Related papers: A Robust Numerical Path Tracking Algorithm for Pol…
Speedup measures how much faster we can solve the same problem using many cores. If we can afford to keep the execution time fixed, then quality up measures how much better the solution will be computed using many cores. In this paper we…
We present a homotopic approach to solving challenging, optimization-based motion planning problems. The approach uses Homotopy Optimization, which, unlike standard continuation methods for solving homotopy problems, solves a sequence of…
Numerical homotopy continuation methods for three classes of polynomial systems are presented. For a generic instance of the class, every path leads to a solution and the homotopy is optimal. The counting of the roots mirrors the resolution…
We design a homotopy continuation algorithm, that is based on numerically tracking Viro's patchworking method, for finding real zeros of sparse polynomial systems. The algorithm is targeted for polynomial systems with coefficients…
While automatically generated polynomial elimination templates have sparked great progress in the field of 3D computer vision, there remain many problems for which the degree of the constraints or the number of unknowns leads to…
Path-following algorithms are frequently used in composite optimization problems where a series of subproblems, with varying regularization hyperparameters, are solved sequentially. By reusing the previous solutions as initialization,…
Given a graph $G$, and terminal vertices $s$ and $t$, the TRACKING PATHS problem asks to compute a minimum number of vertices to be marked as trackers, such that the sequence of trackers encountered in each s-t path is unique. TRACKING…
Link prediction is an important learning task for graph-structured data. In this paper, we propose a novel topological approach to characterize interactions between two nodes. Our topological feature, based on the extended persistent…
We present RobustTP, an end-to-end algorithm for predicting future trajectories of road-agents in dense traffic with noisy sensor input trajectories obtained from RGB cameras (either static or moving) through a tracking algorithm. In this…
We develop a certified numerical algorithm for computing Galois/monodromy groups of parametrized polynomial systems. Our approach employs certified homotopy path tracking to guarantee the correctness of the monodromy action produced by the…
Applications such as traffic engineering and network provisioning can greatly benefit from knowing, in real time, what is the largest input rate at which it is possible to transmit on a given path without causing congestion. We consider a…
This paper focuses on developing an efficient algorithm for analyzing a directed network (graph) from a topological viewpoint. A prevalent technique for such topological analysis involves computation of homology groups and their…
Using validated numerical methods, interval arithmetic and Taylor models, we propose a certified predictor-corrector loop for tracking zeros of polynomial systems with a parameter. We provide a Rust implementation which shows tremendous…
Path tracking system plays a key technology in autonomous driving. The system should be driven accurately along the lane and be careful not to cause any inconvenience to passengers. To address such tasks, this paper proposes hybrid tracker…
Collision-free mobile robot navigation is an important problem for many robotics applications, especially in cluttered environments. In such environments, obstacles can be static or dynamic. Dynamic obstacles can additionally be…
In this paper we propose a method that uses Lagrange multipliers and numerical algebraic geometry to find all critical points, and therefore globally solve, polynomial optimization problems. We design a polyhedral homotopy algorithm that…
Polynomial systems occur in many fields of science and engineering. Polynomial homotopy continuation methods apply symbolic-numeric algorithms to solve polynomial systems. We describe the design and implementation of our web interface and…
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…
For nonlinear equations, the homotopy methods (continuation methods) are popular in engineering fields since their convergence regions are large and they are quite reliable to find a solution. The disadvantage of the classical homotopy…
We consider the numerical irreducible decomposition of a positive dimensional solution set of a polynomial system into irreducible factors. Path tracking techniques computing loops around singularities connect points on the same irreducible…