Curves Ahead: Enhancing the Steering Law for Complex Curved Trajectories

TL;DR

The paper addresses the limitation of the Steering Law for predicting movement time on arbitrarily curved paths by introducing a total-curvature parameter $K$. It derives two additive MT forms and an $L\cdot K$ interaction, and validates them through a controlled mouse-steering experiment with fixed-width sinusoidal tunnels across 9 conditions. Results show that curvature-aware models outperform the traditional Steering Law, with cross-validation confirming generalization and robustness. The work advances movement-time modeling in complex environments and has potential applications in user interface design, speech motor control, and virtual navigation.

Abstract

The Steering Law has long been a fundamental model in predicting movement time for tasks involving navigating through constrained paths, such as in selecting sub-menu options, particularly for straight and circular arc trajectories. However, this does not reflect the complexities of real-world tasks where curvatures can vary arbitrarily, limiting its applications. This study aims to address this gap by introducing the total curvature parameter K into the equation to account for the overall curviness characteristic of a path. To validate this extension, we conducted a mouse-steering experiment on fixed-width paths with varying lengths and curviness levels. Our results demonstrate that the introduction of K significantly improves model fitness for movement time prediction over traditional models. These findings advance our understanding of movement in complex environments and support potential applications in fields like speech motor control and virtual navigation.

Figures (8)

• Figure 1: A children's game akin to a steering task. The goal is to move a metal loop from one end of a wire to the other without the two components touching each other.
• Figure 2: Different types of paths with the same width and length. A) Straight; B) Circular arc; C) Sinusoidal; D) Path with corner.
• Figure 3: Tunnel tasks for each of the 9 trial types.
• Figure 4: Hardware setup for the experiment and mouse sensitivity settings.
• Figure 5: Plots of the a) Mean total time, b) Out of Path Movement, and c) Average Speed for each of the 9 trial types. Note that the boxes present the Interquartile Range (IQR) and median, while whiskers extend to 1.5 * IQR. Each color in the strip plot represents a different participant.