Inverse dynamics and energy optimal trajectories for a wheeled mobile robot

A wheeled mobile robot (WMR) is a typical nonholonomic system in which the wheels have constrained interactions with the ground. To relate these local interactions to some global constraints on the WMR, we start on the contact kinematics and then analyze the robot's dynamics using the Gibbs-Appell equation. This yields motion equations with minimal dimensions that are free of Lagrange multipliers (which would arise from application of the d'Alembert-Lagrange principle). The inverse dynamics of the WMR can then be solved using two methods. The first method looks for servo constraints to meet the control objective and are consistent with the constraints over the WMR. The second method, applying the elegant differential flatness theory, is based on one-to-one mappings from flat output to the state and the input. We also explain the reason why the WMR's energy optimal trajectory requires a cost function related to the integral of the Lagrangian. An optimization algorithm based on the Ritz approximation is offered with efficiency illustrated via two examples.