Model Predictive Control of Omnidirectional Mobile Robots Based on Global Task Coordinate Frame

This paper investigates a novel omnidirectional mobile robot (OMR) equipped with four decoupled active casters (DACs). A real-time calculation model for position contour error based on an orthogonal global task coordinate frame is established for OMR trajectory tracking. To address the non-monotonicity of the parametric equations of the trajectory along the x and y directions within each time interval, the model is extended to derive the Jacobian matrix for the transformation from the contour task space to the Cartesian space when inverse functions exist x for y and separately. This approach accommodates both the practical scenarios where the robot is stationary in either the x or y direction during trajectory tracking and when both directions are in motion simultaneously. The positive direction of motion for the vehicle body and casters is defined, and the orthogonal decomposition method is applied to analyze the motion constraints of the casters, leading to the derivation of the caster kinematic model. This results in a kinematic model based on the contour task space. Combined with a model predictive control algorithm, experimental verification demonstrates its capability to achieve precise trajectory tracking.