满足曲率约束的B样条曲线连续路径平滑方法

Continuous path smoothing method of B-spline curve satisfying curvature constraint

为避免全局路径规划中出现的路径不连续和不平滑,提出了基于三次准均匀B样条曲线的路径平滑算法.基于德布尔三角递推方法,设计了区间模式下的扇形输出算法(FA).通过与传统递推算法对比,FA算法可提高38%的运行效率.在FA算法的基础上,结合曲线曲率与角度构成的映射关系,系统研究了角度变化对分布系数的影响.提出角度变化下的控制点增加方式,建立了移动机器人运动学模型,以路径最大曲率约束条件优化初始控制折线路径.研究结果表明:在满足准均匀B样条曲线的性质下,平滑路径可实现C^(2)连续.以轮式移动机器人为对象进行仿真和实验,验证了所提出算法的有效性.

To avoid the discontinuity and unsmoothness of the global path planning,a path-smoothing algorithm based on the cubic quasi-uniform B-spline curve was proposed.Based on the DeBoor trigonometric recursion algorithm,the fan-shaped output algorithm(FA)in interval mode was designed.Compared with the traditional recursion method,the operational efficiency of the FA algorithm was increased by 38%.Based on the FA algorithm,with the consideration of the mapping relationship between curve curvature and angle,the impact of angular variation on the distribution coefficient was studied systematically.The increase mode of control point under the angular variation was proposed to establish the kinematics model of the mobile robot.The initial control broken-line path was optimized with the constraint condition of maximum path curvature.Research results show that the smooth path can fulfill C^(2)-continuity under the property of the quasi-uniform B-spline.The proposed algorithm was verified by simulation and experiment on the wheeled mobile robot.