Velocity constrained trajectory generation for a collinear Mecanum wheeled robot

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.