## 1 Introduction  
The path planning problem is to find a feasible obstacle-free path that connects the starting point to the goal point. Many path planning algorithms have been presented over the last two decades. Sampling-based algorithms such as probabilistic roadmaps (PRM) and rapidly exploring random tree (RRT) have received great attention because they can search for feasible paths relatively quickly, even in a high-dimensional space. An extensive comparative study and analysis of various sampling-based algorithms can be found in the literature [1; 2; 3; 4; 5]. Even though a sampling-based path planning algorithm is effective and computationally efficient, it typically generates an unnatural path because of its randomness. It thus requires a post-processing procedure called path pruning and smoothing. Path pruning is to remove unnecessary waypoints which are generated by a sampling-based path planning algorithm. While the number of waypoints is reduced after path pruning, the path is still piecewise linear and usually not followable for a moving vehicle with dynamic constraints. Therefore, it is necessary to smooth the path to making it suitable for a vehicle [6; 7; 8; 9; 10]. A smooth path is preferable since the curvature discontinuity results in a discontinuity in the vehicle's desired acceleration command, and these cause tracking errors. Although some mobile robots and flying vehicles such as multicopters can stop and hover at a certain point, this increases the driving or flight time and generally degrades the navigation performance. For a fixed-wing aircraft, it is not possible to follow a piecewise linear path without tracking errors. A popular method to generate a smooth path is the Dubins path [11; 12; 13; 14; 15]. The Dubins path concatenates straight lines and circular arcs considering the vehicle's minimum turning radius. It generates the shortest path between two waypoints with the prescribed pose (or direction vector) to the path in a plane. Another method is the cubic spline method that produces a smooth path of C1 continuity, as with the Dubins path. However, C1 continuity is not smooth enough, and even further smoothness of geometric continuity of 2 nd order (G2 continuity) is required with maximum curvature constraint to be executed smoothly by moving vehicles [6]. Here, C1 continuity means continuity of the tangent vector, and G2 continuity means continuity of the curvature. Although the clothoid path provides a G2 continuous path, it is not a closed-form expression. It requires high computational cost since the evaluation of Fresnel integrals is needed to generate a path [17,18]. While three-dimensional (3D) extensions of the Dubins path have been proposed in the literature [13, 14, 15, 16], they are very complex and difficult to use in practical applications because they are based on a 3D constant-speed point mass model or the decoupled horizontal and vertical plane model. Some G2 continuous paths are also proposed in the literature [7,17,19] based on the Bezier curve, but they generate paths that pass through only the starting and final waypoints. Motivated by these observations, this paper proposes a 3D Dubins-path-guided continuous curvature path design algorithm. Our contribution is threefold. The first is to extend the 2D Dubins path method to 3D, which is conceptually simple and computationally efficient. The second is to use multiple cubic Bezier curves to smooth the Dubins path at the transition points where curvature and path direction discontinuities occur. The proposed smoothing algorithm can generate continuous curvature paths in 3D space that pass through all waypoints without limiting the size of the turning angle. On the other hand, existing algorithms have a limit on the size of the turning angle and do not pass through all waypoints. The third is to provide a criterion to select a required number of Bezier curves to strictly meet the maximum curvature constraint.