Dynamics and design of nonholonomic robotic mechanical systems

摘要

This thesis presents a novel approach in formulating kinematic constraints and a methodology for the dynamic modelling of mechanical systems with nonholonomic couplings. The method presented here is based on the natural orthogonal complement (NOC) of the kinematic constraint matrix associated with the linear homogeneous form of the kinematic constraints. The method of the NOC is used to model mechanical systems consisting of multiple-loop kinematic chains with nonholonomic constraints. Moreover, the method of the NOC, when coupled with an optimization technique, can be used for the feedforward control of redundantly actuated systems, as shown here. The method of the NOC is first discussed in detail with the aid of an example of a two-wheeled mechanical system. Then, nonholonomic robotic mechanical systems, for example, automatic guided vehicles (AGVs), are analysed for simulation purposes. As a result, general-purpose software is developed for the kinematic and dynamic analyses of three-degree-of-freedom (3-DOF) AGVs. These AGVs use omnidirectional wheels which, in contrast to conventional wheels, e.g., the wheels in an automobile, result in 3-DOF motion of the vehicle. Isotropic designs of 3-DOF AGVs for direct kinematics are proposed, which should enhance the control of the vehicle. With advanced computer graphics, a common trend is to use motion animation in assessing the time response of the systems under study. This brought about issues of algorithmic complexity that are inherent to motion animation. These issues are addressed with an example involving the attitude representation of a rigid body and the choice of a suitable coordinate frame in representing the dynamic equations of motion.