The paper deals with the design and testing of a robot for industrial applications featuring omnidirectionality thanks to the use of mecanum wheels. While this architecture provides remarkable manoeuvrability in narrow or cluttered spaces, it has some drawbacks that limit its widespread deployment in practice, especially for heavy-duty and long-duration tasks. As an example, the variability in the mecanum wheel rolling radius leads to undesired dynamic ill-effects, such as slippage and vibrations that affect the accuracy of pose estimation and tracking control systems. Drawing on the modeling of the kinematic and dynamic behaviour of the robot, these effects have been tackled within an adaptive estimation framework that adjusts the robot control system based on the properties of the surface being traversed. The proposed approach has been validated in experimental tests using a physical prototype operating in real industrial settings.