Whole Body Control of a Wheeled Inverted Pendulum Humanoid

We present a method to implement operational space control technique for whole body control of a wheeled-inverted pendulum (WIP) humanoid, a class of robots that feature a redundant manipulator dynamically balancing itself on two wheels. We consider the case in which the base link is not passive, in that, the reaction of the torque driving the wheels is acting on the base link. This makes the system underactuated because the number of actuators is less than the degrees of freedom. However, it is a special form of underactuation where all degrees of freedom are actuated, with one actuator being shared by two degrees of freedom. This special feature of WIP dynamics challenges the straightforward application of operational space techniques, compared to fully actuated, constrained, or underactuated systems with no DOFs sharing the actuators. The key idea is to isolate dynamics of the manipulator from the wheel dynamics and to control the resulting system using operational-space control. A side-effect of this is the resulting asymmetry of the inertia matrix restricting full use of operational space tools. This is addressed by presenting a coordinate transformation that transforms the inertia matrix into a symmetric one. Finally, the wheel dynamics is derived as a function of manipulator joint accelerations so that horizontal motion of the robot can be treated as another task being controlled within the framework developed for manipulator control. Simulation results are presented on a five degree of freedom planar robot, with four DOF serial arm mounted on wheels.