The collinear Mecanum drive (CMD) is a novel robot locomotion system, capable of generating omnidirectional motion while simultaneously dynamically balancing, achieved using a collinear arrangement of three or more Mecanum wheels. The CMD has a significantly thinner ground footprint than existing omnidirectional locomotion methods, which does not need to be enlarged with increasing robot height as to avoid toppling during acceleration or external disturbance. This combination of omnidirectional manoeuvrability and a thin ground footprint allows for the creation of tall robots that are able to navigate through much narrower gaps between obstacles than existing omnidirectional locomotion methods. This allows for greater manoeuvrability in confined and cluttered environments, such as that encountered in the personal service and automated warehousing robotics sectors. This article derives the kinematics and dynamics models of the CMD, analyzes controllability and accessibility, and determines the degree to which a CMD can be linearized by feedback. A partial feedback linearization is then performed, and three practically useful nonlinear controllers are derived using a backstepping design approach, all with convergence and stability guarantees for the fully coupled nonlinear model. These are demonstrated both in simulation and on a real-world CMD experimental prototype.

While much research has been conducted into the generation of smooth trajectories for underactuated unstable aerial vehicles such as quadrotors, less attention has been paid to the application of the same techniques to ground based omnidirectional dynamically balancing robots. These systems have more control authority over their linear accelerations than aerial vehicles, meaning trajectory smoothness is less of a critical design parameter. However, when operating in indoor environments these systems must often adhere to relatively low velocity constraints, resulting in very conservative trajectories when enforced using existing trajectory optimisation methods. This paper makes two contributions; this gap is bridged by the extension of these existing methods to create a fast velocity constrained trajectory planner, with trajectory timing characteristics derived from the optimal minimum-time solution of a simplified acceleration and velocity constrained model. Next, a differentially flat model of an omnidirectional balancing robot utilizing a collinear Mecanum drive is derived, which is used to allow an experimental prototype of this configuration to smoothly follow these velocity constrained trajectories.