Are there smoothness evaluation methods/algorithms of 3 dimensional cartesian trajectorys in the field of robotics

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timling 2021-9-11

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https://ww2.mathworks.cn/matlabcentral/answers/1451279-are-there-smoothness-evaluation-methods-algorithms-of-3-dimensional-cartesian-trajectorys-in-the-fie

回答： Amrtanshu Raj 2022-4-12

I was wondering if there are any methods of determining 3 dimensional cartesian trajectory smoothness for the end effector of a robot for example.

I have heard that in the ROS MoveIt framework a smoothness metric is proposed which looks at the angle formed between three consecutive waypoints for 2 dimensional paths.

Benchmark description — Planners Benchmarking documentation (planners-benchmarking.readthedocs.io)

Smoothness:Looks at three consecutive waypoints and the angle formed between them. Value is calculated as a square of sum of all the angles calculated that way. Formula:S = sumi=2n-1{(2 * (pi - arccos((di-2,i-12+di-1,i2-di-2,i2)/(2 * di-2,i-1 * di-1,i))))2}, where:n - number of waypoints on the path,dx,y - distance between waypoints with index x and y.Aligned points result in S = 0.The lower the value, the smoother plan.