An introduction to the use of splines in computer graphics
An introduction to the use of splines in computer graphics
Adaptive subdivision and the length and energy of Be´zier curves
Computational Geometry: Theory and Applications
Curvature extrema of planar parametric polynomial cubic curves
Journal of Computational and Applied Mathematics
IEEE Computer Graphics and Applications
Geometric Continuity of Parametric Curves
Geometric Continuity of Parametric Curves
Planar G2 transition curves composed of cubic Bézier spiral segments
Journal of Computational and Applied Mathematics
From Reeds and Shepp's to continuous-curvature paths
IEEE Transactions on Robotics
Smooth path and speed planning for an automated public transport vehicle
Robotics and Autonomous Systems
ICIRA'11 Proceedings of the 4th international conference on Intelligent Robotics and Applications - Volume Part II
Collision-free and smooth trajectory computation in cluttered environments
International Journal of Robotics Research
Spline-Based RRT Path Planner for Non-Holonomic Robots
Journal of Intelligent and Robotic Systems
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An efficient and analytical continuous-curvature path-smoothing algorithm, which fits an ordered sequence of waypoints generated by an obstacle-avoidance path planner, is proposed. The algorithm is based upon parametric cubic Bézier curves; thus, it is inherently closed-form in its expression, and the algorithm only requires the maximum curvature to be defined. The algorithm is, thus, computational efficient and easy to implement. Results show the effectiveness of the analytical algorithm in generating a continuous-curvature path, which satisfies an upper bound-curvature constraint, and that the path generated requires less control effort to track and minimizes control-input variability.