Abstract: Bezier curves have useful properties for path
generation problem, for instance, it can generate the reference
trajectory for vehicles to satisfy the path constraints. Both algorithms
join cubic Bezier curve segment smoothly to generate the path. Some
of the useful properties of Bezier are curvature. In mathematics,
curvature is the amount by which a geometric object deviates from
being flat, or straight in the case of a line. Another extrinsic example
of curvature is a circle, where the curvature is equal to the reciprocal
of its radius at any point on the circle. The smaller the radius, the
higher the curvature thus the vehicle needs to bend sharply. In this
study, we use Bezier curve to fit highway-like curve. We use
different approach to find the best approximation for the curve so that
it will resembles highway-like curve. We compute curvature value by
analytical differentiation of the Bezier Curve. We will then compute
the maximum speed for driving using the curvature information
obtained. Our research works on some assumptions; first, the Bezier
curve estimates the real shape of the curve which can be verified
visually. Even though, fitting process of Bezier curve does not
interpolate exactly on the curve of interest, we believe that the
estimation of speed are acceptable. We verified our result with the
manual calculation of the curvature from the map.
Abstract: In this work a software simulation model has been
proposed for two driven wheels mobile robot path planning; that can
navigate in dynamic environment with static distributed obstacles.
The work involves utilizing Bezier curve method in a proposed N
order matrix form; for engineering the mobile robot path. The Bezier
curve drawbacks in this field have been diagnosed. Two directions:
Up and Right function has been proposed; Probability Recursive
Function (PRF) to overcome those drawbacks.
PRF functionality has been developed through a proposed;
obstacle detection function, optimization function which has the
capability of prediction the optimum path without comparison
between all feasible paths, and N order Bezier curve function that
ensures the drawing of the obtained path.
The simulation results that have been taken showed; the mobile
robot travels successfully from starting point and reaching its goal
point. All obstacles that are located in its way have been avoided.
This navigation is being done successfully using the proposed PRF
techniques.
Abstract: The PH curve can be constructed by given parameters, but the shape of the curve is not so easy to image from the value of the parameters. On the contract, Bézier curve can be constructed by the control polygon, and from the control polygon, we can image the figure of the curve. In this paper, we want to use the hodograph of Bézier curve to construct PH curve by selecting part of the control vectors, and produce other control vectors, so the property of PH curve exists.