A distributional study of the path edge-covering numbers for random trees

Local path planning is important in the development of autonomous vehicles since it allows a vehicle to adapt their movements to dynamic environments, for instance, when obstacles are detected. This work presents an evaluation of the performance of different local path planning techniques for an Autonomous Surface Vehicle, using a custom-made simulator based on the open-source Robotarium framework. The conducted simulations allow to verify, compare and visualize the solutions of the different techniques. The selected techniques for evaluation include A*, Potential Fields (PF), Rapidly-Exploring Random Trees* (RRT*) and variations of the Fast Marching Method (FMM), along with a proposed new method called Updating the Fast Marching Square method (uFMS). The evaluation proposed in this work includes ways to summarize time and safety measures for local path planning techniques. The results in a Lake environment present the advantages and disadvantages of using each technique. The proposed uFMS and A* have been shown to achieve interesting performance in terms of processing time, distance travelled and security levels. Furthermore, the proposed uFMS algorithm is capable of generating smoother routes.

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Development of an Improved Rapidly Exploring Random Trees Algorithm for Static Obstacle Avoidance in Autonomous Vehicles

Sensors ◽

10.3390/s21062244 ◽

2021 ◽

Vol 21 (6) ◽

pp. 2244

Author(s):

S. M. Yang ◽

Y. A. Lin

Keyword(s):

Path Planning ◽

Obstacle Avoidance ◽

Autonomous Vehicles ◽

Autonomous Vehicle ◽

Optimal Path ◽

Random Trees ◽

Average Deviation ◽

Lane Changes ◽

Path Smoothing ◽

Rapidly Exploring Random Trees

Safe path planning for obstacle avoidance in autonomous vehicles has been developed. Based on the Rapidly Exploring Random Trees (RRT) algorithm, an improved algorithm integrating path pruning, smoothing, and optimization with geometric collision detection is shown to improve planning efficiency. Path pruning, a prerequisite to path smoothing, is performed to remove the redundant points generated by the random trees for a new path, without colliding with the obstacles. Path smoothing is performed to modify the path so that it becomes continuously differentiable with curvature implementable by the vehicle. Optimization is performed to select a “near”-optimal path of the shortest distance among the feasible paths for motion efficiency. In the experimental verification, both a pure pursuit steering controller and a proportional–integral speed controller are applied to keep an autonomous vehicle tracking the planned path predicted by the improved RRT algorithm. It is shown that the vehicle can successfully track the path efficiently and reach the destination safely, with an average tracking control deviation of 5.2% of the vehicle width. The path planning is also applied to lane changes, and the average deviation from the lane during and after lane changes remains within 8.3% of the vehicle width.

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Perturbative Quantum Field Theory on Random Trees

Communications in Mathematical Physics ◽

10.1007/s00220-020-03874-2 ◽

2021 ◽

Vol 381 (3) ◽

pp. 857-887

Author(s):

Nicolas Delporte ◽

Vincent Rivasseau

Keyword(s):

Field Theory ◽

Quantum Field Theory ◽

Random Trees ◽

Quantum Field ◽

Perturbative Quantum ◽

Perturbative Quantum Field Theory

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Efficient Sampling With Q-Learning to Guide Rapidly Exploring Random Trees

IEEE Robotics and Automation Letters ◽

10.1109/lra.2018.2856927 ◽

2018 ◽

Vol 3 (4) ◽

pp. 3868-3875 ◽

Cited By ~ 2

Author(s):

Jinwook Huh ◽

Daniel D. Lee

Keyword(s):

Random Trees ◽

Q Learning ◽

Efficient Sampling ◽

Rapidly Exploring Random Trees

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Gibbs partitions, Riemann–Liouville fractional operators, Mittag–Leffler functions, and fragmentations derived from stable subordinators

Journal of Applied Probability ◽

10.1017/jpr.2020.93 ◽

2021 ◽

Vol 58 (2) ◽

pp. 314-334

Author(s):

Man-Wai Ho ◽

Lancelot F. James ◽

John W. Lau

Keyword(s):

Special Functions ◽

Dirichlet Distribution ◽

Random Trees ◽

Fractional Integrals ◽

Biased Sampling ◽

Scaling Limits ◽

Fractional Operators ◽

Random Partitions ◽

Two Parameter ◽

Potential Use

AbstractPitman (2003), and subsequently Gnedin and Pitman (2006), showed that a large class of random partitions of the integers derived from a stable subordinator of index $\alpha\in(0,1)$ have infinite Gibbs (product) structure as a characterizing feature. The most notable case are random partitions derived from the two-parameter Poisson–Dirichlet distribution, $\textrm{PD}(\alpha,\theta)$, whose corresponding $\alpha$-diversity/local time have generalized Mittag–Leffler distributions, denoted by $\textrm{ML}(\alpha,\theta)$. Our aim in this work is to provide indications on the utility of the wider class of Gibbs partitions as it relates to a study of Riemann–Liouville fractional integrals and size-biased sampling, and in decompositions of special functions, and its potential use in the understanding of various constructions of more exotic processes. We provide characterizations of general laws associated with nested families of $\textrm{PD}(\alpha,\theta)$ mass partitions that are constructed from fragmentation operations described in Dong et al. (2014). These operations are known to be related in distribution to various constructions of discrete random trees/graphs in [n], and their scaling limits. A centerpiece of our work is results related to Mittag–Leffler functions, which play a key role in fractional calculus and are otherwise Laplace transforms of the $\textrm{ML}(\alpha,\theta)$ variables. Notably, this leads to an interpretation within the context of $\textrm{PD}(\alpha,\theta)$ laws conditioned on Poisson point process counts over intervals of scaled lengths of the $\alpha$-diversity.

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Modules and Techniques for Motion Planning: An Industrial Perspective

Sensors ◽

10.3390/s21020420 ◽

2021 ◽

Vol 21 (2) ◽

pp. 420

Author(s):

Stefano Quer ◽

Luz Garcia

Keyword(s):

Data Fusion ◽

Autonomous Driving ◽

Random Trees ◽

Approximation Techniques ◽

Main Research ◽

Autonomous Cars ◽

Critical Issues ◽

Relative Errors ◽

Path Planner ◽

Many Core

Research on autonomous cars has become one of the main research paths in the automotive industry, with many critical issues that remain to be explored while considering the overall methodology and its practical applicability. In this paper, we present an industrial experience in which we build a complete autonomous driving system, from the sensor units to the car control equipment, and we describe its adoption and testing phase on the field. We report how we organize data fusion and map manipulation to represent the required reality. We focus on the communication and synchronization issues between the data-fusion device and the path-planner, between the CPU and the GPU units, and among different CUDA kernels implementing the core local planner module. In these frameworks, we propose simple representation strategies and approximation techniques which guarantee almost no penalty in terms of accuracy and large savings in terms of memory occupation and memory transfer times. We show how we adopt a recent implementation on parallel many-core devices, such as CUDA-based GPGPU, to reduce the computational burden of rapidly exploring random trees to explore the state space along with a given reference path. We report on our use of the controller and the vehicle simulator. We run experiments on several real scenarios, and we report the paths generated with the different settings, with their relative errors and computation times. We prove that our approach can generate reasonable paths on a multitude of standard maneuvers in real time.

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