Smooth Moves: How Polynomials Tame Robot Trajectories

Smooth Move: Taming Trajectories with Polynomials

This article explores the use of polynomial functions, specifically SmoothStep and SmootherStep, to create smooth trajectories for robots and 3D printers. It explains the importance of matching position, velocity, and acceleration at segment boundaries to avoid jerky movements, and demonstrates how to calculate polynomial coefficients using linear algebra. The author also discusses scaling trajectories to respect physical limits like maximum velocity and acceleration, and hints at extending the approach to multiple dimensions.