Instant Center Based Kinematic Formulation for Planar Wheeled Platforms

For a general $J$ wheeled mobile platform capable of up to three-degrees-of-freedom planar motion, there are up to two $J$ independent input parameters yet the output of the platform is completely represented by three independent variables. This leads to an input parameter resolution problem based on operational criteria, which are in development just as they have been developed for $n$ input manipulator systems. To resolve these inputs into a meaningful decision structure means that all motions at the wheel attachment points must have clear physical meaning. To this effect, we propose a methodology for kinematic modeling of multiwheeled mobile platforms using instant centers to efficiently describe the motion of all system points up to the $nth$ order using a generalized algebraic formulation. This is achieved by using a series of instant centers (velocity, acceleration, jerk, and jerk derivative), where each point in the system has a motion property with its magnitude proportional to the radial distance of the point from the associated instant center and at a constant angle relative to that radius. The method of instant center provides a straightforward and physically intuitive way to synthesize a general order planar motion of mobile platforms. It is shown that a general order motion property of any point on a rigid body follows two properties, namely, directionality and proportionality, with respect to the corresponding instant center. The formulation presents a concise expression for a general order motion property of a general point on the rigid body with the magnitude and direction separated and identified. The results are summarized for up to the fifth order motion in the summary table. Based on the initial formulation, we propose the development of operational criteria using higher order properties to efficiently synthesize the motion of a $J$ wheeled mobile platform.