Generation of Achievable Three-Dimensional Trajectories for Autonomous Wheeled Vehicles via Tracking Differentiators

Planning an achievable trajectory for a mobile robot usually consists of two steps: (i) finding a path in the form of a sequence of discrete waypoints and (ii) transforming this sequence into a continuous and smooth curve. To solve the second problem, this paper proposes algorithms for automatic dynamic smoothing of the primary path using a tracking differentiator with sigmoid corrective actions. Algorithms for setting the gains of the differentiator are developed, considering a set of design constraints on velocity, acceleration, and jerk for various mobile robots. When tracking a non-smooth primary path, the output variables of the differentiator generate smooth trajectories implemented by a mechanical plant. It is shown that the tracking differentiator with a different number of blocks also generates derivatives of the smoothed trajectory of any required order, taking into account the given constraints. Unlike standard analytical methods of polynomial smoothing, the proposed algorithm has a low computational load. It is easily implemented in real time on the on-board computer. In addition, simple methods for modeling a safety corridor are proposed, taking into account the dimensions of the vehicle when planning a polygon with stationary obstacles. Confirming results of numerical simulation of the developed algorithms are presented.