基于S型速度曲线的B样条轨迹规划研究

Research on B-Spline Trajectory Planning Based on S-Shaped Velocity Curve

摘要: 针对三轴联动数控加工过程中存在的曲率突变、速度不连续以及由此引发的伺服冲击与振动问题，本文提出一种基于三次非均匀B样条曲线拟合与S型速度规划相结合的轨迹优化方法。首先，选取三次非均匀B样条曲线并引入复合辛普森积分实现曲线弧长的高精度数值计算。设计分段式S型速度规划，应用切向量分解法将得到曲线一维动态量投影分解至x、y、z三轴。仿真结果表明：在最大速度10 mm/s、最大加速度10 mm/s²、最大加加速度30 mm/s³的约束下，所规划轨迹长度为26.95 mm，总运行时间为2.66 s，速度与加速度无突变，跃度变化受控且整体连续，验证了该方法在轨迹平滑性与动态可控性方面的有效性。

Abstract: To address the issues of curvature discontinuity, velocity discontinuity, and the resulting servo shock and vibration in three-axis CNC machining, this paper proposes a trajectory optimization method combining cubic non-uniform B-spline curve fitting with S-shaped velocity planning. Firstly, cubic non-uniform B-spline curves are selected and the composite Simpson integral is introduced to achieve high-precision numerical calculation of the curve arc length. A piecewise S-shaped velocity planning is designed, and the one-dimensional dynamic quantities of the obtained curve are projected and decomposed into the x, y, and z axes using the tangent vector decomposition method. Simulation results show that under the constraints of a maximum speed of 10 mm/s, a maximum acceleration of 10 mm/s², and a maximum jerk of 30 mm/s³, the planned trajectory length is 26.95 mm, the total running time is 2.66 s, the velocity and acceleration have no sudden changes, the jerk variation is controlled and overall continuous, verifying the effectiveness of this method in terms of trajectory smoothness and dynamic controllability.