# G2 Continuity Smooth Path Planning using Cubic Polynomial Interpolation with Membership Function

• Chang, Seong-Ryong ;
• Huh, Uk-Youl
• Accepted : 2014.10.27
• Published : 2015.03.01
• 46 6

#### Abstract

Path planning algorithms are used to allow mobile robots to avoid obstacles and find ways from a start point to a target point. The general path planning algorithm focused on constructing of collision free path. However, a high continuous path can make smooth and efficiently movements. To improve the continuity of the path, the searched waypoints are connected by the proposed polynomial interpolation. The existing polynomial interpolation methods connect two points. In this paper, point groups are created with three points. The point groups have each polynomial. Polynomials are made by matching the differential values and simple matrix calculation. Membership functions are used to distribute the weight of each polynomial at overlapped sections. As a result, the path has $G^2$ continuity. In addition, the proposed method can analyze path numerically to obtain curvature and heading angle. Moreover, it does not require complex calculation and databases to save the created path.

#### Keywords

Continuous-curvature path;Geometric continuity;Interpolation;Path planning;Cubic polynomial;Mobile robot;Robot motion;Smooth path;Spline interpolation;Vehicles navigation

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#### Cited by

1. Discrete-Time Circular Walking Pattern for Biped Robots vol.11, pp.5, 2016, https://doi.org/10.5370/JEET.2016.11.5.1395
2. Optimization of collision-free paths in a differential-drive robot by a smoothing piecewise-linear approach vol.37, pp.4, 2018, https://doi.org/10.1007/s40314-018-0602-x

#### Acknowledgement

Supported by : National Research Foundation of Korea (NRF)