Smooth Move: Taming Trajectories with Polynomials
Summary
This article analyzes smoothing trajectories for motion planning using polynomial functions, focusing on SmoothStep and its variants (Smootherstep and higher-order forms) to ensure zero velocity and acceleration at endpoints. It covers the mathematical derivations, including derivatives and linear-algebra-based coefficient solving, plus Python/Numpy examples and considerations for time scaling and multi-dimensional trajectories in 3D printing and robotics.