# Global Time-Varying Path Planning Method Based on Tunable Bezier Curves
## 2 Characteristics of GTVP  
The high-order Bezier curve has the disadvantages of large computation, oscillations and complex trajectory, so it cannot be applied to dynamic environment. Although the low-order Bezier curve can guarantee the continuity of the path, it cannot provide continuous curvature and arbitrary setting of the second derivative of the characteristic points of the Bezier curve. The more feature points the Bezier curve has, the more flexible the smooth path is, but the more computational the complexity is and vice versa. In conclusion, in the process of path planning, it is necessary to balance the amount of calculation with the flexibility of the trajectory.  
The planned path should meet the following conditions:  
1. The manipulator can realize dynamic obstacle avoidance along the path;
2. Realize G3 continuity and continuous curvature derivative;
3. Minimize the maximum curvature of smooth paths;
4. The length of the smooth path is as short as possible under the premise of meeting the basic conditions.  
It is difficult to satisfy the requirements of real-time obstacle avoidance by using a traditional intelligent algorithm to optimize the solution. In order to address the problems of real-time path planning and Bezier curves, the GTVP method is improved on the premise of satisfying the elementary criteria. The novelty and contributions of this paper are summarized and listed as following.  
1. Considering obstacles of different positions and shapes, the GTVP method extracts a finite number of feature points to characterize the key information of dynamic obstacles, which reduces the complexity of the obstacle model. In this way, the dynamic obstacle information can be analyzed in real time during path planning.
2. Before real-time path planning, the GTVP method has formulated the conversion relationship between feature points and paths through equation deduction (Step 5, Step 6, Step 7). In real-time path planning, the corresponding spline curve can be generated by bringing in the real-time data of feature points and the spline curve is the motion path of the snake manipulator, which greatly reduces the calculation time.
3. There are many inflection points in the path planned by traditional methods and the variation curve of the joint declination angle is unsmooth when the snake manipulator moves along the path. By virtue of the characteristics of Bezier curves, the smooth path can be directly planned by the GTVP method and then the smooth path can be adjusted in real time according to the nodes on the path and the feature points of dynamic obstacles.
4. The traditional method can be applied to the dynamic obstacle avoidance of a trolley or car, but it cannot be applied to the snake manipulator to avoid obstacles on the global path. Built on the global characteristics of Bezier curves, the GTVP method can adjust the global path in real time by adjusting the obstacle feature points and curve feature points.
5. The GTVP method extracts real-time information of dynamic obstacles and utilizes feature points to generate the corresponding smooth trajectory curve, which can realize real-time obstacle avoidance of the manipulator. This method avoids numerous unnecessary calculations, improves search efficiency and efficiently solves path planning problems in multi-target conditions or multi-obstacle environments.
6. The GTVP method can not only adjust the direction of the start point of the path, but also adjust the direction of the end point of the path.
7. There are several adjustable parameters in the GTVP method: center point of obstacle, number and position of obstacle feature points, location of scaling center point, scaling ratio coefficient, etc. Individual parameters can be selected or adjusted according to the specific application environment, so this method has good environmental adaptability.