Related papers: Computing Funnels Using Numerical Optimization Bas…

The computational efficiency of stochastic simulation algorithms is notoriously limited by the kinetic trapping of the simulated trajectories within low energy basins. Here we present a new method that overcomes kinetic trapping while still…

This paper presents a data driven universal ball trajectory prediction method integrated with physics equations. Existing methods are designed for specific ball types and struggle to generalize. This challenge arises from three key factors.…

We present effective numerical algorithms for locally recovering unknown governing differential equations from measurement data. We employ a set of standard basis functions, e.g., polynomials, to approximate the governing equation with high…

This paper addresses the problem of efficiently computing higher-order variational integrators in simulation and trajectory optimization of mechanical systems as those often found in robotic applications. We develop $O(n)$ algorithms to…

A penalization method for a suitable reformulation of the governing equations as a constrained optimization problem provides accurate numerical simulations for large-amplitude travelling water waves in irrotational flows and in flows with…

Optimization of expensive computer models with the help of Gaussian process emulators in now commonplace. However, when several (competing) objectives are considered, choosing an appropriate sampling strategy remains an open question. We…

In this paper we solve the problem of finding a trajectory that shows that a given hybrid dynamical system with deterministic evolution leaves a given set of states considered to be safe. The algorithm combines local with global search for…

This contribution deals with identification of fractional-order dynamical systems. System identification, which refers to estimation of process parameters, is a necessity in control theory. Real processes are usually of fractional order as…

Differential drive robots are widely used in various scenarios thanks to their straightforward principle, from household service robots to disaster response field robots. There are several types of driving mechanisms for real-world…

We introduce two efficient algorithms for computing the partial Fourier transforms in one and two dimensions. Our study is motivated by the wave extrapolation procedure in reflection seismology. In both algorithms, the main idea is to…

In autonomous systems, a motion planner generates reference trajectories which are tracked by a low-level controller. For safe operation, the motion planner should account for inevitable controller tracking error when generating avoidance…

Predicting human motion in unstructured and dynamic environments is difficult as humans naturally exhibit complex behaviors that can change drastically from one environment to the next. In order to alleviate this issue, we propose to encode…

Clustering points in a vector space or nodes in a graph is a ubiquitous primitive in statistical data analysis, and it is commonly used for exploratory data analysis. In practice, it is often of interest to "refine" or "improve" a given…

The methodology of funnel control was introduced in the early 2000s, and it has developed since then in many respects achieving a level of mathematical maturity balanced by practical applications. Its fundamental tenet is the attainment of…

Approximating a function with a finite series, e.g., involving polynomials or trigonometric functions, is a critical tool in computing and data analysis. The construction of such approximations via now-standard approaches like least squares…

This paper presents a numerical function optimization framework designed for constrained optimization problems in robotics. The tool is designed with real-time considerations and is suitable for online trajectory and control input…

Machine learning operates at the intersection of statistics and computer science. This raises the question as to its underlying methodology. While much emphasis has been put on the close link between the process of learning from data and…

This paper develops a correspondence relating convex hulls of fractional functions with those of polynomial functions over the same domain. Using this result, we develop a number of new reformulations and relaxations for fractional…

Ordinary differential equations that model technical systems often contain states, that are considered dangerous for the system. A trajectory that reaches such a state usually indicates a flaw in the design. In this paper, we present and…

Recurrent Neural Network, Long Short-Term Memory, and Transformer have made great progress in predicting the trajectories of moving objects. Although the trajectory element with the surrounding scene features has been merged to improve…