dense Human Crowds
For robots to be a part of our daily life, they need to be able to navigate
among crowds not only safely but also in a socially compliant fashion. This is
a challenging problem because humans tend to navigate by implicitly cooperating
with one another to avoid collisions, while heading toward their respective
destinations. Previous approaches have used hand-crafted functions based on
proximity to model human-human and human-robot interactions. However, these
approaches can only model simple interactions and fail to generalize for
complex crowded settings. In this paper, we develop an approach that models the
joint distribution over future trajectories of all interacting agents in the
crowd, through a local interaction model that we train using real human
trajectory data. The interaction model infers the velocity of each agent based
on the spatial orientation of other agents in his vicinity. During prediction,
our approach infers the goal of the agent from its past trajectory and uses the
learned model to predict its future trajectory. We demonstrate the performance
of our method against a state-of-the-art approach on a public dataset and show
that our model outperforms when predicting future trajectories for longer
horizons.Comment: Accepted at ICRA 201
Human Motion Trajectory Prediction: A Survey
With growing numbers of intelligent autonomous systems in human environments,
the ability of such systems to perceive, understand and anticipate human
behavior becomes increasingly important. Specifically, predicting future
positions of dynamic agents and planning considering such predictions are key
tasks for self-driving vehicles, service robots and advanced surveillance
systems. This paper provides a survey of human motion trajectory prediction. We
review, analyze and structure a large selection of work from different
communities and propose a taxonomy that categorizes existing methods based on
the motion modeling approach and level of contextual information used. We
provide an overview of the existing datasets and performance metrics. We
discuss limitations of the state of the art and outline directions for further
research.Comment: Submitted to the International Journal of Robotics Research (IJRR),
37 page
Portfolio Optimization and Model Predictive Control: A Kinetic Approach
In this paper, we introduce a large system of interacting financial agents in
which each agent is faced with the decision of how to allocate his capital
between a risky stock or a risk-less bond. The investment decision of
investors, derived through an optimization, drives the stock price. The model
has been inspired by the econophysical Levy-Levy-Solomon model (Economics
Letters, 45). The goal of this work is to gain insights into the stock price
and wealth distribution. We especially want to discover the causes for the
appearance of power-laws in financial data. We follow a kinetic approach
similar to (D. Maldarella, L. Pareschi, Physica A, 391) and derive the mean
field limit of our microscopic agent dynamics. The novelty in our approach is
that the financial agents apply model predictive control (MPC) to approximate
and solve the optimization of their utility function. Interestingly, the MPC
approach gives a mathematical connection between the two opponent economic
concepts of modeling financial agents to be rational or boundedly rational.
Furthermore, this is to our knowledge the first kinetic portfolio model which
considers a wealth and stock price distribution simultaneously. Due to our
kinetic approach, we can study the wealth and price distribution on a
mesoscopic level. The wealth distribution is characterized by a lognormal law.
For the stock price distribution, we can either observe a lognormal behavior in
the case of long-term investors or a power-law in the case of high-frequency
trader. Furthermore, the stock return data exhibits a fat-tail, which is a well
known characteristic of real financial data
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