Generation of Smooth Reference Trajectories for Unmanned Wheeled Platforms Considering Automatic Constraints On Velocity, Acceleration and Jerk

Abstract

The problem of generating smooth and achievable trajectories for the center of mass of unmanned wheeled platforms approximating a reference sequence of waypoints considering time is considered. A typical solution consists in spline interpolation of separate route sections with their subsequent stitching. At the same time, the problem of satisfying constraints on robot motion features such as velocity, acceleration, and jerk requires additional algorithmization. In contrast to labor-intensive analytical methods, this paper proposes a fundamentally new approach, simple in computational implementation, which provides dynamic smoothing of primitive trajectories. The principle of organization and method of designing an autonomous dynamic model (tracking differentiator) whose output variables, while tracking a primitive non-smooth trajectory, generate smooth curves whose derivatives do not exceed the design constraints of a particular robot and are achievable reference trajectories for it. Block control principle and smooth and bounded S-shaped sigmoidal local links are used to design the differentiator. The paper presents a procedure for setting up a three-block tracking differentiator, whose variables generate a smooth reference trajectory, as well as its first and second derivatives, in a signal pocoordinate form. It is shown that the developed procedure extends to tracking differentiators of any required order without limitation of generality. In particular, the structure and setting of a single-block tracking differentiator for obtaining express results at the stage of robot or polygon motion planning is specified. Numerical simulation results confirming the efficiency of the designed algorithms are presented.