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Automated driving has become more and more popular due to its potential to eliminate road accidents by taking over driving tasks from humans. One of the remaining challenges is to follow a planned path autonomously, especially when…
Markov Chain Monte Carlo (MCMC) method is a widely used algorithm design scheme with many applications. To make efficient use of this method, the key step is to prove that the Markov chain is rapid mixing. Canonical paths is one of the two…
This paper proposes a local search algorithm for a specific combinatorial optimisation problem in graph theory: the Hamiltonian Completion Problem (HCP) on undirected graphs. In this problem, the objective is to add as few edges as possible…
Non-linear Trajectory Optimisation (TO) methods require good initial guesses to converge to a locally optimal solution. A feasible guess can often be obtained by allocating a large amount of time for the trajectory to complete. However for…
A general overview of the phenomenon of automatic continuity of homomorphisms between Polish groups is given. In particular, we study variants and improvements of the closed graph theorem, applying these to the problem of continuity of…
Safe navigation within a workspace is a fundamental skill for autonomous robots to accomplish more complex tasks. Harmonic potentials are artificial potential fields that are analytical, globally convergent and provably free of local…
In this article, we consider the residual regularization path-following method with the trust-region updating strategy for the linear complementarity problem. This time-stepping selection based on the trust-region updating strategy…
A comparative study of different block matching alternatives for motion estimation is presented. The study is focused on computational burden and objective measures on the accuracy of prediction. Together with existing algorithms several…
Map construction methods automatically produce and/or update road network datasets using vehicle tracking data. Enabled by the ubiquitous generation of georeferenced tracking data, there has been a recent surge in map construction…
We consider fact-checking approaches that aim to predict the veracity of assertions in knowledge graphs. Five main categories of fact-checking approaches for knowledge graphs have been proposed in the recent literature, of which each is…
In this paper, we describe a new, systematic and explicit way of approximating solutions of mixed hyperbolic systems with constant coefficients satisfying a Uniform Lopatinski Condition via different Penalization approaches.
We give a brief discussion of the recently developed Constrained-Path Monte Carlo Method. This method is a quantum Monte Carlo technique that eliminates the fermion sign problem plaguing simulations of systems of interacting electrons. The…
We develop algorithms for certifying an approximation to a nonsingular solution of a square system of equations built from univariate analytic functions. These algorithms are based on the existence of oracles for evaluating basic data about…
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…
In this paper, we propose an efficient continuation method for locating multiple power flow solutions. We adopt the holomorphic embedding technique to represent solution curves as holomorphic functions in the complex plane. The…
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 propose a strategy for improving camera location estimation in structure from motion. Our setting assumes highly corrupted pairwise directions (i.e., normalized relative location vectors), so there is a clear room for improving current…
This paper addresses the problem of finding shortest paths homotopic to a given disjoint set of paths that wind amongst point obstacles in the plane. We present a faster algorithm than previously known.
We present a method to approximate pairwise distance on a graph, having an amortized sub-linear complexity in its size. The proposed method follows the so called heat method due to Crane et al. The only additional input are the values of…
We study the navigation problem for a robot moving amidst static and dynamic obstacles and rely on a hierarchical approach to solve it. First, the reference trajectory is planned by the safe interval path planning algorithm that is capable…