Path planning with Pythagorean-hodograph curves for unmanned or autonomous vehicles

Pythagorean-hodograph (PH) curves offer distinct advantages in planning curvilinear paths for unmanned or autonomous air, ground, or underwater vehicles. Although several authors have discussed their use in these contexts, prior studies contain misconceptions about the properties of PH curves or invoke heuristic approximate constructions when exact methods are available. To address these issues, the present study provides a basic introduction to the key properties of PH curves, and describes some exact constructions of particular interest in path planning. These include (a) maintenance of minimum safe separations within vehicle swarms; (b) construction of paths of different shape but identical arc length, ensuring simultaneous arrival of vehicles travelling at a constant speed; (c) determination of the curvature extrema of PH paths, and their modification to satisfy a given curvature bound; and (d) construction of curvature-continuous paths of bounded curvature through fields of polygonal obstacles.

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Local and Global Path Generation for Autonomous Vehicles Using Splines

Ingeniería ◽

10.14483/udistrital.jour.reving.2016.2.a05 ◽

2016 ◽

Vol 21 (2) ◽

pp. 188-200 ◽

Cited By ~ 1

Author(s):

Randerson Lemos ◽

Olmer Garcia ◽

Janito Vaqueiro Ferreira

Keyword(s):

Path Planning ◽

Autonomous Vehicles ◽

Planning Problem ◽

Arc Length ◽

Raw Data ◽

Planning Technique ◽

Global Route ◽

Autonomous Mobility ◽

Highly Correlated ◽

Global And Local

Context: Before autonomous vehicles being a reality in daily situations, outstanding issues regarding the techniques of autonomous mobility must be solved. Hence, relevant aspects of a path planning for terrestrial vehicles are shown.Method: The approached path planning technique uses splines to generate the global route. For this goal, waypoints obtained from online map services are used. With the global route parametrized in the arc-length, candidate local paths are computed and the optimal one is selected by cost functions.Results: Different routes are used to show that the number and distribution of waypoints are highly correlated to a satisfactory arc-length parameterization of the global route, which is essential to the proper behavior of the path planning technique.Conclusions: The cubic splines approach to the path planning problem successfully generates the global and local paths. Nevertheless, the use of raw data from the online map services showed to be unfeasible due the consistency of the data. Hence, a preprocessing stage of the raw data is proposed to guarantee the well behavior and robustness of the technique.

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COMPARISON BETWEEN A* BASED SPLINES AND STATE LATTICE PATH PLANNING FOR AUTONOMOUS VEHICLES

10.37099/mtu.dc.etdr/807 ◽

2019 ◽

Author(s):

Om Kukunuru

Keyword(s):

Path Planning ◽

Autonomous Vehicles ◽

Lattice Path

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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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Auction-Based Consensus of Autonomous Vehicles for Multi-Target Dynamic Task Allocation and Path Planning in an Unknown Obstacle Environment

Applied Sciences ◽

10.3390/app11115057 ◽

2021 ◽

Vol 11 (11) ◽

pp. 5057

Author(s):

Wan-Yu Yu ◽

Xiao-Qiang Huang ◽

Hung-Yi Luo ◽

Von-Wun Soo ◽

Yung-Lung Lee

Keyword(s):

Path Planning ◽

Task Allocation ◽

Autonomous Vehicles ◽

Autonomous Vehicle ◽

Dynamic Task ◽

The Core ◽

Dynamic Task Allocation ◽

Vehicle Technology ◽

Future Work ◽

Complicated Task

The autonomous vehicle technology has recently been developed rapidly in a wide variety of applications. However, coordinating a team of autonomous vehicles to complete missions in an unknown and changing environment has been a challenging and complicated task. We modify the consensus-based auction algorithm (CBAA) so that it can dynamically reallocate tasks among autonomous vehicles that can flexibly find a path to reach multiple dynamic targets while avoiding unexpected obstacles and staying close as a group as possible simultaneously. We propose the core algorithms and simulate with many scenarios empirically to illustrate how the proposed framework works. Specifically, we show that how autonomous vehicles could reallocate the tasks among each other in finding dynamically changing paths while certain targets may appear and disappear during the movement mission. We also discuss some challenging problems as a future work.

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On the Distributed Path Planning of Multiple Autonomous Vehicles Under Uncertainty Based on Model-Predictive Control and Convex Optimization

IEEE Systems Journal ◽

10.1109/jsyst.2020.3007795 ◽

2020 ◽

pp. 1-10

Author(s):

Seyed Mohsen Ahmadi Mousavi ◽

Behzad Moshiri ◽

Zainabolhoda Heshmati

Keyword(s):

Convex Optimization ◽

Path Planning ◽

Model Predictive Control ◽

Predictive Control ◽

Autonomous Vehicles

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Path Planning of Multiple UAV’s in an Environment of Restricted Regions

Dynamic Systems and Control, Parts A and B ◽

10.1115/imece2005-79682 ◽

2005 ◽

Author(s):

Madhavan Shanmugavel ◽

Antonios Tsourdos ◽

Rafal Zbikowski ◽

Brian White

Keyword(s):

Path Planning ◽

Path Length ◽

Mathematical Property ◽

Multiple Uavs ◽

Safety Margins ◽

Pythagorean Hodograph ◽

Offset Curves ◽

Safety Constraints ◽

Continuous Curvature ◽

Ph Curve

This paper describes a novel idea of path planning for multiple UAVs (Unmanned Aerial Vehicles). The path planning ensures safe and simultaneous arrival of the UAVs to the target while meeting curvature and safety constraints. Pythagorean Hodograph (PH) curve is used for path planning. The PH curve provides continuous curvature of the paths. The offset curves of the PH paths define safety margins around and along each flight path. The simultaneous arrival is satisfied by generation of paths of equal lengths. This paper highlights the mathematical property — changing path-shape and path-length by manipulating the curvature and utilises this to achieve the following constraints: (i) Generation of paths of equal length, (ii) Achieving maximum bound on curvature, and, (iii) Meeting the safety constraints by offset paths.

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An Algorithm of Complete Coverage Path Planning for Autonomous Underwater Vehicles

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.467-469.1377 ◽

2011 ◽

Vol 467-469 ◽

pp. 1377-1385 ◽

Cited By ~ 4

Author(s):

Ming Zhong Yan ◽

Da Qi Zhu

Keyword(s):

Path Planning ◽

Autonomous Underwater Vehicles ◽

Underwater Vehicles ◽

Time Varying ◽

Simulation Studies ◽

Complete Coverage ◽

Biologically Inspired ◽

Coverage Path Planning ◽

Underwater Environment ◽

Global Cost

Complete coverage path planning (CCPP) is an essential issue for Autonomous Underwater Vehicles’ (AUV) tasks, such as submarine search operations and complete coverage ocean explorations. A CCPP approach based on biologically inspired neural network is proposed for AUVs in the context of completely unknown environment. The AUV path is autonomously planned without any prior knowledge of the time-varying workspace, without explicitly optimizing any global cost functions, and without any learning procedures. The simulation studies show that the proposed approaches are capable of planning more reasonable collision-free complete coverage paths in unknown underwater environment.

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Research on the Algorithm of Measurement Path Planning for Inner Wall of Air-Intake Pipe Based on Spraying Robot System

International Journal of Pattern Recognition and Artificial Intelligence ◽

10.1142/s0218001417590182 ◽

2017 ◽

Vol 31 (09) ◽

pp. 1759018 ◽

Cited By ~ 4

Author(s):

Zhiqiang Chao ◽

Fei Wang ◽

Chuanqing Zhang ◽

Huaying Li ◽

Feng Wang

Keyword(s):

Path Planning ◽

Plane Curve ◽

Displacement Sensor ◽

Sensor Technology ◽

Arc Length ◽

Robot System ◽

Intake Pipe ◽

Different Types ◽

Air Intake ◽

Measurement Path

To solve the problems with spraying over the inner wall of air-intake pipe, this paper introduces an algorithm of measurement path planning based on the spraying robot system and the laser displacement sensor technology. Scanning measurement path planning is the premise and basis of model construction and spray. Traditional methods, such as arc length extrapolation and polynomial are applicable only for the measurement of a plane curve with finite maximum curvature. Drawing references from existing method, this paper focuses on the pre-scanning measurement method for different types of cross-section curves. Algorithm simulation and model reconstruction show that this study solves the problem of collision avoidance for scanning measurement of the inner wall of air-intake pipe.

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