Extending interconnection and damping assignment passivity-based control (IDA-PBC) to underactuated mechanical systems with nonholonomic Pfaffian constraints: The mobile inverted pendulum robot

In this paper, we extend the interconnection and damping assignment passivity-based control strategy to systems subjected to nonholonomic Pfaffian constraints. The results are applied to stabilize the pitch dynamics of an underactuated mobile inverted pendulum (MIP) robot subjected to nonholonomic constraints arising out of no-slip conditions. A novel feature of this paper is that we reduce the kinetic energy partial differential equations and potential energy partial differential equation to a set of ordinary differential equations, that are explicitly solved.