Kinematics and Dynamics of a Wheeled Mobile Inverted Pendulum

The kinematics and dynamics relations of a non-holonomic four wheeled mobile inverted pendulum (FWMIP) are developed to investigate various control schemes for keeping the inverted pendulum in balance. The kinematics relations are developed in homogeneous coordinates. The symbolic equation of motion of the FWMIP is derived in terms of platform and rod dimensions for a list of assumptions simplifying the expressions using a symbolic math toolbox. The presented method is suitable for more accurate modeling of an FWMIP system. The developed symbolic equations of motion are suitable to test the available control algorithms, as well as to develop new control algorithms and strategies for the presented control problem.