# Extending the kinematic theory of rapid movements with new primitives

arXiv: https://arxiv.org/abs/2401.16519 · HTML: https://mlsanity.com/paper/2401.16519/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 24 references that are in the map.
- First posted on arXiv 29 Jan 2024.

## Builds on (most cited first, 1 of 1)

- [iDeLog: Iterative Dual Spatial and Kinematic Extraction of Sigma-Lognormal Parameters](https://mlsanity.com/paper/2401.15473/) (2024)

## Abstract (arXiv)

The Kinematic Theory of rapid movements, and its associated Sigma-Lognormal, model 2D spatiotemporal trajectories. It is constructed mainly as a temporal overlap of curves between virtual target points. Specifically, it uses an arc and a lognormal as primitives for the representation of the trajectory and velocity, respectively. This paper proposes developing this model, in what we call the Kinematic Theory Transform, which establishes a mathematical framework that allows further primitives to be used. Mainly, we evaluate Euler curves to link virtual target points and Gaussian, Beta, Gamma, Double-bounded lognormal, and Generalized Extreme Value functions to model the bell-shaped velocity profile. Using these primitives, we report reconstruction results with spatiotemporal trajectories executed by human beings, animals, and anthropomorphic robots.