Intention-Aware Motion Modeling Using GP Priors With Conditional Kernels

For the challenging task of modeling actual complex motions, we propose a new class of Gaussian process (GP) models that are data-driven and also take into account prior knowledge of the motion intention. As a theoretical basis, we show that the GP regression is mathematically equivalent to regularized least-squares estimation for random functions with known prior means. Compared with the popular GP models in machine learning literature, the proposed GP motion model priors with conditional kernels have at least two advantages: 1) they are nonstationary and more applicable to represent complex motions by integrating the basic kinematic principles; 2) conditional kernels are further devised by incorporating the motion intent so that the resultant GP models are more versatile and would expectedly entail more accurate trajectory prediction. A superior property of the GP models with conditional kernels is found to improve the computational efficiency. Finally, illustrative examples are provided to show the superiority of the proposed motion models and to verify the theoretical results given in the paper.