Path Planning with Obstacle Avoidance Based on Normalized R-Functions

Abstract

Existing methods for path planning with obstacle avoidance need to check having the interference between a moving part and an obstacle at iteration and even to calculate their shortest distance in the case of given motion parameters. Besides, the tasks like collision-checking and minimum-distance calculating themselves are complicated and time-consuming. Rigorous mathematical analysis might be a practical way for dealing with the above-mentioned problems. An R-function is a real-valued function whose properties are fully determined by corresponding attributes of their parameters, which is usually applied to express a geometrical object. Thus, a signed distance function based on R-functions is created to represent whether two objects intervene and their level of intervention or separation. As the signed function is continuous and differentiable, the gradient information of the objective function guides a moving part to avoid its obstacles and to approach its target position rapidly. Therefore, a path planning approach with obstacle avoidance based on normalized R-functions is proposed in this paper. A discrete convex hull approach is adopted to solve the problem that R-function is inappropriate to represent a geometric object with some curves or surfaces, and pendent points and edges are generated in Boolean operations. Besides, a normalized approach ensures accuracy calculation of signed distance function. Experimental results have shown that the presented approach is a feasible way for path planning with obstacle avoidance.

Motion Control and Path Planning and Tracking Algorithm of Football Robot

“…Modified Simulated Annealing (MSA) not only retains the characteristics of global optimization of SA algorithm, but also improves its convergence speed. The MSA algorithm is based on the graph search technology, removing redundant points generated during the simulated annealing process and regenerating path points, thereby reducing unnecessary path twists and turns, and finally finding a collision-free optimal path for the robot quickly [21][22]. The MSA algorithm is to remove the path points generated in the annealing process and some path points that do not require annealing in advance, and then regenerate the path points.…”

Environment Potential Field Modeling for Ship Automatic Collision Avoidance in Restricted Waters

“…To solve the awkward EPF modeling problems of complicated geometry, R-function theory was introduced [34]- [36]. The researches in [37]- [39] studied EPF modeling approaches based on R-function theory; they realized automatic EPF modeling using the discrete-convex hull method and conducted several experiments in APF-based CA projects. Owing to their mathematical properties and natural ability to express complex geometric objects, R-functions have been widely used in computer graphics and geometric modeling [40]- [43].…”

A practical environment potential field modelling method for complex geometric objects

“…To solve the awkward EPF modelling problems, the R -function theory was introduced (Dobkin et al., 1993; Fougerolle et al., 2005; Tao and Tan, 2018) into EPF modelling, and the automatic EPF modelling of face obstacles was realised using the discrete-convex hull method. Accordingly, many experiments have been conducted on APF-based CA projects.…”

“…However, the potential field of the face objects cannot be efficiently and accurately constructed by simple ‘concave lines’ or implicit curves. Therefore, it is necessary to propose a practical method using rigorous mathematical analysis to address the potential field modelling for complicated face objects (Tao and Tan, 2018). The R -function theory can be applied to solve the implicit function construction and potential field modelling problems of a complicated geometry (Liu and Ahang, 2001; Wu et al., 2003; Ren et al., 2007).…”