A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Study motion planning for points avoiding obstacles in a plane.
New approach for obstacle avoidance in robotics using learned representations.
Fast and efficient motion planning algorithms are crucial for many state-of-the-art robotics applications such as self-driving cars. Existing motion planning methods become ineffective as their computational complexity increases exponentially with the dimensionality of the motion planning problem. To address this issue…
CoMPNetX uses neural networks to efficiently solve constrained motion planning problems.
In this paper we study a notion of topological complexity for the motion planning problem. The topological complexity is a number which measures discontinuity of the process of motion planning in the configuration space X. More precisely, it is the minimal number k such that there are k different motion planning rules,…
Survey on manifold complexities and motion planning in robotics.
End-to-end learnable network for safer self-driving with interpretable intermediate representations.
PBCS combines RL and motion planning for better exploration.
Intelligent motion planning is one of the core components in automated vehicles, which has received extensive interests. Traditional motion planning methods suffer from several drawbacks in terms of optimality, efficiency and generalization capability. Sampling based methods cannot guarantee the optimality of the gener…
Geodesics in R^n configuration spaces for points apart by epsilon.
Deep network predicts action sequences for complex tasks from a scene image.
We consider the problem of robot motion planning in an oriented Riemannian manifold as a topological motion planning problem in its oriented frame bundle. For this purpose, we study the topological complexity of oriented frame bundles, derive an upper bound for this invariant and certain lower bounds from cup length co…
Motion planning is an essential component in most of today's robotic applications. In this work, we consider the learning setting, where a set of solved motion planning problems is used to improve the efficiency of motion planning on different, yet similar problems. This setting is important in applications with rapidl…
This paper presents preliminary work on learning the search heuristic for the optimal motion planning for automated driving in urban traffic. Previous work considered search-based optimal motion planning framework (SBOMP) that utilized numerical or model-based heuristics that did not consider dynamic obstacles. Optimal…
Let X be a subcomplex of the standard CW-decomposition of the n-dimensional torus. We exhibit an explicit optimal motion planning algorithm for X. This construction is used to calculate the topological complexity of complements of general position arrangements and Eilenberg-Mac Lane spaces associated to right-angled Ar…
New TC variant dTC better fits motion planning for some systems.
Paper proposes incorporating road rules as a loss function for better motion planning.
New geometric approach controls motion of a spinning sphere on a plane.
This paper surveys DRL for autonomous vehicle motion planning.
We study an elementary problem of topological robotics: rotation of a line, which is fixed by a revolving joint at a base point: one wants to bring the line from its initial position to a final position by a continuous motion in the space. The final goal is to construct an algorithm which will perform this task once th…
Motion planning and control are key problems in a collection of robotic applications including the design of autonomous agile vehicles and of minimalist manipulators. These problems can be accurately formalized within the language of affine connections and of geometric control theory. In this paper we overview recent r…
Motion planning for robots of high degrees-of-freedom (DOFs) is an important problem in robotics with sampling-based methods in configuration space C as one popular solution. Recently, machine learning methods have been introduced into sampling-based motion planning methods, which train a classifier to distinguish coll…
We design an algorithm writing down presentations of graph braid groups. Generators are represented in terms of actual motions of robots moving without collisions on a given graph. A key ingredient is a new motion planning algorithm whose complexity is linear in the number of edges and quadratic in the number of robots…
This work improves motion planning for quadcopters by learning and reasoning about controller performance.
Swept Volume (SV), the volume displaced by an object when it is moving along a trajectory, is considered a useful metric for motion planning. First, SV has been used to identify collisions along a trajectory, because it directly measures the amount of space required for an object to move. Second, in sampling-based moti…
The topological complexity TC(X) is a numerical homotopy invariant of a topological space X which is motivated by robotics and is similar in spirit to the classical Lusternik-Schnirelmann category of X. Given a mechanical system with configuration space X, the invariant TC(X) measures the complexity of all possible mot…
We propose in this paper a constructive procedure that transforms locally, even at singular configurations, the kinematics of a car towing trailers into Kumpera-Ruiz normal form. This construction converts the nonholonomic motion planning problem into an algebraic problem (the resolution of a system of polynomial equat…
Study geodesic complexity in homogeneous Riemannian manifolds.
New method for predicting paths of unpredictable objects with high confidence.
We prove that the topological complexity of (a motion planning algorithm on) the complement of generic complex essential hyperplane arrangement of hyperplanes in an -dimensional linear space is min.
New metric invariant GC connects to TC, with applications in robotics.
We study an elementary problem of the topological robotics: collective motion of a set of distinct particles which one has to move from an initial configuration to a final configuration, with the requirement that no collisions occur in the process of motion. The ultimate goal is to construct an algorithm which will…
Safe autonomous decisions made with machine learning predictions using Conformal Decision Theory.
The paper teaches robots to navigate by learning costs from expert demonstrations.
We introduce a variant of Farber's topological complexity, defined for smooth compact orientable Riemannian manifolds, which takes into account only motion planners with the lowest possible "average length" of the output paths. We prove that it never differs from topological complexity by more than , thus showing th…
The paper develops a method to learn navigation costs from expert demonstrations in partially observable environments.
We present a new approach to equivariant version of the topological complexity, called a symmetric topological complexity. It seems that the presented approach is more adequate for the analysis of an impact of symmetry on the the motion planning algoritm than the one introduced and studied by Colman and Grant. We show …
Learning and inference movement is a very challenging problem due to its high dimensionality and dependency to varied environments or tasks. In this paper, we propose an effective probabilistic method for learning and inference of basic movements. The motion planning problem is formulated as learning on a directed grap…
Machine learning can provide efficient solutions to the complex problems encountered in autonomous driving, but ensuring their safety remains a challenge. A number of authors have attempted to address this issue, but there are few publicly-available tools to adequately explore the trade-offs between functionality, scal…
The paper reviews machine learning safety techniques for autonomous vehicles.
Bayesian optimization usually assumes that a Bayesian prior is given. However, the strong theoretical guarantees in Bayesian optimization are often regrettably compromised in practice because of unknown parameters in the prior. In this paper, we adopt a variant of empirical Bayes and show that, by estimating the Gaussi…
In this paper, we describe a constrained Lagrangian and Hamiltonian formalism for the optimal control of nonholonomic mechanical systems. In particular, we aim to minimize a cost functional, given initial and final conditions where the controlled dynamics is given by nonholonomic mechanical system. In our paper, the co…
The paper proposes a model to forecast traffic motion from sensor data.
Autonomous robots need to interact with unknown, unstructured and changing environments, constantly facing novel challenges. Therefore, continuous online adaptation for lifelong-learning and the need of sample-efficient mechanisms to adapt to changes in the environment, the constraints, the tasks, or the robot itself a…
{\em Riemannian cubics} are curves in a manifold that satisfy a variational condition appropriate for interpolation problems. When is the rotation group SO(3), Riemannian cubics are track-summands of {\em Riemannian cubic splines}, used for motion planning of rigid bodies. Partial integrability results are know…
Graph neural networks (GNNs) have emerged as a powerful tool for nonlinear processing of graph signals, exhibiting success in recommender systems, power outage prediction, and motion planning, among others. GNNs consists of a cascade of layers, each of which applies a graph convolution, followed by a pointwise nonlinea…
A single-vertex origami is a piece of paper with straight-line rays called creases emanating from a fold vertex placed in its interior or on its boundary. The Single-Vertex Origami Flattening problem asks whether it is always possible to reconfigure the creased paper from any configuration compatible with the metric, t…
Predicting human behavior is a difficult and crucial task required for motion planning. It is challenging in large part due to the highly uncertain and multi-modal set of possible outcomes in real-world domains such as autonomous driving. Beyond single MAP trajectory prediction, obtaining an accurate probability distri…