Curvature-Continuous 3D Path-Planning Using QPMI Method

Abstract

It is impossible to achieve vertex movement and rapid velocity control in aerial robots and aerial vehicles because of momentum from the air. A continuous-curvature path ensures such robots and vehicles can fly with stable and continuous movements. General continuous path-planning methods use spline interpolation, for example Bspline and Bézier curves. However, these methods cannot be directly applied to continuous path planning in a 3D space. These methods use a subset of the waypoints to decide curvature and some waypoints are not included in the planned path. This paper proposes a method for constructing a curvature-continuous path in 3D space that includes every waypoint. The movements in each axis, x, y and z, are separated by the parameter u. Waypoint groups are formed, each with its own continuous path derived using quadratic polynomial interpolation. The membership function then combines each continuous path into one continuous path. The continuity of the path is verified and the curvature-continuous path is produced using the proposed method.

Spline Trajectory Planning for Road-Like Path with Piecewise Linear Boundaries Allowing Double Corner Points

“…Important future issues include extensions of the present method to the cases of higher order boundary curves and to the planning in 3-dimensional space for, e.g., aircrafts and aerial robots [4], [26] with airspace constraints. In either case, the central issues will be the concise description of boundary curves or planes for the path and smooth trajectory planning guaranteed to stay within the path.…”

Deep Reinforcement Learning Controller for 3D Path Following and Collision Avoidance by Autonomous Underwater Vehicles

“…Methods such as cubic and spline interpolation establish continuity and are straightforward to implement in 2D but cannot be applied directly in 3D interpolation. In fact, some spline methods have been shown to produce paths that do not visit all waypoints in 3D ( Chang and Huh, 2015 ). This is undesirable as the path should visit all waypoints in the correct sequence.…”

Path Planning and Replanning for Mobile Robot Navigation on 3D Terrain: An Approach Based on Geodesic

“…Reference [5] selected a B-spline curve to link two distinct locations and avoid collisions with the obstacles in 3D environment or 3D terrain. The established techniques and novel concepts of 2D path planning like optimization, metaheuristic, grid search algorithms, and potential fields could be extended with some success to plan a 3D path ( [4,[15][16][17][18][19] to cite a few). The potential field approach that navigates a robot to the target position by the sum of attractive force exerted at the goal and the repulsive forces from the obstacles is efficient and simple, which is applicable in two-dimensional and threedimensional environments.…”