# Global Time-Varying Path Planning Method Based on Tunable Bezier Curves
###### Abstract  
In this paper, a novel global time-varying path planning (GTVP) method is proposed. In the method, real-time paths can be generated based on tunable Bezier curves, which can realize obstacle avoidance of manipulators. First, finite feature points are extracted to represent the obstacle information according to the shape information and position information of the obstacle. Then, the feature points of the obstacle are converted into the feature points of the curve, according to the scale coefficient and the center point of amplification. Furthermore, a Bezier curve representing the motion path at this moment is generated to realize real-time adjustment of the path. In addition, the 5-degree Bezier curve planning method consider the start direction and the end direction is used in the path planning to avoid the situation of abrupt change with oscillation of the trajectory. Finally, the GTVP method is applied to multi-obstacle environment to realize global time-varying dynamic path planning. Through theoretical derivation and simulation, it can be proved that the path planned by the GTVP method can meet the performance requirements of global regulation, real-time change and multi-obstacle avoidance simultaneously. Bezier curve; path planning; obstacle avoidance; global time-varying; dynamic obstacle; real-time +
Footnote †: journal: Applied Sciences  
in path planning in a given environment by using network mapping. In order to reduce the computational cost of motion planning, [PERSON] [17] adopts the parameter matching reduction method to make multiple low-order Bezier segments approximate the high-order Bezier curve adaptively. This method can be implemented in the trajectory optimization of non-holonomic constrained mobile robots. [PERSON] [18] proposed an improved particle swarm optimization algorithm to plan the smooth path of mobile robots in order to meet the requirements of continuous curvature derivative continuity, combined with the continuous high-order Bezier curve, so as to solve the local optimal solution and premature convergence problems. [PERSON] [19] proposed a new parameterization method of motion primitive based on Bezier curves, which is suitable for path planning applications of wheeled mobile robots. In this paper, the analytical solution of the motion primitive of a 3-order Bezier curve is given under the given boundary conditions that guarantee the continuous curvature of the combined spline path. [PERSON] [20] proposed the use of quintic triangular Bezier curves with two shape parameters and C3 continuity for path planning. When there is an obstacle, the predetermined path can be adjusted only by the shape parameter in this method. [PERSON] [21] proposed a new smooth path planning method for mobile robots based on quadratic Bezier transition curve and improved particle swarm optimization algorithm. Simulation results demonstrate the effectiveness and superiority of this method combined with quadratic Bezier transition curve and improved PSO-AWDV algorithm. Researchers have proposed a number of path planning methods for multi-obstacle environments. [PERSON] [22] proposed a multi-obstacle path planning and optimization method for multi-obstacle avoidance. This method uses the convex hull to optimize obstacles, so as to obtain the base point set and generate the corresponding extension point set. The multi-objective D* Lite algorithm is utilized to design the distance and smoothness of the path planner to obtain a reasonably optimized path in a complex environment. Finally, the third Bezier curve is used to smooth the path. To solve the dynamic obstacle avoidance problem, many methods have been proposed. However, the traditional method [23] can realize the local dynamic obstacle avoidance of a mobile car, but it cannot be applied to the global dynamic obstacle avoidance of a manipulator.