Steering-angle computation for the multibody modelling of differential-driving mobile robots with a caster

Abstract

Since many off-the-shelf motor drives are supplied with complete control capability in the current, velocity and position loop, the robot model in the navigation control architecture can be oriented either to kinematics, interfaced with the velocity loop, or to dynamics, with the motor-current loop. Moreover, no constraints are imposed by a caster on the mobility of differential-driving mobile robots. Hence, a reduced model, containing only the platform, is sufficient for navigation control based only on the robot kinematics. However, if the multibody system model is used for navigation control based on the robot dynamics, to cope with the demands of high-speed manoeuvres and/or heavy-load operations, then the caster kinematics, especially the knowledge of the steering angle, is required to calculate the inertia matrix and the terms of Coriolis and centrifugal forces. While this angle can be measured by means of dedicated encoders to be installed for casters, the computation technique based on the existing tachometers, already mounted on the motor shafts for the servo control of the two driving wheels, is proved to be sufficient. Both a thorough kinematics model and a multibody dynamics model, including the platform and all different wheels, are formulated here for differential-driving mobile robots. Computational methods based on velocity compatibility and rigid body twists are proposed to estimate the steering angle. Simulation results of the differential-driving mobile robot moving on a smooth trajectory show the feasibility of the steering-angle computational scheme, which obviates the need of installing caster encoders. Moreover, a performance comparison on system modelling is implemented via simulation, between the differential-driving mobile robot model with and without caster dynamics. This further validates the importance of the dynamic effects of casters on the whole system model. Therefore, the multibody modelling approach for casters with the steering-angle computation technique can facilitate the navigation control architecture under dynamics conditions.