Robot continuous trajectory planning based on Frenet-Serret formulas

Many industrial applications like gluing, arc welding, spraying, laser or high pressure cutting etc. requires very small feed-rate fluctuation to move along continuous parametric curve with constant direction. The paper proposed Frenet-Serret formulas to describe the curve direction and use parametric which is expressed as a function of time to describe the curve path. Once given the time expression of curve path and direction, we can achieve continuous trajectories of robot control by joint coordinate transformation to joint space. This methods update a parameter in real-time so as to get a trajectory from the parametric curve equation at each point. The simulation results show the welding torch can keep the fixed direction and constant speed along the welding curve in the whole operation process.