机械臂途经N路径点的连续轨迹插补算法研究

Efficient Interpolation Algorithms through N Points in Robotic Continuous Path

为减小时工业机械臂振动和机构磨损,提高机械臂轨迹跟踪精度,在关节空间分别研究了通过起点和终点的三次、五次和七次多项式轨迹算法,以及途经2、4个中间点的4-3-4、3-5-3、3-3-3-3-3多项式轨迹插补算法。在此基础上,给出了贯穿N路径点的机械臂连续三次样条轨迹快速迭代算法。试验表明:机械臂途经期望的N-2(N≥4)中间点时,充分满足轨迹给定的约束条件,保证关节位五、速度轨迹连续可导和加速度轨迹的连续性,可进一步提高关节轨迹的平滑性,减少额外游移运动,提高高精度平稳控制。

To reduce vibration and wear on the mechanism, and improve trajectory tracking in the robots, some interpolation algorithms with cubic,quintic and seventh order polynomials are investigated between two points for robotics joint space trajectory, and including the 4-3-4,3-5-3 and 3-3-3-3-3 polynomials algorithms through the two or four intermediate points in continuous path. On this basis, fast iterative algorithm is given which can interpolate through the N-points in continuous path with cubic spline. The results show that the ro-bot passing through the desired N-2 （ N≥4 ） intermediate points, it can fully satisfy the constraints given trajectory, to ensure be continuously differentiable for the joint position,velocity and keep still continuously for the acceleration, so it can be further improved smoothness of the joint trajectory and reduce movement of the additional wander, and can be increased for the precision and stability control.