Input-Output Force-Torque Mappings for the Chassis of Robocars with Three Ilon’s Wheels

Abstract

The current stage of development of robotics is increasingly focused on the research, development, production and operation of mobile robots. Their diversity in terms of functional purpose, operating environment (ground, subterranean, subaquatic, aerial, space), according to the requirements for technical, economic and operational characteristics objectively generates a broad variety of such robots. The types of kinematic schemes, propellers and their drives used in mobile robots are also important factors determining their existing and future fleet. The prospects for the implementation and achievement of the aforementioned characteristics in wheeled automatic vehicles (robocars), which constitute a substantial part of modern mobile robots, depend largely on the design of their chassis, and, first of all, on the number and type of wheels used and their relative position on the chassis. Therefore, when choosing a design option for the chassis, the development of robocars involves their multidimensional analysis, based on a comparison of various potentially applicable circuit solutions. The paper contains mathematical descriptions of input-output force-torque mappings (connections) of the shaft torques of the Ilon’s wheels that ensure the motion of robocars along a horizontal plane. The proposed descriptions can be used for comparative analysis and selection of circuit solutions for the chassis of robocars. Such descriptions are specified and analyzed for four variants of kinematic designs of the chassis of robocars with three Ilon’s wheels (Mecanum wheels, Swedish wheels). They are determined for all possible directions of torques applied to the wheels of such robocars, as well as for those cases when no torque is applied to one of these wheels. Thus, the author describes and analyzes the operation modes of such robocars using all three or any two wheels to ensure the forces and torques applied to the chassis of the robocars necessary for their movement. Additionally, the article contains the estimates of the structures of the input-output force-torque mappings for the selected four variants of kinematic designs of the chassis of robocars with three Ilon’s wheels. The influence of their internal input-output cross couplings on the implementation of control algorithms for such robocars is also estimated, as well as the relationship in their controlled variables, maneuverability, controllability and reachability. The author describes a variant of the algorithm for solving the inverse force-torque problems for the chassis in the aforementioned design, and also indicates the preferability for the use of such robocars in the implementation of typical control problems including finite, terminal control, servo and software.