Related papers: Validated numerics for algebraic path tracking

This paper presents a method for algebraic fault detection and identification of nonlinear mechanical systems, describing rigid robots, by using an approximation with orthonormal Jacobi polynomials. An explicit expression is derived for the…

This note briefly introduces the computed torque control method for trajectory tracking. The method is applicable to fully actuated robots, i.e, those whose inverse dynamics can be solved for any feasible acceleration. This includes many…

Rust's novel type system has proved an attractive target for verification and program analysis tools, due to the rich guarantees it provides for controlling aliasing and mutability. However, fully understanding, extracting and exploiting…

Let $\mathbb{Q}$ (resp. $\mathbb{R}$) be the field of rational (resp. real) numbers and $X = (X_1, \ldots, X_n)$ be variables. Deciding the non-negativity of polynomials in $\mathbb{Q}[X]$ over $\mathbb{R}^n$ or over semi-algebraic domains…

For a wide variety of regularization methods, algorithms computing the entire solution path have been developed recently. Solution path algorithms do not only compute the solution for one particular value of the regularization parameter but…

This paper deals with the use of numerical methods based on random root sampling techniques to solve some theoretical problems arising in the analysis of polynomials. These methods are proved to be practical and give solutions where…

We propose a method for tracing implicit real algebraic curves defined by polynomials with rank-deficient Jacobians. For a given curve $f^{-1}(0)$, it first utilizes a regularization technique to compute at least one witness point per…

We present necessary and sufficient conditions for the termination of linear homogeneous programs. We also develop a complete method to check termination for this class of programs. Our complete characterization of termination for such…

The accelerated deployment of service robots have spawned a number of algorithm variations to better handle real-world conditions. Many local trajectory planning techniques have been deployed on practical robot systems successfully. While…

Often in applications ranging from medical imaging and sensor networks to error correction and data science (and beyond), one needs to solve large-scale linear systems in which a fraction of the measurements have been corrupted. We consider…

In this paper we provide a new method to certify that a nearby polynomial system has a singular isolated root with a prescribed multiplicity structure. More precisely, given a polynomial system f $=(f\_1, \ldots, f\_N)\in C[x\_1, \ldots,…

Lack of numerical precision in control software -- in particular, related to trajectory computation -- can lead to incorrect results with costly or even catastrophic consequences. Various tools have been proposed to analyze the precision of…

This article is concerned with numerical methods to approximate effective coefficients in stochastic homogenization of discrete linear elliptic equations, and their numerical analysis --- which has been made possible by recent contributions…

Predicting human trajectories is essential for the safe operation of autonomous vehicles, yet current data-driven models often lack robustness in case of noisy inputs such as adversarial examples or imperfect observations. Although some…

We investigate the use of piecewise linear systems, whose coefficient matrix is a piecewise constant function of the solution itself. Such systems arise, for example, from the numerical solution of linear complementarity problems and in the…

The Rust programming language provides a powerful type system that checks linearity and borrowing, allowing code to safely manipulate memory without garbage collection and making Rust ideal for developing low-level, high-assurance systems.…

We present exact mixed-integer linear programming formulations for verifying the performance of first-order methods for parametric quadratic optimization. We formulate the verification problem as a mixed-integer linear program where the…

Runtime verification (RV) is a pragmatic and scalable, yet rigorous technique, to assess the correctness of complex systems, including cyber-physical systems (CPS). By measuring how robustly a CPS run satisfies a specification, RV allows in…

We design and analyze new protocols to verify the correctness of various computations on matrices over the ring F[x] of univariate polynomials over a field F. For the sake of efficiency, and because many of the properties we verify are…

This paper proposes a metric for sets of trajectories to evaluate multi-object tracking algorithms that includes time-weighted costs for localisation errors of properly detected targets, for false targets, missed targets and track switches.…