scholarly journals The critical radius in sampling-based motion planning

2019 ◽  
Vol 39 (2-3) ◽  
pp. 266-285 ◽  
Author(s):  
Kiril Solovey ◽  
Michal Kleinbort
Keyword(s):  
Motion Planning ◽  
Critical Radius ◽  
Practical Implication ◽  
Subsequent Work ◽  
Probabilistic Roadmap ◽  
Probability Of Success ◽  
Explicit Lower Bound ◽  
Uniform Random Sampling ◽  
Similar Theory ◽  
Near Optimality

We develop a new analysis of sampling-based motion planning in Euclidean space with uniform random sampling, which significantly improves upon the celebrated result of Karaman and Frazzoli and subsequent work. In particular, we prove the existence of a critical connection radius proportional to [Formula: see text] for n samples and d dimensions: below this value the planner is guaranteed to fail (similarly shown by Karaman and Frazzoli). More importantly, for larger radius values the planner is asymptotically (near-)optimal. Furthermore, our analysis yields an explicit lower bound of [Formula: see text] on the probability of success. A practical implication of our work is that asymptotic (near-)optimality is achieved when each sample is connected to only [Formula: see text] neighbors. This is in stark contrast to previous work that requires [Formula: see text] connections, which are induced by a radius of order [Formula: see text]. Our analysis applies to the probabilistic roadmap method (PRM), as well as a variety of “PRM-based” planners, including RRG, FMT*, and BTT. Continuum percolation plays an important role in our proofs. Lastly, we develop similar theory for all the aforementioned planners when constructed with deterministic samples, which are then sparsified in a randomized fashion. We believe that this new model, and its analysis, is interesting in its own right.

Synthesis of Vortex Rossby Waves. Part II: Vortex Motion and Waves in the Outer Waveguide

2015 ◽  
Vol 72 (10) ◽  
pp. 3958-3974 ◽  
Author(s):  
Israel Gonzalez ◽  
Amaryllis Cotto ◽  
Hugh E. Willoughby
Keyword(s):  
Nonlinear Model ◽  
Rossby Waves ◽  
Critical Radius ◽  
Vortex Motion ◽  
Low Frequency ◽  
Wave Interaction ◽  
Linear Acceleration ◽  
Propagation Speed ◽  
Large Radius ◽  
Subsequent Work

Abstract Beta, the meridional gradient of planetary vorticity, causes tropical cyclones to propagate poleward and westward at approximately 2 m s−1. In a previous shallow-water linear model, the simulated vortex accelerated without limit, ostensibly because beta forced a free linear mode. In the analogous nonlinear model, wave–wave interaction limited the propagation speed. Subsequent work based upon the asymmetric balance (AB) approximation was unable to replicate the linear result. The present barotropic nondivergent model replicates the linear beta gyres as a streamfunction dipole with a uniform southeasterly ventilation flow across the vortex. The simulated storm accelerates to unphysical, but finite, speeds that are limited by vorticity filamentation. In the analogous nonlinear model, nonlinearly forced wavenumber-1 gyres have opposite phase to the linear gyres so that their ventilation flow counteracts advection by the linear gyres to limit the overall vortex speed to approximately 3 m s−1. A bounded mean vortex with zero circulation at large radius must contain an outer annulus of anticyclonic vorticity to satisfy the circulation theorem. The resulting positive mean vorticity gradient constitutes an outer waveguide that supports downstream-propagating, very-low-frequency vortex Rossby waves. It is confined between an inner critical radius where the waves are absorbed and an outer turning point where they are reflected. Vorticity filamentation at the critical radius limits the beta-drift acceleration. The original unlimited linear acceleration stemmed from too-weak dissipation caused by second-order diffusion applied to velocity components instead of vorticity. Fourth-order diffusion and no outer waveguide in the Rankine-like vortex of the AB simulations plausibly explain the different results.

scholarly journals New perspective on sampling-based motion planning via random geometric graphs

2018 ◽  
Vol 37 (10) ◽  
pp. 1117-1133 ◽  
Author(s):  
Kiril Solovey ◽  
Oren Salzman ◽  
Dan Halperin
Keyword(s):  
Motion Planning ◽  
Geometric Graphs ◽  
Optimal Motion ◽  
Random Geometric Graphs ◽  
Probabilistic Roadmaps ◽  
Optimal Motion Planning ◽  
Unit Hypercube ◽  
Standard Models ◽  
New Perspective ◽  
Near Optimality

Roadmaps constructed by many sampling-based motion planners coincide, in the absence of obstacles, with standard models of random geometric graphs (RGGs). Those models have been studied for several decades and by now a rich body of literature exists analyzing various properties and types of RGGs. In their seminal work on optimal motion planning, Karaman and Frazzoli conjectured that a sampling-based planner has a certain property if the underlying RGG has this property as well. In this paper, we settle this conjecture and leverage it for the development of a general framework for the analysis of sampling-based planners. Our framework, which we call localization–tessellation, allows for easy transfer of arguments on RGGs from the free unit hypercube to spaces punctured by obstacles, which are geometrically and topologically much more complex. We demonstrate its power by providing alternative and (arguably) simple proofs for probabilistic completeness and asymptotic (near-)optimality of probabilistic roadmaps (PRMs) in Euclidean spaces. Furthermore, we introduce three variants of PRMs, analyze them using our framework, and discuss the implications of the analysis.

scholarly journals A Grid-Based Motion Planning Approach for Coherent Groups

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Yue-wen Fu ◽  
Meng Li ◽  
Jia-hong Liang ◽  
Xiao-qian Hu
Keyword(s):  
Motion Planning ◽  
Medial Axis ◽  
Evaluation Function ◽  
Degree Relative ◽  
Deformation Degree ◽  
Probabilistic Roadmap ◽  
Planning Approach ◽  
Constant Area ◽  
Grid Based

This paper presents a novel motion planning approach for coherent groups with constant area, and it integrates C-L method into the probabilistic roadmap algorithm with sampling on the medial axis (MAPRM). In the preprocessing phase, the group is discretized into a grid-set which represents the configuration of the group. Then, a number of samples are generated on workspace by medial axis technique. These samples are extended into group’s configuration nodes of the roadmap using an extending strategy. Also, the group's deformation degree relative to the desired shape is introduced to improve the evaluation function. It gives users more flexibility to determine the respective weights of the group’s deformation degree and its distance to the goal in the query phase. After that, a novel local planner is constructed to connect any two neighbor configurations by using C-L method and the improved evaluation function. Experiments show that our approach is able to find paths for the coherent group efficiently and keep its area invariant when moving toward the goal.

What is engineering education for? Listening to the voices of some Spanish building engineers

2016 ◽  
Vol 14 (4) ◽  
pp. 897-919 ◽  
Author(s):  
Joaquín Fuentes-Del-Burgo ◽  
Elena Navarro-Astor
Keyword(s):  
Engineering Education ◽  
Curriculum Design ◽  
Practical Implication ◽  
Research Approach ◽  
Construction Site ◽  
Subsequent Work ◽  
Content Type ◽  
La Mancha ◽  
Building Engineering ◽  
Site Managers

Purpose Aristotle’s concepts of “episteme”, “techne” and “phronesis” are used to understand the relevance of the education that Spanish building engineers receive to their subsequent work as construction site managers. This paper aims to clarify the role of educational factors as they influence any disparities that building engineers who are working as site managers may feel. More specifically, the objectives are to explore the satisfactions and dissatisfactions they experience in doing their job; to describe the ways they find to cope with educational deficiencies; and to gather their suggestions for improving building engineering education. Design/methodology/approach Using an interpretive approach within the qualitative paradigm, this study draws on data obtained from semi-structured interviews with a sample of 34 building engineers working as site managers in Castilla-La Mancha (Spain). Findings According to the site managers themselves, Spanish universities mainly teach Aristotle’s episteme (abstract knowledge and general principles) and some techne (applied, technical knowledge and skills), which fall short of the expectations placed upon them by their employers. Research limitations/implications Because of the chosen research approach, the sample size is relatively small and results may lack generalisability. Practical implications The results have practical implication for building engineering curriculum design related to the enhancement of building engineers employability and job satisfaction. Originality/value The existing literature offers insight into job-educational mismatches of different occupations in different countries, drawing on survey questionnaires. There is, however, a gap in respect of Spain and the job of the construction site manager. This paper goes some way towards filling that gap, reporting on the experiences of some higher education “customers”: Spanish building engineers working as site managers.

Efficient and Safe Motion Planning for Quadrotors Based on Unconstrained Quadratic Programming

Robotica ◽  
2020 ◽  
pp. 1-17
Author(s):  
Yanhui Li ◽  
Chao Liu
Keyword(s):  
Path Planning ◽  
Quadratic Programming ◽  
Motion Planning ◽  
Computational Efficiency ◽  
Short Path ◽  
Trajectory Generation ◽  
Probabilistic Roadmap ◽  
Planning Framework ◽  
Unconstrained Quadratic Programming ◽  
Trajectory Problem

SUMMARY An autonomous motion planning framework is proposed, consisting of path planning and trajectory generation. Primarily, a spacious preferred probabilistic roadmap algorithm is utilized to search a safe and short path, considering kinematics and threats from obstacles. Subsequently, a minimum-snap and position-clearance polynomial trajectory problem is transformed into an unconstrained quadratic programming and solved in a two-step optimization. Finally, comparisons with other methods based on statistical simulations are implemented. The results show that the proposed method achieves computational efficiency and a safe trajectory.

Probabilistic Roadmaps with Higher Expressive Power

2016 ◽  
Vol 25 (04) ◽  
pp. 1650027
Author(s):  
Amol D. Mali
Keyword(s):  
Motion Planning ◽  
Expressive Power ◽  
State Transitions ◽  
Robot Motion ◽  
Multiple Robots ◽  
Probabilistic Roadmap ◽  
Temporal Intervals ◽  
Robot Configuration ◽  
Multiple Samples ◽  
Planning Problems

Sampling-based motion planning had an enormous impact on robot motion planning because of its efficiency and scalability. Many sampling-based motion planners construct a probabilistic roadmap (PRM) that captures the connectivity of the robot's free configuration space. A valid node of a PRM contains a collision-free robot configuration (also known as a sample) and a valid edge of a PRM connects two valid nodes with a collision-free path. Nodes connected by an edge are usually also required to satisfy additional requirements based on the distance between them. PRM planners use PRMs. Increasing the expressive power will allow PRMs to be used for a wider set of motion planning problems. In this paper we report on increasing the expressive power of PRMs by including the following five features in PRMs-nodes with multiple samples that need not be organized as a graph, temporal intervals of validity of nodes and edges, nodes with samples of multiple robots, special edges for the state transitions performed by humans sharing a workspace with robots, and conditional validity of samples and edges. We report on motion planning problems solvable using these new features.

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