Possibilities and Challenges in Kinematic Modeling of Highly Redundant,Non-Holonomic and Omnidirectional Mobile Robots

Industry as well as the private domain show an increasing interest to the field of mobile robotics. With a higher number of applications, the complexity of the required tasks rises, and therefore the community tends to use robots with many degrees of freedom (DOF). The present paper takes this topic up and focuses on challenges of the kinematical modeling of redundant, non-holonomic mobile robots by considering a 12 DOF platform. To reach an omnidirectional behaviour, the actuated wheels are diagonally mounted on the chassis. Well known problems resulting from this set-up are parametric singularities which unnecessarily restrict the motion of the mathematical model. As it turns out, this problem can be avoided by the use of a non-minimal parametrized model. An additional challenge results from the inverse kinematic (IK) problem on velocity level. The corresponding equations are highly underdetermined and, due to the non-holonomic wheels, not directly affected by the steering angle velocities. This problem is solved by performing a local optimization on acceleration level. Finally, simulation results are presented. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)