SP‐search‐based path planning algorithm for mobile robots using quintic trigonometric Bézier curves

Abstract

Path planning is an essential step for mobile robots. This paper presents a novel shape parameter search‐ (SP‐Search) based path planning algorithm for mobile robots using quintic trigonometric Bézier curve and its two shape parameters. The proposed search algorithm recursively divides the shape parameter space into a grid and uses a multi‐objective function to determine the shape parameter values. The multi‐objective function is expressed by the sum of four terms multiplied by coefficients: the integral of the squared jerk, the integral of the squared curvature, the mean of minimum distances between the predefined skeleton and quintic trigonometric Bézier path, and the arclength. Optimal shape parameters can be determined according to the required cases by the user using four coefficient values. Experimental results illustrate the feasibility of the proposed SP‐Search algorithm. Also, we have developed another intuitive algorithm, the Brute Force Grid Search algorithm, which is the brute force approach for shape parameter search to compare the performance of the proposed SP‐search algorithm for path planning problems as a baseline. The experimental results show that the SP‐Search algorithm finds better shape parameter values with a considerably small number of searched points.

Enhancing curve and surface applications with trigonometric polynomial basis functions

“…In robotics and autonomous systems, trigonometric Bézier curves can be used for path planning [ 18 ], especially when you need robots to follow circular or curved trajectories [ 19 ].…”

Efficient Path Planning Algorithm for Mobile Robots Performing Floor Cleaning Like Operations

“…A multi-agent coverage path planning algorithm inspired by social behaviors in the biological world is also proposed, effectively addressing uncertain and random decision-making, showing advantages in make span and coverage repetition rate [62]. Another work introduces a novel Clustering Obstacles (CO)-based path planning algorithm for mobile robots using quintic trigonometric Bézier curves, achieving better collision-free paths compared to existing algorithms [63]. Moreover, a hybrid navigation system for mobile robots is presented, combining autonomous positioning and path planning, showcasing effectiveness in unstructured scenarios [64].…”

A quartic trigonometric interpolatory spline with local free parameters

“…Such as the trigonometric Be´zier curves, [1][2][3][4] the trigonometric B-spline curves, [5][6][7] the trigonometric Hermite curves, 8,9 the trigonometric rational curves, 10,11 etc. The curves constructed in trigonometric function space have been applied in signal analysis, 12 kitchen product design, 13 robot path planning, 14 and other engineering problems.…”