Asymmetric Configuration for a Four-Motor Omnidirectional Robot

Abstract

Four-wheel omnidirectional robots are commonly designed under the assumption of symmetric wheel placement. However, compact platforms and mechanically constrained layouts often require asymmetric configurations, where front and rear wheel angles differ. In such cases, symmetric inverse-kinematics formulations may introduce non-negligible errors. This paper presents an explicit analytical formulation for inverse kinematics in four-wheel omnidirectional robots with arbitrary wheel angles 𝛼 and β. The derivation is based on a structured linear-algebraic treatment that avoids symmetry assumptions and yields closed-form expressions for motor velocities. The kinematic error introduced by applying symmetric-case equations to asymmetric layouts is analytically quantified. Experimental validation was conducted on a four-wheel omnidirectional robot configured with 𝛼 = 55° and β = 45°. Two representative steering angles (15° and 30°) were tested with repeated runs per condition. The proposed formulation showed improved directional accuracy compared to standard symmetric RoboCup-based equations. At 15°, the mean angular error was significantly reduced, while at 30°, the symmetric approximation exhibited a large systematic deviation, with heading errors exceeding 16° on average. Although the current validation is limited to selected configurations, the results demonstrate that asymmetric geometries require dedicated kinematic treatment to ensure motion fidelity. The proposed formulation provides a practical engineering solution for compact omnidirectional robots where symmetry cannot be maintained.

Received: 16 November 2025 | Revised: 18 March 2026 | Accepted: 29 June 2026

Conflicts of Interest

The authors declare that they have no conflicts of interest to this work.

Data Availability Statement

Data are available from the corresponding author upon reasonable request.

Author Contribution Statement

Raimondo Sgrò: Conceptualization, Software, Validation, Investigation, Resources, Data curation, Writing – original draft, Writing – review & editing, Visualization, Project administration. Sergio Cacciatori: Methodology, Validation, Formal analysis, Writing – original draft, Writing – review and editing.