Kinematic Time-invariant Control of a 2D Nonholonomic Vehicle

A closed loop, time-invariant and globally stable control law for a bicycle-like kinematic model is proposed. The resulting paths are smooth and the curvature bounded on the whole state space trajectories. As linear velocity can be kept arbitrary small, thus avoiding large lateral accelerations and actuator saturation problems, it is suggested that the proposed law may be also adopted for the planar control of autonomous underwater vehicles. The target configuration is always approached on a straight line and the vehicle is requested to move in only one specified forward direction thus avoiding cusps in the paths and satisfying a major requirement for the implementation of such strategy on many real systems.