Related papers: Generating stochastic trajectories with global dyn…
This study in centered on models accounting for stochastic deformations of sample paths of random walks, embedded either in $\mathbb{Z}^2$ or in $\mathbb{Z}^3$. These models are immersed in multi-type particle systems with exclusion.…
The measured time series from complex systems are renowned for their intricate stochastic behavior, characterized by random fluctuations stemming from external influences and nonlinear interactions. These fluctuations take diverse forms,…
A result of A.M. Davie [Int. Math. Res. Not. 2007] states that a multidimensional stochastic equation $dX_t = b(t, X_t)\,dt + dW_t$, $X_0=x$, driven by a Wiener process $W= (W_t)$ with a coefficient $b$ which is only bounded and measurable…
We consider the stochastic target problem of finding the collection of initial laws of a mean-field stochastic differential equation such that we can control its evolution to ensure that it reaches a prescribed set of terminal probability…
Continued great efforts have been dedicated towards high-quality trajectory generation based on optimization methods, however, most of them do not suitably and effectively consider the situation with moving obstacles; and more particularly,…
Soft robots have the potential to interact with sensitive environments and perform complex tasks effectively. However, motion plans and trajectories for soft manipulators are challenging to calculate due to their deformable nature and…
Generation of robust trajectories for legged robots remains a challenging task due to the underlying nonlinear, hybrid and intrinsically unstable dynamics which needs to be stabilized through limited contact forces. Furthermore,…
This paper addresses the air traffic flow management research problem of determining reroute, ground delay and air delay for flights using stochastic weather forecast information. The overall goal is to minimize system-wide reroute and…
We present a trajectory generation framework for control of wheeled vehicles under steering actuator constraints. The motivation is smooth autonomous driving of heavy vehicles. The key idea is to take into account rate, and additionally,…
Brownian motion is a well-known model for normal diffusion, but not all physical phenomena behave according to a Brownian motion. Many phenomena exhibit irregular diffusive behavior, called anomalous diffusion. Examples of anomalous…
Trajectory optimization (TO) is an efficient tool to generate a redundant manipulator's joint trajectory following a 6-dimensional Cartesian path. The optimization performance largely depends on the quality of initial trajectories. However,…
In car-following models, the driver reacts according to his physical and psychological abilities which may change over time. However, most car-following models are deterministic and do not capture the stochastic nature of human perception.…
We consider random walks in dynamic random environments, with an environment generated by the time-reversal of a Markov process from the oriented percolation universality class. If the influence of the random medium on the walk is small in…
Uncertain dynamic obstacles, such as pedestrians or vehicles, pose a major challenge for optimal robot navigation with safety guarantees. Previous work on motion planning has followed two main strategies to provide a safe bound on an…
The paper is devoted to the relationship between the continuous Markovian description of Levy flights developed previously and their equivalent representation in terms of discrete steps of a wandering particle, a certain generalization of…
The aim of this paper is to represent any continuous local martingale as an almost sure limit of a nested sequence of simple, symmetric random walks, time changed by a discrete quadratic variation process. One basis of this is a similar…
Trajectory prediction facilitates effective planning and decision-making, while constrained trajectory prediction integrates regulation into prediction. Recent advances in constrained trajectory prediction focus on structured constraints by…
Pedestrian crowds encompass a complex interplay of intentional movements aimed at reaching specific destinations, fluctuations due to personal and interpersonal variability, and interactions with each other and the environment. Previous…
In this note, by an elementary use of Girsanov's transform we show that the exit time for either a biased random walk or a drifted Brownian motion on a symmetric interval is stochastically monotone with respect to the drift parameter. In…
Trajectory optimization methods for motion planning attempt to generate trajectories that minimize a suitable objective function. Such methods efficiently find solutions even for high degree-of-freedom robots. However, a globally optimal…