A smooth control law for graceful motion of differential wheeled mobile robots in 2D environment

Although recent progress in 2D mobile robot navigation has been significant, the great majority of existing work focuses only on ensuring that the robot reaches its goal. But to make autonomous navigation truly successful, the “quality” of planned motion is important as well. Here, we develop and analyze a pose-following kinematic control law applicable to unicycle-type robots, such that the robot can generate intuitive, fast, smooth, and comfortable trajectories. The Lyapunov-based feedback control law is derived via singular perturbation. It is made up of three components: (i) egocentric polar coordinates with respect to an observer on the vehicle, (ii) a slow subsystem which describes the position of the vehicle, where the reference heading is obtained via state feedback, and (iii) a fast subsystem which describes the steering of the vehicle, where the vehicle heading is exponentially stabilized to the obtained reference heading. The resulting path is a smooth and intuitive curve, globally converging to an arbitrary target pose without singularities, from any given initial pose. Furthermore, we present a simple path following strategy based on the proposed control law to satisfy arbitrary velocity, acceleration and jerk bounds imposed by the user. Such requirements are important to any autonomous vehicle so as to avoid actuator overload and to make the path physically realizable, and they are critical for applications like autonomous wheelchairs where passengers can be physically fragile.