Convolution-based trajectory generation methods using physical system limits

This paper proposes two novel convolution-based trajectory generation methods using physical system limits such as maximum velocity, maximum acceleration, and maximum jerk. Convolution is a mathematical operation on two functions of an input function and a convoluted function, producing an output function that is typically viewed as a modified version of input function. Time duration parameters of the convoluted functions with a unit area are determined from the given physical system limits. The convolution-based trajectory generation methods to be proposed in this paper have three advantages; first, a continuously differentiable trajectory is simply obtained by applying successive convolution operations; second, a resultant trajectory is always generated satisfying the given physical system limits; third, the suggested methods have low computational burden thanks to recursive form of convolution operation. The suggested methods consider both zero and nonzero initial/terminal conditions. Finally, the effectiveness of the suggested methods is shown through numerical simulations.