A Practical Joint-Space Trajectory Generation Method Based on Convolution in Real-Time Control

This paper proposes a joint-space trajectory generation method for practical navigation with a high curvature path of mobile robots. A technique to generate central velocity commands using a convolution operator that considers only the physical limits of a mobile robot was discussed. In practical application, controlling the heading angles along a curved path is required and the existence of obstacles is inevitable. First, we suggested an algorithm that generates a trajectory to consider the heading angles along a smooth Bezier curve by redefinition of the curve parameter. However, the presence of an obstacle along the planned path requires redirection to a new path where geometrical limitations such as high curvature turning points exist, resulting in tracking error. We propose a method that manages a variation of linear interpolation to generate a feasible trajectory while conserving the high curvature path and the merits of convolution. Joint-space trajectories are produced by scaling down the generated central velocity through reduction of the given maximum velocity limit. We show through a simulation example that the proposed method is able to generate a trajectory that can accurately track a planned path on a designed platform based on actual parameters. Finally, an experiment is successfully conducted on a two-wheeled mobile robot, Tetra DS-III, in a real-time control system. The experiment results display distinct advantages in the criteria of time optimality and periodicity of control tasks, while conserving all possible limitations that could occur during navigation compared with previous studies.