scholarly journals Examining the Use of B-Splines in Parking Assist Systems

2014 ◽  
Vol 490-491 ◽  
pp. 1025-1029 ◽  
Author(s):  
Mohamed Elbanhawi ◽  
Milan Simic
Keyword(s):  
Intelligent Vehicles ◽  
Parallel Parking ◽  
B Splines ◽  
Spline Curves ◽  
Parking Spot ◽  
Feasible Range ◽  
Automatic Parking ◽  
Path Curvature ◽  
Continuous Curvature ◽  
The Relationship

The main objective of the presented study and simulations conducted was to investigate the prospect of using B-spline curves for the automatic parking, i.e. self-driving, or intelligent vehicles. We consider the problem of parallel parking for a non-holonomic vehicle with a known maximum path curvature. The relationship between the properties of the path and the geometry of corresponding parking spot is revealed. The unique properties of B-splines are exploited to synthesize a path that is smooth and of continuous curvature. The contributions of this project are in the generations of better, smooth continuous paths. This improves passenger comfort during the parallel parking maneuver and allow vehicles to park in tighter spots by increasing the feasible range of the parking manoeuver.

Autonomous Parking Strategy

2008 ◽  
Author(s):  
Nikolai Moshchuk ◽  
Shih-Ken Chen
Keyword(s):  
Path Planning ◽  
Parking Space ◽  
Novice Drivers ◽  
Parallel Parking ◽  
Parking Spot ◽  
Innovative System ◽  
Planning Strategies ◽  
Vehicle Configuration

Parallel parking can be a difficult task for novice drivers or drivers who seldom drive in congested city where parking space is limited. Parking Assist is an innovative system designed to aid the driver in performing sometimes difficult parallel parking maneuvers. Many companies are developing such systems with major automakers, such as Valeo, Aisin Seiki, Hella, Robert Bosch, and TRW. For example, Toyota IPA (Intelligent Parking Assist) system uses a rear view camera and automatically steer the vehicle into the parking spot with driver controlling braking. This paper describes the development of parking path planning strategies based on available parking space. A virtual turn center will first be defined and derived based on vehicle configuration. Required parking space for one or two cycle parking maneuver will then be determined. Path planning strategies for both one and two turn parking maneuvers will be developed next. Finally CarSim simulation will be performed to verify the design.

scholarly journals Automatic Parking Path Planning and Tracking Control Research for Intelligent Vehicles

2020 ◽  
Vol 10 (24) ◽  
pp. 9100
Author(s):  
Chenxu Li ◽  
Haobin Jiang ◽  
Shidian Ma ◽  
Shaokang Jiang ◽  
Yue Li
Keyword(s):  
Path Planning ◽  
Tracking Control ◽  
Control Method ◽  
Sliding Mode ◽  
Vehicle Control ◽  
Path Tracking ◽  
Intelligent Vehicles ◽  
Parking System ◽  
Automatic Parking ◽  
Real Vehicle

As a key technology for intelligent vehicles, automatic parking is becoming increasingly popular in the area of research. Automatic parking technology is available for safe and quick parking operations without a driver, and improving the driving comfort while greatly reducing the probability of parking accidents. An automatic parking path planning and tracking control method is proposed in this paper to resolve the following issues presented in the existing automatic parking systems, that is, low degree of automation in vehicle control; lack of conformity between segmented path planning and real vehicle motion models; and low success rates of parking due to poor path tracking. To this end, this paper innovatively proposes preview correction which can be applied to parking path planning, and detects the curvature outliers in the parking path through the preview algorithm. In addition, it is also available for correction in advance to optimize the reasonable parking path. Meanwhile, the dual sliding mode variable structure control algorithm is used to formulate path tracking control strategies to improve the path tracking control effect and the vehicle control automation. Based on the above algorithm, an automatic parking system was developed and the real vehicle test was completed, thus exploring a highly intelligent automatic parking technology roadmap. This paper provides two key aspects of system solutions for an automatic parking system, i.e., parking path planning and path tracking control.

scholarly journals Path Planning Optimization for Driverless Vehicle in Parallel Parking Integrating Radial Basis Function Neural Network

2021 ◽  
Vol 11 (17) ◽  
pp. 8178
Author(s):  
Leiyan Yu ◽  
Xianyu Wang ◽  
Zeyu Hou ◽  
Zaiyou Du ◽  
Yufeng Zeng ◽  
...  
Keyword(s):  
Neural Network ◽  
Radial Basis Function ◽  
Basis Function ◽  
Bézier Curve ◽  
Bezier Curve ◽  
Control Points ◽  
Parallel Parking ◽  
Radial Basis ◽  
Initial Path ◽  
Continuous Curvature

To optimize performances such as continuous curvature, safety, and satisfying curvature constraints of the initial planning path for driverless vehicles in parallel parking, a novel method is proposed to train control points of the Bézier curve using the radial basis function neural network method. Firstly, the composition and working process of an autonomous parking system are analyzed. An experiment concerning parking space detection is conducted using an Arduino intelligent minicar with ultrasonic sensor. Based on the analysis of the parallel parking process of experienced drivers and the idea of simulating a human driver, the initial path is planned via an arc-line-arc three segment composite curve and fitted by a quintic Bézier curve to make up for the discontinuity of curvature. Then, the radial basis function neural network is established, and slopes of points of the initial path are used as input to train and obtain horizontal ordinates of four control points in the middle of the Bézier curve. Finally, simulation experiments are carried out by MATLAB, whereby parallel parking of driverless vehicle is simulated, and the effects of the proposed method are verified. Results show the trained and optimized Bézier curve as a planning path meets the requirements of continuous curvature, safety, and curvature constraints, thus improving the abilities for parallel parking in small parking spaces.

The effect of saddle height and saddle position changes from pedal on muscles and joints behaviors in ergometer: A parametric study

2018 ◽  
Vol 232 (12) ◽  
pp. 1219-1229 ◽  
Author(s):  
Elham Hazrati ◽  
Mahmood Reza Azghani
Keyword(s):  
Nonlinear Behavior ◽  
Biomechanical Model ◽  
Human Movement ◽  
Behavior Changes ◽  
Hip Joints ◽  
Lower Limb Muscles ◽  
Feasible Range ◽  
Reaction Forces ◽  
Movement System ◽  
The Relationship

The physical activities such as pedaling can affect the lower limb muscles strength and rehabilitation. Improper pedaling can cause injury. In this study, we would investigate the effects of saddle place (saddle position and saddle height) on the behavior of muscles and joints. Moreover, we would try to reveal the relationship between the muscles activity (Act) and the joints reaction forces ( F) and saddle position and saddle height. To this end, the pedaling conditions are obtained from the biomechanical model of the human movement system presented in AnyBody software. The variations in 12 muscles Act and total, normal and shear F of ankle, knee and hip joints are studied for the various saddle places in the pedaling feasible range. The relationships of those muscles Act and joints F are predicted by the response surface method. The results indicate that the muscles and the joints behavior changes for various saddle position and saddle height. The maximum and the minimum of the total response are acquired in the ankle and hip joints, respectively. In contrast to the ankle and hip joints, the knee shear response is greater than the normal response. The predictive models of the muscles Act and the joints F (the regression coefficients ( R2) are 0.60–0.95 and 0.76–0.97, respectively) indicate their nonlinear behavior with saddle position and saddle height variations. Studying the muscles and joints behavior in different pedaling condition can be helpful for the suitable saddle placement in order for rehabilitation, muscles soreness reduction, and joints disorder treatment.

BEZIER AND B-SPLINE CURVES WITH KNOTS IN THE COMPLEX PLANE

Fractals ◽  
2011 ◽  
Vol 19 (01) ◽  
pp. 67-86 ◽  
Author(s):  
KONSTANTINOS I. TSIANOS ◽  
RON GOLDMAN
Keyword(s):  
Complex Domain ◽  
Polynomial Algorithms ◽  
Control Points ◽  
Knot Insertion ◽  
Real Numbers ◽  
Koch Curve ◽  
Natural Manner ◽  
B Spline ◽  
B Splines ◽  
Spline Curves

We extend some well known algorithms for planar Bezier and B-spline curves, including the de Casteljau subdivision algorithm for Bezier curves and several standard knot insertion procedures (Boehm's algorithm, the Oslo algorithm, and Schaefer's algorithm) for B-splines, from the real numbers to the complex domain. We then show how to apply these polynomial and piecewise polynomial algorithms in a complex variable to generate many well known fractal shapes such as the Sierpinski gasket, the Koch curve, and the C-curve. Thus these fractals also have Bezier and B-spline representations, albeit in the complex domain. These representations allow us to change the shape of a fractal in a natural manner by adjusting their complex Bezier and B-spline control points. We also construct natural parameterizations for these fractal shapes from their Bezier and B-spline representations.

Automated Optimisation of T-Root Rotor Grooves With B-Splines and Finite Element Analysis

2015 ◽  
Author(s):  
Jonathan Henson ◽  
Richard Dolan ◽  
Gareth Thomas ◽  
Christos Georgakis
Keyword(s):  
Finite Element ◽  
Steam Turbine ◽  
Peak Stress ◽  
Turbine Rotor ◽  
Element Analysis ◽  
B Splines ◽  
Steam Turbine Rotor ◽  
Spline Curves ◽  
Python Scripting ◽  
Gradient Based

An Alstom tool is described for the automated and simultaneous design optimisation of 2 and 4-hook T-root grooving of multiple steam turbine rotor stages in order to minimise the peak stress. The finite element axisymmetric thermal-stress calculation is performed with Abaqus in a few hours on modest hardware. The tool embeds Python scripting to facilitate the rotor groove model definition and meshing within Abaqus/CAE, with emphasis placed on minimising the effort for the initial setup. Rotor groove shapes are described with B-splines, maintained and modified within the in-house tool. Their shape is progressively refined as directed by a hybrid evolutionary-gradient based optimisation engine in order to achieve the minimum stress objective. In the region of highest stress, the groove boundary shape adjusts as the optimisation proceeds to conform to the local contours of stress. Application to a low pressure steam turbine rotor demonstrates comparable or lower stresses with this tool compared to those from manual expert optimisation. The method can be readily extended to other geometric entities on the rotor described with B-spline curves, e.g. cavities, seals.

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